Details

Time bar (total: 8.5s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample3.2s (38%)

Results
1.9s2141×body2048valid
837.0ms4552×body256valid
337.0ms1080×body1024valid
177.0ms483×body512valid
Bogosity

preprocess32.0ms (0.4%)

Algorithm
2×egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
15×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32311
43211
54911
68611
712211
816811
920411
1023011
1123211
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify13.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
15×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32311
43211
54911
68611
712211
816811
920411
1023011
1123211
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

eval0.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
15.3b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶15.3b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 8 to 6 computations (25% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
1.2b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓1.2b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
0.0ms
N
@0
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms
N
@-inf
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms
N
@inf
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite162.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
890×pow1_binary64
828×log1p-expm1-u_binary64
828×expm1-log1p-u_binary64
827×add-log-exp_binary64
810×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
115611
2221311
Stop Event
1×node limit
Counts
1 → 36
Calls
Call 1
Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (*.f64 (neg.f64 (atan.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (atan.f64 N)) 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (pow.f64 (cbrt.f64 (atan.f64 N)) 2) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (/.f64 1 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (/.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))) (neg.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (neg.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (neg.f64 (atan.f64 N)) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (*.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N))) (*.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N)))) (-.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))))

simplify19.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
52×fma-def_binary64
43×fma-neg_binary64
23×cancel-sign-sub-inv_binary64
18×sub-neg_binary64
14×associate--r+_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0952
12044
23144
36144
48844
513444
618244
721544
825844
929444
1032044
1132244
Stop Event
1×saturated
Counts
40 → 38
Calls
Call 1
Inputs
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
Outputs
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))

eval16.0ms (0.2%)

Compiler

Compiled 599 to 388 computations (35.2% saved)

prune14.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New34438
Fresh000
Picked011
Done000
Total34539
Error
14.2b
Counts
39 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶42.7b
(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))
▶30.7b
(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
▶30.5b
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
✓15.3b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶14.4b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 73 to 52 computations (28.8% saved)

localize19.0ms (0.2%)

Local error

Found 8 expressions with local error:

NewErrorProgram
2.9b
(+.f64 N (-.f64 1 N))
0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0b
(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0b
(*.f64 N (+.f64 N 1))
✓0.0b
(*.f64 N (+.f64 N 1))
✓0.0b
(+.f64 1 (*.f64 N (+.f64 N 1)))
✓0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓2.9b
(+.f64 N (-.f64 1 N))
Compiler

Compiled 39 to 26 computations (33.3% saved)

series5.0ms (0.1%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
N
@inf
(*.f64 N (+.f64 N 1))
0.0ms
N
@inf
(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0ms
N
@-inf
(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0ms
N
@inf
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms
N
@-inf
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite149.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
616×fma-def_binary64
473×log-prod_binary64
352×pow-prod-down_binary64
297×fma-neg_binary64
270×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0943
121037
2307637
Stop Event
1×node limit
Counts
4 → 240
Calls
Call 1
Inputs
(+.f64 N (-.f64 1 N))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(+.f64 1 (*.f64 N (+.f64 N 1)))
(*.f64 N (+.f64 N 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 N (-.f64 1 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 N N) (+.f64 (+.f64 N -1) N)) (/.f64 (pow.f64 (-.f64 1 N) 2) (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 N (-.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 N (-.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (cbrt.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) (sqrt.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (/.f64 1 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2)) (/.f64 1 (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)) (-.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N)) (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 N -1) N) (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (+.f64 (pow.f64 (-.f64 1 N) 2) (-.f64 (*.f64 N N) (*.f64 N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 N 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2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 N N)) (exp.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 N N)) (+.f64 1 (expm1.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log1p.f64 (fma.f64 N N N))) 1/3))))) (#(struct:change #<rule egg-rr> (2) 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(fma.f64 N N N)) (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2) (cbrt.f64 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (pow.f64 N 3/2) (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 N 1)) (*.f64 (sqrt.f64 (+.f64 N 1)) N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 N (sqrt.f64 N)) (hypot.f64 N (sqrt.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 N) N) (cbrt.f64 (*.f64 N N)) (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (pow.f64 (cbrt.f64 (+.f64 N 1)) 2)) (cbrt.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (sqrt.f64 (+.f64 N 1))) (sqrt.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 N 1) (cbrt.f64 (*.f64 N N))) (cbrt.f64 N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 N 1) (sqrt.f64 N)) (sqrt.f64 N) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 N N) 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 6) (pow.f64 N 3)) (+.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 N (sqrt.f64 N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 N) (exp.f64 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (exp.f64 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 N N)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 N (sqrt.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x 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(*.f64 N N)) (cbrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (*.f64 (cbrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (*.f64 (cbrt.f64 N) 1) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (sqrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (pow.f64 N 3/2) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) 1) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3)) (/.f64 1 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) 1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (-.f64 1 (fma.f64 N N N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 N) N) (cbrt.f64 (*.f64 N N)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))))

simplify135.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
968×fma-neg_binary64
532×unswap-sqr_binary64
447×distribute-rgt-neg-in_binary64
354×cancel-sign-sub-inv_binary64
329×fma-def_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
019327
144269
267269
3163269
4583269
51634269
63616269
75643269
87339269
Stop Event
1×node limit
Counts
288 → 253
Calls
Call 1
Inputs
1
1
1
1
1
1
1
1
1
1
1
1
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
1
(+.f64 N 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
Outputs
1
1
1
1
1
1
1
1
1
1
1
1
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1
(+.f64 N 1)
(+.f64 1 N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)

localize41.0ms (0.5%)

Local error

Found 6 expressions with local error:

NewErrorProgram
27.9b
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
1.0b
(cbrt.f64 (atan.f64 (+.f64 N 1)))
0.5b
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)
✓0.5b
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)
✓1.0b
(cbrt.f64 (atan.f64 (+.f64 N 1)))
✓27.9b
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
Compiler

Compiled 44 to 31 computations (29.5% saved)

series46.0ms (0.5%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
35.0ms
N
@0
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
5.0ms
N
@inf
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
4.0ms
N
@-inf
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
0.0ms
N
@-inf
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)
0.0ms
N
@0
(cbrt.f64 (atan.f64 (+.f64 N 1)))

rewrite97.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
886×pow1_binary64
821×add-log-exp_binary64
821×log1p-expm1-u_binary64
821×expm1-log1p-u_binary64
803×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01132
122630
2260830
Stop Event
1×node limit
Counts
3 → 58
Calls
Call 1
Inputs
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(cbrt.f64 (atan.f64 (+.f64 N 1)))
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) 0) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (pow.f64 (atan.f64 N) 2) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 1/3) (pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4)) (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2)) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))))))))

simplify100.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
1003×fma-def_binary64
772×fma-neg_binary64
506×associate-*l*_binary64
390×distribute-rgt-neg-in_binary64
361×associate-*r*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
023396
168360
2104360
3168360
4286360
5664360
62252360
73256360
84885360
96855360
Stop Event
1×node limit
Counts
94 → 66
Calls
Call 1
Inputs
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
Outputs
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
15.1b
(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
0.7b
(sqrt.f64 (atan.f64 (+.f64 N 1)))
✓0.7b
(sqrt.f64 (atan.f64 (+.f64 N 1)))
✓15.1b
(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
Compiler

Compiled 34 to 22 computations (35.3% saved)

series37.0ms (0.4%)

Counts
2 → 16
Calls

6 calls:

TimeVariablePointExpression
32.0ms
N
@0
(sqrt.f64 (atan.f64 (+.f64 N 1)))
1.0ms
N
@0
(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
1.0ms
N
@-inf
(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
1.0ms
N
@inf
(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
0.0ms
N
@inf
(sqrt.f64 (atan.f64 (+.f64 N 1)))

rewrite87.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
773×pow1_binary64
714×log1p-expm1-u_binary64
714×expm1-log1p-u_binary64
713×add-log-exp_binary64
697×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0921
118319
2224019
Stop Event
1×node limit
Counts
2 → 42
Calls
Call 1
Inputs
(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(sqrt.f64 (atan.f64 (+.f64 N 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) 0) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (pow.f64 (atan.f64 N) 2) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (atan.f64 (+.f64 N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/4) (pow.f64 (atan.f64 (+.f64 N 1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)) (sqrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1/2) (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))))))))

simplify65.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
52×fma-def_binary64
43×fma-neg_binary64
22×cancel-sign-sub-inv_binary64
19×sub-neg_binary64
14×associate--r+_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
013172
126164
236164
366164
493164
5139164
6187164
7220164
8266164
9302164
10328164
11330164
Stop Event
1×saturated
Counts
58 → 45
Calls
Call 1
Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(sqrt.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))))
(sqrt.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))))
(sqrt.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))))
(sqrt.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))))
Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(sqrt.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))))
(sqrt.f64 (atan.f64 (-.f64 1 (neg.f64 N))))
(sqrt.f64 (atan.f64 (+.f64 N 1)))
(sqrt.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))))
(sqrt.f64 (atan.f64 (-.f64 1 (neg.f64 N))))
(sqrt.f64 (atan.f64 (+.f64 N 1)))
(sqrt.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))))
(sqrt.f64 (atan.f64 (-.f64 1 (neg.f64 N))))
(sqrt.f64 (atan.f64 (+.f64 N 1)))
(sqrt.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))))
(sqrt.f64 (atan.f64 (-.f64 1 (neg.f64 N))))
(sqrt.f64 (atan.f64 (+.f64 N 1)))

localize34.0ms (0.4%)

Local error

Found 6 expressions with local error:

NewErrorProgram
33.6b
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
1.2b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.2b
(sqrt.f64 (atan.f64 N))
✓0.2b
(sqrt.f64 (atan.f64 N))
1.2b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓33.6b
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
Compiler

Compiled 54 to 20 computations (63% saved)

series8.0ms (0.1%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
4.0ms
N
@-inf
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
1.0ms
N
@0
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
1.0ms
N
@inf
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
0.0ms
N
@0
(sqrt.f64 (atan.f64 N))
0.0ms
N
@inf
(sqrt.f64 (atan.f64 N))

rewrite103.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
463×pow1_binary64
446×add-sqr-sqrt_binary64
438×*-un-lft-identity_binary64
427×add-log-exp_binary64
426×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0622
112213
2149013
Stop Event
1×node limit
Counts
2 → 53
Calls
Call 1
Inputs
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
(sqrt.f64 (atan.f64 N))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (atan.f64 N) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 N)) (+.f64 (sqrt.f64 (atan.f64 N)) (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 N) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) (pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2) (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 N) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 N) 2) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 N) 2)) (-.f64 (atan.f64 N) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 N)) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 N)) (neg.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N))) (cbrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 N) 1/4) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 N) 1/4) (neg.f64 (pow.f64 (atan.f64 N) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 N)) 2)) (sqrt.f64 (cbrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan.f64 N)) 2) 1/2) (pow.f64 (cbrt.f64 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (atan.f64 N) 1/4)) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (cbrt.f64 (atan.f64 N))) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (pow.f64 (atan.f64 N) 1/4)) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (pow.f64 (atan.f64 N) 3/2)) (+.f64 0 (+.f64 (atan.f64 N) (*.f64 0 (sqrt.f64 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (atan.f64 N)) (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 N) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 N) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 N) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 N) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (atan.f64 N))))))))

simplify40.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
4×fma-def_binary64
3×+-commutative_binary64
3×sub-neg_binary64
2×*-commutative_binary64
1×associate-+l-_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0672
11312
21912
32012
42212
52612
63012
73512
Stop Event
1×saturated
Counts
65 → 55
Calls
Call 1
Inputs
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
Outputs
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0

eval512.0ms (6%)

Compiler

Compiled 10330 to 6077 computations (41.2% saved)

prune108.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New5295534
Fresh000
Picked101
Done314
Total5336539
Error
0.5b
Counts
539 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.5b
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
▶14.3b
(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))
▶14.4b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
▶28.7b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
✓15.3b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 154 to 108 computations (29.9% saved)

localize58.0ms (0.7%)

Local error

Found 6 expressions with local error:

NewErrorProgram
0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0b
(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0b
(*.f64 N (+.f64 N 1))
0.0b
(*.f64 N (+.f64 N 1))
0.0b
(+.f64 1 (*.f64 N (+.f64 N 1)))
✓0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 27 to 19 computations (29.6% saved)

series1.0ms (0%)

Counts
1 → 8
Calls

3 calls:

TimeVariablePointExpression
0.0ms
N
@0
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms
N
@inf
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms
N
@-inf
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite50.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
798×pow1_binary64
742×log1p-expm1-u_binary64
742×expm1-log1p-u_binary64
741×add-log-exp_binary64
727×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0713
115211
2205711
Stop Event
1×node limit
Counts
1 → 16
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))

simplify77.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
968×fma-neg_binary64
532×unswap-sqr_binary64
451×distribute-rgt-neg-in_binary64
353×cancel-sign-sub-inv_binary64
312×neg-sub0_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
014104
13388
25488
315188
457588
5163888
6362788
7566288
8735988
Stop Event
1×node limit
Counts
24 → 19
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
Outputs
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
0.0b
(+.f64 N (+.f64 1 (pow.f64 N 2)))
✓0.0b
(+.f64 N (+.f64 1 (pow.f64 N 2)))
✓0.5b
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
Compiler

Compiled 28 to 21 computations (25% saved)

series3.0ms (0%)

Counts
2 → 10
Calls

6 calls:

TimeVariablePointExpression
2.0ms
N
@0
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
0.0ms
N
@-inf
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
0.0ms
N
@-inf
(+.f64 N (+.f64 1 (pow.f64 N 2)))
0.0ms
N
@inf
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
0.0ms
N
@inf
(+.f64 N (+.f64 1 (pow.f64 N 2)))

rewrite74.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
895×pow1_binary64
838×add-log-exp_binary64
836×log1p-expm1-u_binary64
836×expm1-log1p-u_binary64
821×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0823
117719
2233719
Stop Event
1×node limit
Counts
2 → 51
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 N N) (-.f64 N (fma.f64 N N 1))) (/.f64 (pow.f64 (fma.f64 N N 1) 2) (-.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 N (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 N (fma.f64 N N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 2) (cbrt.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (hypot.f64 1 N) (sqrt.f64 N)) (hypot.f64 (hypot.f64 1 N) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3)) (/.f64 1 (fma.f64 N N (*.f64 (fma.f64 N N 1) (-.f64 (fma.f64 N N 1) N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N 1) 2)) (/.f64 1 (-.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 N N (*.f64 (fma.f64 N N 1) (-.f64 (fma.f64 N N 1) N))) (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 N (fma.f64 N N 1)) (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3)) (fma.f64 N N (*.f64 (fma.f64 N N 1) (-.f64 (fma.f64 N N 1) N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3)) (+.f64 (pow.f64 (fma.f64 N N 1) 2) (-.f64 (*.f64 N N) (+.f64 N (pow.f64 N 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N 1) 2)) (-.f64 N (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3))) (neg.f64 (fma.f64 N N (*.f64 (fma.f64 N N 1) (-.f64 (fma.f64 N N 1) N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N 1) 2))) (neg.f64 (-.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 N) 3) (pow.f64 N 6)) (+.f64 (*.f64 (+.f64 1 N) (+.f64 1 N)) (-.f64 (pow.f64 N 4) (*.f64 (+.f64 1 N) (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 2) (*.f64 N N)) (-.f64 (fma.f64 N N 1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 N) (+.f64 1 N)) (pow.f64 N 4)) (-.f64 (+.f64 1 N) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 N (fma.f64 N N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (hypot.f64 1 N) (sqrt.f64 N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 N (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N 1)) 2) (cbrt.f64 (fma.f64 N N 1)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 N) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 N) (hypot.f64 1 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (sqrt.f64 N) (fma.f64 N N 1))))))

simplify82.0ms (1%)

Algorithm
1×egg-herbie
Rules
1010×fma-neg_binary64
532×unswap-sqr_binary64
450×distribute-rgt-neg-in_binary64
362×cancel-sign-sub-inv_binary64
312×neg-sub0_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01287
13067
25867
316467
458767
5166067
6362067
7565367
8734067
Stop Event
1×node limit
Counts
61 → 60
Calls
Call 1
Inputs
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
1
(+.f64 N 1)
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
Outputs
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 (*.f64 N N) (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 (*.f64 N N) (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 (*.f64 N N) (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 (*.f64 N N) (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1
(+.f64 N 1)
(+.f64 1 N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)

localize81.0ms (0.9%)

Local error

Found 8 expressions with local error:

NewErrorProgram
11.8b
(-.f64 (pow.f64 N 4) (*.f64 N N))
2.9b
(+.f64 N (-.f64 1 N))
0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
0.0b
(+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N))))
✓0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
2.9b
(+.f64 N (-.f64 1 N))
✓11.8b
(-.f64 (pow.f64 N 4) (*.f64 N N))
✓33.2b
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
Compiler

Compiled 81 to 36 computations (55.6% saved)

series5.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
N
@0
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms
N
@-inf
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms
N
@inf
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms
N
@-inf
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
0.0ms
N
@inf
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))

rewrite97.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
798×fma-def_binary64
545×fma-neg_binary64
218×expm1-udef_binary64
218×log1p-udef_binary64
181×log-div_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01460
133030
2521430
Stop Event
1×node limit
Counts
3 → 286
Calls
Call 1
Inputs
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N)) (neg.f64 (/.f64 N (/.f64 (fma.f64 N N N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (fma.f64 N N N) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N)) (/.f64 N (/.f64 (fma.f64 N N N) N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 N N 0) N)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (+.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) 2) (/.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) (*.f64 (fma.f64 N N N) (/.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 N N N)) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (neg.f64 (cbrt.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (pow.f64 N 8) (pow.f64 N 4))) (*.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (neg.f64 (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 N N N)) (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 N 8) (pow.f64 N 4)))) (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (/.f64 (pow.f64 (fma.f64 N N N) 2) (cbrt.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 N (sqrt.f64 N))) (/.f64 (pow.f64 (fma.f64 N N N) 2) (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 N 8) (pow.f64 N 4))) 1) (/.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 N 8) (pow.f64 N 4))) (hypot.f64 N (sqrt.f64 N))) (/.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 N N N) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (/.f64 (fma.f64 N N N) (cbrt.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 N N N) 1) (/.f64 (fma.f64 N N N) (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 N) (sqrt.f64 (+.f64 N 1))) (*.f64 (sqrt.f64 N) (sqrt.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (hypot.f64 N (sqrt.f64 N))) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 N (pow.f64 (cbrt.f64 (+.f64 N 1)) 2)) (cbrt.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) 2) (cbrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) (sqrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) 1))))))

simplify52.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
824×associate-/r*_binary64
749×fma-def_binary64
681×associate-*l*_binary64
377×associate-*l/_binary64
256×associate-/r/_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
025593
157566
2101566
3280434
41636374
Stop Event
1×node limit
Counts
322 → 298
Calls
Call 1
Inputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(*.f64 -1 (pow.f64 N 2))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
Outputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(*.f64 -1 (pow.f64 N 2))
(neg.f64 (*.f64 N N))
(*.f64 N (neg.f64 N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))

localize25.0ms (0.3%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
0.0b
(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
0.0b
(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))
0.0b
(+.f64 1 (fma.f64 N N N))
✓0.0b
(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))
✓0.0b
(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
✓0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
2.9b
(+.f64 N (-.f64 1 N))
Compiler

Compiled 60 to 31 computations (48.3% saved)

series3.0ms (0%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
0.0ms
N
@inf
(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
0.0ms
N
@0
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
0.0ms
N
@0
(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
0.0ms
N
@-inf
(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
0.0ms
N
@0
(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))

rewrite105.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
868×prod-diff_binary64
605×unpow-prod-down_binary64
430×log-prod_binary64
405×fma-def_binary64
258×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01053
120153
2277053
Stop Event
1×node limit
Counts
3 → 91
Calls
Call 1
Inputs
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))
Outputs
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(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2) (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) -1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log1p.f64 (pow.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2) (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 1 (pow.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2))) (log.f64 (-.f64 1 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)) 1/3) (cbrt.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3) (cbrt.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2) 3) (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 1))))))

simplify88.0ms (1%)

Algorithm
1×egg-herbie
Rules
25×fma-def_binary64
7×+-commutative_binary64
4×distribute-lft-in_binary64
3×distribute-rgt1-in_binary64
2×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08420
117420
224420
333420
441420
545420
657420
770420
875420
976420
Stop Event
1×saturated
Counts
127 → 67
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
Outputs
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

localize43.0ms (0.5%)

Local error

Found 8 expressions with local error:

NewErrorProgram
2.9b
(+.f64 N (-.f64 1 N))
0.1b
(pow.f64 (fma.f64 N N N) 3)
0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
0.0b
(+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3)))
✓0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
✓0.1b
(pow.f64 (fma.f64 N N N) 3)
2.9b
(+.f64 N (-.f64 1 N))
✓29.3b
(cbrt.f64 (pow.f64 (fma.f64 N N N) 3))
Compiler

Compiled 53 to 28 computations (47.2% saved)

series6.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
N
@0
(pow.f64 (fma.f64 N N N) 3)
1.0ms
N
@-inf
(pow.f64 (fma.f64 N N N) 3)
1.0ms
N
@inf
(pow.f64 (fma.f64 N N N) 3)
1.0ms
N
@0
(cbrt.f64 (pow.f64 (fma.f64 N N N) 3))
1.0ms
N
@inf
(cbrt.f64 (pow.f64 (fma.f64 N N N) 3))

rewrite121.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
986×prod-diff_binary64
458×log-prod_binary64
412×fma-def_binary64
278×pow2_binary64
217×fma-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01130
124730
2301330
Stop Event
1×node limit
Counts
3 → 105
Calls
Call 1
Inputs
(cbrt.f64 (pow.f64 (fma.f64 N N N) 3))
(pow.f64 (fma.f64 N N N) 3)
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 N N) 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (fma.f64 N N N) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 N N N)) (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 N N) 3) (pow.f64 N 3)) (+.f64 (pow.f64 (*.f64 N N) 2) (-.f64 (*.f64 N N) (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 N N) 2) (*.f64 N N)) (-.f64 (*.f64 N N) N))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 N (sqrt.f64 N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 N) (exp.f64 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (exp.f64 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 N N)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 N N N))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N N N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N 1 (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (fma.f64 N N N) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (fma.f64 N N N) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N N) 1 N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 N) (pow.f64 (cbrt.f64 N) 2) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) (cbrt.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 2)) (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (sqrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 N (sqrt.f64 (+.f64 N 1))) (hypot.f64 N (sqrt.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (fma.f64 N N N) 3) 1) (/.f64 1 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) 1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (-.f64 1 (fma.f64 N N N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (sqrt.f64 N)) (sqrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 N) 2) 2) (pow.f64 (cbrt.f64 N) 2) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) N)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (fma.f64 N N N) 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 N N) (pow.f64 (fma.f64 N N N) 2)) (*.f64 N (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 (fma.f64 N N N) 2) (*.f64 N N)) (*.f64 (pow.f64 (fma.f64 N N N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 N N N) 3))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 N N N) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 N N N) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 N N N) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 (fma.f64 N N N) 3) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (fma.f64 N N N) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2) (*.f64 (cbrt.f64 (fma.f64 N N N)) (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (*.f64 (hypot.f64 N (sqrt.f64 N)) (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) 3/2) (pow.f64 (fma.f64 N N N) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (fma.f64 N N N) 2) 1) (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (fma.f64 N N N) 2) (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2)) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (fma.f64 N N N) 2) (hypot.f64 N (sqrt.f64 N))) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N N) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (fma.f64 N N N) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (fma.f64 N N N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (fma.f64 N N N) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (fma.f64 N N N) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (fma.f64 N N N) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3 (log.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 N N N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (pow.f64 (fma.f64 N N N) 3) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N N) (pow.f64 (fma.f64 N N N) 2) (*.f64 N (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 2) (*.f64 N N) (*.f64 (pow.f64 (fma.f64 N N N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 N N N) 3) 1)) 2) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 N N N) 3) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (fma.f64 N N N) 3/2)) (hypot.f64 1 (pow.f64 (fma.f64 N N N) 3/2)) -1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) (pow.f64 (cbrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) 2) (cbrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) (sqrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) 1))))))

simplify149.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
534×associate-+l+_binary64
492×unswap-sqr_binary64
466×associate-+r+_binary64
424×distribute-rgt-in_binary64
412×sqr-pow_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
026365
169357
2163351
3453348
41697346
53431346
64093346
74662346
85394346
96570346
107813346
Stop Event
1×node limit
Counts
141 → 123
Calls
Call 1
Inputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 3)
(+.f64 (*.f64 3 (pow.f64 N 4)) (pow.f64 N 3))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 3)))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(pow.f64 N 6)
(+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5)))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5))))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(pow.f64 N 6)
(+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5)))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5))))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
Outputs
N
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(pow.f64 N 3)
(+.f64 (*.f64 3 (pow.f64 N 4)) (pow.f64 N 3))
(fma.f64 3 (pow.f64 N 4) (pow.f64 N 3))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 3)))
(fma.f64 3 (pow.f64 N 4) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)))
(fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 3))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(fma.f64 3 (pow.f64 N 4) (+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (fma.f64 3 (pow.f64 N 4) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 3)) (pow.f64 N 6))
(fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)))
(fma.f64 3 (pow.f64 N 5) (fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (pow.f64 N 3)))
(pow.f64 N 6)
(+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5)))
(+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 6))
(fma.f64 3 (pow.f64 N 5) (pow.f64 N 6))
(*.f64 (pow.f64 N 5) (+.f64 N 3))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5))))
(fma.f64 3 (pow.f64 N 4) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 6)))
(fma.f64 3 (pow.f64 N 4) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 6)))
(fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 6))
(fma.f64 3 (pow.f64 N 4) (*.f64 (pow.f64 N 5) (+.f64 N 3)))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(fma.f64 3 (pow.f64 N 4) (+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (fma.f64 3 (pow.f64 N 4) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 3)) (pow.f64 N 6))
(fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)))
(fma.f64 3 (pow.f64 N 5) (fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (pow.f64 N 3)))
(pow.f64 N 6)
(+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5)))
(+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 6))
(fma.f64 3 (pow.f64 N 5) (pow.f64 N 6))
(*.f64 (pow.f64 N 5) (+.f64 N 3))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5))))
(fma.f64 3 (pow.f64 N 4) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 6)))
(fma.f64 3 (pow.f64 N 4) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 6)))
(fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 6))
(fma.f64 3 (pow.f64 N 4) (*.f64 (pow.f64 N 5) (+.f64 N 3)))
(+.f64 (*.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(fma.f64 3 (pow.f64 N 4) (+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (fma.f64 3 (pow.f64 N 4) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 3)) (pow.f64 N 6))
(fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)))
(fma.f64 3 (pow.f64 N 5) (fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (pow.f64 N 3)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

eval769.0ms (9%)

Compiler

Compiled 21663 to 12093 computations (44.2% saved)

prune138.0ms (1.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New98510995
Fresh000
Picked101
Done325
Total989121001
Error
0.5b
Counts
1001 → 12
Alt Table
Click to see full alt table
StatusErrorProgram
1.0b
(expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
▶27.9b
(atan2.f64 1 (*.f64 N N))
1.1b
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
29.8b
(atan2.f64 1 (+.f64 1 N))
22.7b
(atan2.f64 1 (/.f64 (-.f64 (*.f64 (+.f64 1 N) (+.f64 1 N)) (pow.f64 N 4)) (-.f64 (+.f64 1 N) (*.f64 N N))))
▶0.5b
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
10.8b
(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
▶22.7b
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
▶30.4b
(atan2.f64 1 1)
✓0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶1.9b
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
✓15.3b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 244 to 182 computations (25.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
0.0b
(fma.f64 N N (+.f64 N 1))
✓0.0b
(fma.f64 N N (+.f64 N 1))
✓0.5b
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
Compiler

Compiled 20 to 12 computations (40% saved)

series2.0ms (0%)

Counts
2 → 16
Calls

6 calls:

TimeVariablePointExpression
0.0ms
N
@0
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
0.0ms
N
@-inf
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
0.0ms
N
@inf
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
0.0ms
N
@-inf
(fma.f64 N N (+.f64 N 1))
0.0ms
N
@0
(fma.f64 N N (+.f64 N 1))

rewrite60.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
586×pow1_binary64
543×log1p-expm1-u_binary64
543×expm1-log1p-u_binary64
542×add-log-exp_binary64
531×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0619
112219
2149219
Stop Event
1×node limit
Counts
2 → 39
Calls
Call 1
Inputs
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
(fma.f64 N N (+.f64 N 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 2) (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) (sqrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) (+.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 N N) 1) (+.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 N N) 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 N N) N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 N N (+.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 N N (+.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N (+.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 N N (+.f64 1 N))) (pow.f64 (cbrt.f64 (fma.f64 N N (+.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N (+.f64 1 N))) 2) (cbrt.f64 (fma.f64 N N (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 (+.f64 1 N))) (hypot.f64 N (sqrt.f64 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 N N) 3) (pow.f64 (+.f64 1 N) 3)) (+.f64 (*.f64 (*.f64 N N) (*.f64 N N)) (-.f64 (pow.f64 (+.f64 1 N) 2) (*.f64 (*.f64 N N) (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 N N) (*.f64 N N)) (pow.f64 (+.f64 1 N) 2)) (-.f64 (*.f64 N N) (+.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 N N (+.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N (+.f64 1 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 N N (+.f64 1 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 N (sqrt.f64 (+.f64 1 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N (+.f64 1 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 N N (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 N N (+.f64 1 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 N N (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 N N (+.f64 1 N))))))))

simplify85.0ms (1%)

Algorithm
1×egg-herbie
Rules
957×fma-neg_binary64
532×unswap-sqr_binary64
470×distribute-rgt-neg-in_binary64
353×cancel-sign-sub-inv_binary64
327×fma-def_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
014139
134115
257115
3145115
4524115
51579115
63507115
75703115
87556115
Stop Event
1×node limit
Counts
55 → 50
Calls
Call 1
Inputs
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
1
(+.f64 N 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
Outputs
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1
(+.f64 N 1)
(+.f64 1 N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))

localize3.0ms (0%)

Compiler

Compiled 5 to 5 computations (0% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.5b
(atan2.f64 1 (*.f64 N N))
✓0.5b
(atan2.f64 1 (*.f64 N N))
Compiler

Compiled 11 to 5 computations (54.5% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
N
@0
(atan2.f64 1 (*.f64 N N))
0.0ms
N
@-inf
(atan2.f64 1 (*.f64 N N))
0.0ms
N
@inf
(atan2.f64 1 (*.f64 N N))

rewrite45.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
361×pow1_binary64
347×add-sqr-sqrt_binary64
341×*-un-lft-identity_binary64
332×add-log-exp_binary64
331×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
1917
29617
Stop Event
1×node limit
Counts
1 → 36
Calls
Call 1
Inputs
(atan2.f64 1 (*.f64 N N))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 1 (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (atan2.f64 1 (*.f64 N N))))) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 1 (*.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 1 (*.f64 N N))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 1 (*.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (*.f64 N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (*.f64 N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (*.f64 N N))) (cbrt.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 2)) (cbrt.f64 (atan2.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (*.f64 N N))) (sqrt.f64 (atan2.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 1/4) (sqrt.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 5/2)) (pow.f64 (atan2.f64 1 (*.f64 N N)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (atan2.f64 1 (*.f64 N N)) (cbrt.f64 (atan2.f64 1 (*.f64 N N)))) 2)) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 3/2)) (pow.f64 (atan2.f64 1 (*.f64 N N)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (*.f64 N N))) 5)) (pow.f64 (atan2.f64 1 (*.f64 N N)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (atan2.f64 1 (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (atan2.f64 1 (*.f64 N N)) (cbrt.f64 (atan2.f64 1 (*.f64 N N)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 5/2) 1/3) (pow.f64 (atan2.f64 1 (*.f64 N N)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (atan2.f64 1 (*.f64 N N))) 3) 1) (+.f64 (*.f64 (+.f64 1 (atan2.f64 1 (*.f64 N N))) (+.f64 1 (atan2.f64 1 (*.f64 N N)))) (+.f64 1 (*.f64 (+.f64 1 (atan2.f64 1 (*.f64 N N))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (*.f64 N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (atan2.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (*.f64 N N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (*.f64 N N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (atan2.f64 1 (*.f64 N N))))) (sqrt.f64 (log.f64 (atan2.f64 1 (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (atan2.f64 1 (*.f64 N N)))) 2)) (cbrt.f64 (log.f64 (atan2.f64 1 (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (atan2.f64 1 (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 1 (*.f64 N N)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (atan2.f64 1 (*.f64 N N)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (atan2.f64 1 (*.f64 N N)))) 2))))))

simplify164.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
1366×sqr-pow_binary64
695×pow-sqr_binary64
617×cube-prod_binary64
612×fabs-mul_binary64
434×unswap-sqr_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
21784
32884
45484
515084
657984
7142784
8159184
9177584
10198384
11227484
12266784
13314884
14371484
15440684
16524384
17563584
18592184
19620384
20627784
21631384
22725484
Stop Event
1×node limit
Counts
48 → 38
Calls
Call 1
Inputs
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (pow.f64 N 2))
Outputs
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (*.f64 N N))

localize35.0ms (0.4%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (+.f64 1 (pow.f64 N 3)) N)
0.0b
(-.f64 (fma.f64 N N 1) N)
0.0b
(+.f64 1 (pow.f64 N 3))
0.0b
(+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N)))
✓0.0b
(-.f64 (fma.f64 N N 1) N)
✓0.0b
(*.f64 (+.f64 1 (pow.f64 N 3)) N)
✓0.5b
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
✓19.7b
(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
Compiler

Compiled 77 to 52 computations (32.5% saved)

series7.0ms (0.1%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
N
@-inf
(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
1.0ms
N
@inf
(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
1.0ms
N
@0
(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
1.0ms
N
@-inf
(*.f64 (+.f64 1 (pow.f64 N 3)) N)
1.0ms
N
@inf
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))

rewrite104.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
661×fma-def_binary64
652×log-prod_binary64
350×pow2_binary64
264×fma-neg_binary64
240×pow1/3_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01264
127564
2390458
Stop Event
1×node limit
Counts
4 → 224
Calls
Call 1
Inputs
(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
(*.f64 (+.f64 1 (pow.f64 N 3)) N)
(-.f64 (fma.f64 N N 1) N)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 (/.f64 (+.f64 1 (pow.f64 N 3)) (fma.f64 N N (-.f64 1 N))) N 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (*.f64 (+.f64 1 (pow.f64 N 3)) (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 N 3)) (/.f64 1 (/.f64 (fma.f64 N N (-.f64 1 N)) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 N 3)) (*.f64 N (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N (pow.f64 N 3) N) (/.f64 1 (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) 2) (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) 2) (*.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) (sqrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) (*.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (fma.f64 N (pow.f64 N 3) N)) (/.f64 1 (neg.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 N N (-.f64 1 N))) (fma.f64 N (pow.f64 N 3) N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 N 1) (/.f64 (+.f64 1 (pow.f64 N 3)) (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (pow.f64 N 3)) (fma.f64 N N (-.f64 1 N))) N)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (pow.f64 N 3)) 1) (/.f64 N (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) 2) 1) (/.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) 1) (/.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2)) (/.f64 (fma.f64 N (pow.f64 N 3) N) (cbrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 N (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2)) (/.f64 (+.f64 1 (pow.f64 N 3)) (cbrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (pow.f64 N 3)) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2)) (/.f64 N (cbrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) 2) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2)) (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2)) (/.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) (cbrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (fma.f64 N N (-.f64 1 N)))) (/.f64 (fma.f64 N (pow.f64 N 3) N) (sqrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 N (sqrt.f64 (fma.f64 N N (-.f64 1 N)))) (/.f64 (+.f64 1 (pow.f64 N 3)) (sqrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (pow.f64 N 3)) (sqrt.f64 (fma.f64 N N (-.f64 1 N)))) (/.f64 N (sqrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) 2) (sqrt.f64 (fma.f64 N N (-.f64 1 N)))) (/.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) (sqrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (-.f64 (pow.f64 (fma.f64 N N 1) 3) (pow.f64 N 3))) (fma.f64 N (fma.f64 N N (+.f64 1 N)) (pow.f64 (fma.f64 N N 1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (-.f64 (pow.f64 (fma.f64 N N 1) 2) (*.f64 N N))) (fma.f64 N N (+.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 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(2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 N N 1))) (/.f64 1 (exp.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 N)) (exp.f64 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (exp.f64 N)) (exp.f64 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 N)) (+.f64 1 (expm1.f64 (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (exp.f64 N)) (+.f64 1 (expm1.f64 (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 N N (-.f64 1 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 N N (-.f64 1 N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N 1) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N 1) (*.f64 (neg.f64 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N (-.f64 1 N)) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N (-.f64 1 N)) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N (-.f64 1 N)) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 N N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 N N) (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 N) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N N (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N N (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N 1) 1 (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N 1) 1 (*.f64 (neg.f64 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N (-.f64 1 N)) 1 (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N (-.f64 1 N)) 1 (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N (-.f64 1 N)) 1 (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 N N 1)) (cbrt.f64 (pow.f64 (fma.f64 N N 1) 2)) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 N N 1)) (cbrt.f64 (pow.f64 (fma.f64 N N 1) 2)) (*.f64 (neg.f64 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 N N 1) 2)) (cbrt.f64 (fma.f64 N N 1)) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 N N 1) 2)) (cbrt.f64 (fma.f64 N N 1)) (*.f64 (neg.f64 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (neg.f64 (cbrt.f64 N)) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 N) (hypot.f64 1 N) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 N) (hypot.f64 1 N) (*.f64 (neg.f64 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (pow.f64 N 3/2) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (pow.f64 N 3/2) (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (neg.f64 (sqrt.f64 N)) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 3) (pow.f64 N 3)) (/.f64 1 (fma.f64 N (fma.f64 N N (+.f64 1 N)) (pow.f64 (fma.f64 N N 1) 2))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 3) (pow.f64 N 3)) (/.f64 1 (fma.f64 N (fma.f64 N N (+.f64 1 N)) (pow.f64 (fma.f64 N N 1) 2))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 3) (pow.f64 N 3)) (/.f64 1 (fma.f64 N (fma.f64 N N (+.f64 1 N)) (pow.f64 (fma.f64 N N 1) 2))) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 2) (*.f64 N N)) (/.f64 1 (fma.f64 N N (+.f64 1 N))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 2) (*.f64 N N)) (/.f64 1 (fma.f64 N N (+.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 2) (*.f64 N N)) (/.f64 1 (fma.f64 N N (+.f64 1 N))) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 N) 2) 2) (pow.f64 (cbrt.f64 N) 2) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 N) 2) 2) (pow.f64 (cbrt.f64 N) 2) (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (neg.f64 N)) 2) (cbrt.f64 (neg.f64 N)) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 N)) (sqrt.f64 (neg.f64 N)) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 N)) (sqrt.f64 N) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 N (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 N) (sqrt.f64 N)) (-.f64 (hypot.f64 1 N) (sqrt.f64 N)) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 N) (sqrt.f64 N)) (-.f64 (hypot.f64 1 N) (sqrt.f64 N)) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 N) (sqrt.f64 N)) (-.f64 (hypot.f64 1 N) (sqrt.f64 N)) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) (+.f64 1 (neg.f64 N)))))))

simplify61.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
451×associate-/l*_binary64
396×fma-neg_binary64
382×fma-def_binary64
350×div-sub_binary64
301×sub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
032561
178477
2143477
3360477
41393477
54958477
Stop Event
1×node limit
Counts
272 → 241
Calls
Call 1
Inputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (*.f64 -1 N)))))
N
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
1
(+.f64 1 (*.f64 -1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(pow.f64 N 2)
(+.f64 (pow.f64 N 2) (*.f64 -1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(pow.f64 N 2)
(+.f64 (pow.f64 N 2) (*.f64 -1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
Outputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
N
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
1
(+.f64 1 (*.f64 -1 N))
(+.f64 1 (neg.f64 N))
(-.f64 1 N)
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 (pow.f64 N 2) (*.f64 -1 N))
(+.f64 (*.f64 N N) (neg.f64 N))
(*.f64 N (+.f64 N -1))
(-.f64 (*.f64 N N) N)
(fma.f64 N N (neg.f64 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 (pow.f64 N 2) (*.f64 -1 N))
(+.f64 (*.f64 N N) (neg.f64 N))
(*.f64 N (+.f64 N -1))
(-.f64 (*.f64 N N) N)
(fma.f64 N N (neg.f64 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))

localize18.0ms (0.2%)

Local error

Found 8 expressions with local error:

NewErrorProgram
14.2b
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
0.5b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
0.2b
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
0.0b
(+.f64 1 (fma.f64 N N N))
✓0.0b
(+.f64 1 (fma.f64 N N N))
✓0.2b
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
✓0.5b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓14.2b
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
Compiler

Compiled 42 to 22 computations (47.6% saved)

series20.0ms (0.2%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
6.0ms
N
@0
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
3.0ms
N
@inf
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
2.0ms
N
@inf
(+.f64 1 (fma.f64 N N N))
2.0ms
N
@0
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
2.0ms
N
@-inf
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite80.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
761×pow1_binary64
714×add-log-exp_binary64
713×log1p-expm1-u_binary64
713×expm1-log1p-u_binary64
698×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0943
118843
2197643
Stop Event
1×node limit
Counts
4 → 93
Calls
Call 1
Inputs
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
(+.f64 1 (fma.f64 N N N))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (pow.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1/3) (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) 3) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) 3) (pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) 1) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2)) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6)) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) 3) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) 3) (pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) 1) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2)) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6)) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (fma.f64 N N N))) (/.f64 (pow.f64 (fma.f64 N N N) 2) (-.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 2) (cbrt.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3)) (/.f64 1 (+.f64 1 (-.f64 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (-.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N N))) (+.f64 1 (pow.f64 (fma.f64 N N N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (fma.f64 N N N)) (-.f64 1 (pow.f64 (fma.f64 N N N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3)) (+.f64 1 (-.f64 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3)) (+.f64 (pow.f64 (fma.f64 N N N) 2) (-.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (-.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3))) (neg.f64 (+.f64 1 (-.f64 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2))) (neg.f64 (-.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 N N N) 2) 1) (-.f64 (fma.f64 N N N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2) (cbrt.f64 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 N (sqrt.f64 N)) (hypot.f64 N (sqrt.f64 N)) 1)))))

simplify138.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
922×fma-def_binary64
796×unswap-sqr_binary64
694×sqr-pow_binary64
453×cube-prod_binary64
429×pow-sqr_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
017503
140491
258491
388491
4169491
5462491
61530491
73426491
83966491
94361491
104760491
115342491
126075491
136966491
147525491
Stop Event
1×node limit
Counts
141 → 88
Calls
Call 1
Inputs
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
1
(+.f64 N 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
Outputs
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1
(+.f64 N 1)
(+.f64 1 N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))

eval203.0ms (2.4%)

Compiler

Compiled 8485 to 5844 computations (31.1% saved)

prune107.0ms (1.3%)

Pruning

16 alts after pruning (12 fresh and 4 done)

PrunedKeptTotal
New4089417
Fresh235
Picked101
Done246
Total41316429
Error
0.4b
Counts
429 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
10.8b
(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
35.4b
(*.f64 (cbrt.f64 (atan2.f64 1 (*.f64 N N))) (cbrt.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 2)))
1.0b
(expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
22.7b
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (+.f64 (*.f64 N N) (-.f64 1 N)))))
✓27.9b
(atan2.f64 1 (*.f64 N N))
11.9b
(pow.f64 (cbrt.f64 (atan2.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 3)))) 3)
28.0b
(pow.f64 (sqrt.f64 (atan2.f64 1 (*.f64 N N))) 2)
0.5b
(atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 1 N)))
28.3b
(pow.f64 (cbrt.f64 (atan2.f64 1 (*.f64 N N))) 3)
1.9b
(pow.f64 (cbrt.f64 (atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))) 3)
✓30.4b
(atan2.f64 1 1)
✓0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
29.8b
(atan2.f64 1 (+.f64 1 N))
✓15.3b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
22.7b
(atan2.f64 1 (/.f64 (-.f64 (*.f64 (+.f64 1 N) (+.f64 1 N)) (pow.f64 N 4)) (-.f64 (+.f64 1 N) (*.f64 N N))))
1.9b
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
Compiler

Compiled 181 to 137 computations (24.3% saved)

regimes49.0ms (0.6%)

Counts
29 → 1
Calls
Call 1
Inputs
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (+.f64 (*.f64 N N) (-.f64 1 N)))))
(atan2.f64 1 (/.f64 (-.f64 (*.f64 (+.f64 1 N) (+.f64 1 N)) (pow.f64 N 4)) (-.f64 (+.f64 1 N) (*.f64 N N))))
(pow.f64 (sqrt.f64 (atan2.f64 1 (*.f64 N N))) 2)
(pow.f64 (cbrt.f64 (atan2.f64 1 (*.f64 N N))) 3)
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
(expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
(*.f64 (cbrt.f64 (atan2.f64 1 (*.f64 N N))) (cbrt.f64 (pow.f64 (atan2.f64 1 (*.f64 N N)) 2)))
(pow.f64 (cbrt.f64 (atan2.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 3)))) 3)
(pow.f64 (cbrt.f64 (atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))) 3)
(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))
Outputs
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
Calls

3 calls:

15.0ms
N
7.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
6.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Results
ErrorSegmentsBranch
0.5b1N
0.5b1(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.5b1(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 357 to 235 computations (34.2% saved)

regimes17.0ms (0.2%)

Counts
9 → 1
Calls
Call 1
Inputs
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Outputs
(atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 1 N)))
Calls

3 calls:

6.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
6.0ms
N
2.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Results
ErrorSegmentsBranch
0.5b1N
0.5b1(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.5b1(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 82 to 58 computations (29.3% saved)

regimes8.0ms (0.1%)

Counts
5 → 1
Calls
Call 1
Inputs
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
Outputs
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
Calls

1 calls:

6.0ms
N
Results
ErrorSegmentsBranch
1.9b1N
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes13.0ms (0.2%)

Counts
4 → 3
Calls
Call 1
Inputs
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (+.f64 1 N))
Outputs
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (*.f64 N N))
Calls

1 calls:

12.0ms
N
Results
ErrorSegmentsBranch
1.7b3N
Compiler

Compiled 21 to 16 computations (23.8% saved)

bsearch55.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
28.0ms
1.5419197210007654
422.6936260233725
27.0ms
-2825946.7282828824
-0.0013079059934821581
Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0%)

Accuracy

Total -0.6b remaining (-2.1%)

Threshold costs -0.6b (-2.1%)

Counts
2 → 1
Calls
Call 1
Inputs
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 1 N))
Outputs
(atan2.f64 1 (+.f64 1 N))
Calls

1 calls:

3.0ms
N
Results
ErrorSegmentsBranch
29.8b1N
Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
3×+-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02278
12778
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
(atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(if (<=.f64 N -6068674389106589/2147483648) (atan2.f64 1 (*.f64 N N)) (if (<=.f64 N 3472094540467133/2251799813685248) (atan2.f64 1 (+.f64 1 N)) (atan2.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 1)
Outputs
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(if (<=.f64 N -6068674389106589/2147483648) (atan2.f64 1 (*.f64 N N)) (if (<=.f64 N 3472094540467133/2251799813685248) (atan2.f64 1 (+.f64 1 N)) (atan2.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 1)
Compiler

Compiled 61 to 44 computations (27.9% saved)

soundness0.0ms (0%)

end46.0ms (0.5%)

Compiler

Compiled 56 to 37 computations (33.9% saved)

Profiling

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