Details

Time bar (total: 8.5s)

analyze0.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample3.1s (36.5%)

Results
1.7s2172×body2048valid
826.0ms4552×body256valid
347.0ms1055×body1024valid
161.0ms477×body512valid

preprocess24.0ms (0.3%)

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)

simplify14.0ms (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
13.8b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶13.8b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 8 to 6 computations (25% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(atan.f64 (+.f64 N 1))
✓2.5b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0%)

Counts
2 → 8
Calls

6 calls:

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

rewrite84.0ms (1%)

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
0717
115617
2221317
Stop Event
1×node limit
Counts
2 → 52
Calls
Call 1
Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(atan.f64 (+.f64 N 1))
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)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan.f64 (+.f64 N 1))))))))

simplify25.0ms (0.3%)

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
0984
12068
23168
36168
48868
513468
618268
721568
825868
929468
1032068
1132268
Stop Event
1×saturated
Counts
60 → 56
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))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 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))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (neg.f64 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (neg.f64 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (neg.f64 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (neg.f64 N)))
(atan.f64 (+.f64 1 N))

eval18.0ms (0.2%)

Compiler

Compiled 786 to 518 computations (34.1% saved)

prune17.0ms (0.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New50656
Fresh000
Picked011
Done000
Total50757
Error
12.1b
Counts
57 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
▶12.3b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
45.7b
(+.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)))
▶30.0b
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
▶14.3b
(log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
✓13.8b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶22.9b
(-.f64 (expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
▶29.1b
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
Compiler

Compiled 158 to 114 computations (27.8% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(*.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)

series23.0ms (0.3%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
19.0ms
N
@0
(*.f64 N (+.f64 N 1))
1.0ms
N
@-inf
(*.f64 N (+.f64 N 1))
1.0ms
N
@inf
(*.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))))

rewrite119.0ms (1.4%)

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
0933
121029
2307629
Stop Event
1×node limit
Counts
3 → 181
Calls
Call 1
Inputs
(+.f64 N (-.f64 1 N))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(*.f64 N (+.f64 N 1))
Outputs
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((#(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 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 1 (fma.f64 N N N)) -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 1 (fma.f64 N N N)) 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 (+.f64 1 (fma.f64 N N N))) (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 2) (cbrt.f64 (+.f64 1 (fma.f64 N N N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 N) (cbrt.f64 (*.f64 N N)) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.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)))))

simplify86.0ms (1%)

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
019240
144198
267198
3163198
4583198
51634198
63616198
75643198
87339198
Stop Event
1×node limit
Counts
217 → 190
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)))))
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)))
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)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(atan.f64 (+.f64 N 1))
✓0.0b
(exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
2.5b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓3.0b
(log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
Compiler

Compiled 36 to 23 computations (36.1% saved)

series2.0ms (0%)

Counts
2 → 16
Calls

6 calls:

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

rewrite146.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
965×pow1_binary64
896×log1p-expm1-u_binary64
896×expm1-log1p-u_binary64
895×add-log-exp_binary64
92×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0924
118024
2241224
Stop Event
1×node limit
Counts
2 → 66
Calls
Call 1
Inputs
(log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(exp.f64 (-.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 0 (-.f64 (atan.f64 (+.f64 N 1)) (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 (log.f64 (sqrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (+.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 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) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (/.f64 (pow.f64 (atan.f64 N) 2) (+.f64 (atan.f64 (+.f64 N 1)) (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))) (cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.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 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)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (atan.f64 (+.f64 N 1))) (exp.f64 (neg.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (atan.f64 (+.f64 N 1))) (/.f64 1 (exp.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 2) (cbrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (sqrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (exp.f64 (atan.f64 N)) (exp.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 (atan.f64 (+.f64 N 1))) (exp.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (exp.f64 (atan.f64 (+.f64 N 1)))) (neg.f64 (exp.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cbrt.f64 (pow.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 pow.f64 (exp.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 sqrt.f64 (pow.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))))

simplify95.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
605×associate-/r*_binary64
553×fma-def_binary64
386×fma-neg_binary64
263×associate-*l/_binary64
238×associate-/l/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
013192
129184
241184
375184
4117184
5185184
6296184
7561184
81617184
94076184
104667184
115581184
126933184
Stop Event
1×node limit
Counts
82 → 69
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))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 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))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N)))
(exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(atan.f64 (+.f64 N 1))
✓0.5b
(log1p.f64 (atan.f64 (+.f64 N 1)))
✓0.5b
(expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1))))
✓12.5b
(-.f64 (expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
Compiler

Compiled 32 to 23 computations (28.1% saved)

series84.0ms (1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
36.0ms
N
@0
(log1p.f64 (atan.f64 (+.f64 N 1)))
30.0ms
N
@inf
(log1p.f64 (atan.f64 (+.f64 N 1)))
16.0ms
N
@-inf
(log1p.f64 (atan.f64 (+.f64 N 1)))
0.0ms
N
@0
(-.f64 (expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
0.0ms
N
@-inf
(-.f64 (expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))

rewrite142.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
916×pow1_binary64
850×expm1-log1p-u_binary64
849×add-log-exp_binary64
849×log1p-expm1-u_binary64
831×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0925
117225
2228825
Stop Event
1×node limit
Counts
3 → 70
Calls
Call 1
Inputs
(-.f64 (expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
(expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
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 (+.f64 N 1) N) (+.f64 1 (*.f64 (+.f64 N 1) 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 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)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 3) 1) (+.f64 (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 1 (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1)))) 1) (+.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x atan.f64 (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan.f64 (+.f64 N 1))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log1p.f64 (atan.f64 (+.f64 N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) (pow.f64 (cbrt.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) 2) (cbrt.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) (sqrt.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (atan.f64 (+.f64 N 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (atan.f64 (+.f64 N 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))))))))

simplify296.0ms (3.5%)

Algorithm
1×egg-herbie
Rules
2176×fma-def_binary64
1905×associate-+l+_binary64
1651×associate-+r+_binary64
233×distribute-rgt-out_binary64
232×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
016300
133300
243300
373300
4100300
5148300
6196300
7234300
8291300
9344300
10386300
11399300
12409300
13434300
14521300
15579300
16647300
17692300
18700300
19702300
20902300
211131300
221264300
231428300
241434300
251434300
262266300
272521300
282769300
292902300
302917300
312917300
324583300
334583300
344583300
354583300
364583300
377711300
387760300
397942300
Stop Event
1×node limit
Counts
106 → 75
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))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))))
(log.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))))
(log.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))))
(log.f64 (+.f64 1 (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))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 N 1))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 N 1))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 N 1))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 N 1))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))))
(log1p.f64 (atan.f64 (+.f64 N 1)))
(log.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))))
(log1p.f64 (atan.f64 (+.f64 N 1)))

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(atan.f64 (+.f64 N 1))
✓0.5b
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))
✓1.0b
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
✓2.5b
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
Compiler

Compiled 36 to 27 computations (25% saved)

series5.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
1.0ms
N
@-inf
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
1.0ms
N
@0
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
1.0ms
N
@inf
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
0.0ms
N
@inf
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))
0.0ms
N
@0
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))

rewrite90.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
534×prod-diff_binary64
401×log-prod_binary64
304×exp-prod_binary64
293×fma-def_binary64
261×pow-prod-down_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01026
121926
2253426
Stop Event
1×node limit
Counts
3 → 163
Calls
Call 1
Inputs
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (atan.f64 (+.f64 N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (atan.f64 (+.f64 N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (*.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (pow.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)) 5/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3/2) (pow.f64 (atan.f64 (+.f64 N 1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 5/2) (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 9))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 9)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 3/2) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan.f64 (+.f64 N 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan.f64 (+.f64 N 1))))) (log.f64 (sqrt.f64 (exp.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 6) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 9) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/3) (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (atan.f64 (+.f64 N 1)))) 2)) (cbrt.f64 (log.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (atan.f64 (+.f64 N 1))))) (sqrt.f64 (log.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x atan.f64 (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) 1) 1/3))))))

simplify117.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
1109×fma-def_binary64
691×fma-neg_binary64
419×neg-mul-1_binary64
417×neg-sub0_binary64
362×unswap-sqr_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
014248
135240
250240
389240
4137240
5274240
6735240
71465240
81659240
91998240
103207240
113866240
125688240
137968240
Stop Event
1×node limit
Counts
191 → 168
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))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(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))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (neg.f64 N))) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (neg.f64 N))) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (neg.f64 N))) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (neg.f64 N))) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 N 1))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 N 1))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 N 1))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 N 1))

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(atan.f64 (+.f64 N 1))
✓0.5b
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3)
✓1.0b
(cbrt.f64 (atan.f64 (+.f64 N 1)))
✓28.6b
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
Compiler

Compiled 35 to 26 computations (25.7% saved)

series10.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
3.0ms
N
@0
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
3.0ms
N
@-inf
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
2.0ms
N
@inf
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
0.0ms
N
@0
(cbrt.f64 (atan.f64 (+.f64 N 1)))
0.0ms
N
@-inf
(cbrt.f64 (atan.f64 (+.f64 N 1)))

rewrite108.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
631×prod-diff_binary64
404×log-prod_binary64
303×exp-prod_binary64
300×fma-def_binary64
265×pow-prod-down_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01025
122025
2258125
Stop Event
1×node limit
Counts
3 → 174
Calls
Call 1
Inputs
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
(cbrt.f64 (atan.f64 (+.f64 N 1)))
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3)
Outputs
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(+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (fma.f64 (neg.f64 (atan.f64 N)) 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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))) (fma.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (cbrt.f64 (pow.f64 (atan.f64 N) 2)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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))) (+.f64 (neg.f64 (atan.f64 N)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (atan.f64 N) 2))) (cbrt.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 5/6) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 5/6) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (*.f64 (neg.f64 (atan.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1) (cbrt.f64 (atan.f64 (+.f64 N 1))) (*.f64 (neg.f64 (atan.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 2) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 2) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (*.f64 (neg.f64 (atan.f64 N)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (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 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.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 (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 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 (E.f64) (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) 1/9)))) (#(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 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 2/3)))) (#(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 pow.f64 (exp.f64 1/3) (log.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 2)) (cbrt.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))) (sqrt.f64 (log.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))) 2))))) (#(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 log.f64 (+.f64 1 (expm1.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 exp.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan.f64 (+.f64 N 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan.f64 (+.f64 N 1))))) (log.f64 (sqrt.f64 (exp.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (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))) 2)) (*.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (pow.f64 (atan.f64 (+.f64 N 1)) 5/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 5/6) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (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 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x atan.f64 (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (atan.f64 (+.f64 N 1)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2/3 (log.f64 (atan.f64 (+.f64 N 1)))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 3/2) 2))))))

simplify219.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
1292×sqr-pow_binary64
666×pow-sqr_binary64
625×cube-prod_binary64
470×fabs-mul_binary64
362×unswap-sqr_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
018372
151300
276300
3116300
4173300
5313300
6746300
71433300
81560300
91732300
101921300
112162300
122489300
132915300
143423300
154027300
164752300
175075300
185357300
195581300
205759300
215841300
226784300
237761300
Stop Event
1×node limit
Counts
210 → 182
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)
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N))))
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 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (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 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))

eval497.0ms (5.9%)

Compiler

Compiled 13124 to 8714 computations (33.6% saved)

prune307.0ms (3.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New7895794
Fresh101
Picked101
Done505
Total7965801
Error
0.2b
Counts
801 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶12.4b
(exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3))
▶0.2b
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
▶0.2b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶12.3b
(cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))
▶12.8b
(pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)
Compiler

Compiled 142 to 104 computations (26.8% saved)

localize75.0ms (0.9%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(*.f64 N (+.f64 N 1))
✓0.2b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 27 to 19 computations (29.6% saved)

series2.0ms (0%)

Counts
1 → 8
Calls

3 calls:

TimeVariablePointExpression
1.0ms
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))))

rewrite92.0ms (1.1%)

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)))))))))

simplify88.0ms (1%)

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)))

localize38.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (pow.f64 N 2))
✓0.0b
(+.f64 N (+.f64 1 (pow.f64 N 2)))
✓0.2b
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
Compiler

Compiled 28 to 21 computations (25% saved)

series3.0ms (0%)

Counts
3 → 13
Calls

9 calls:

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

rewrite72.0ms (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
0830
117724
2233724
Stop Event
1×node limit
Counts
3 → 81
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.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))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 N N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (*.f64 N N))) (/.f64 (pow.f64 N 4) (-.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 N N 1)) (pow.f64 (cbrt.f64 (fma.f64 N N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N 1)) 2) (cbrt.f64 (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 N) (hypot.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 N 6)) (/.f64 1 (+.f64 1 (-.f64 (pow.f64 N 4) (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 N 4)) (/.f64 1 (-.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (pow.f64 N 4) (*.f64 N N))) (+.f64 1 (pow.f64 N 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (*.f64 N N)) (-.f64 1 (pow.f64 N 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 N 6)) (+.f64 1 (-.f64 (pow.f64 N 4) (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 N 6)) (+.f64 (pow.f64 N 4) (-.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 N 4)) (-.f64 1 (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 N 6))) (neg.f64 (+.f64 1 (-.f64 (pow.f64 N 4) (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 N 4))) (neg.f64 (-.f64 1 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 N 4) 1) (-.f64 (*.f64 N N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 N N 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 N N 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 N) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 N N 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N N 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 N 4)) (pow.f64 (cbrt.f64 N) 2) 1)))))

simplify81.0ms (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
01296
13076
25876
316476
458776
5166076
6362076
7565376
8734076
Stop Event
1×node limit
Counts
94 → 90
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))
1
(pow.f64 N 2)
(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)
1
(pow.f64 N 2)
(*.f64 N N)
(pow.f64 N 2)
(*.f64 N N)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
✓0.1b
(cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))
✓0.6b
(pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)
2.9b
(+.f64 N (-.f64 1 N))
Compiler

Compiled 63 to 34 computations (46% saved)

series5.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
N
@0
(pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)
1.0ms
N
@inf
(pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)
1.0ms
N
@-inf
(pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)
0.0ms
N
@-inf
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
0.0ms
N
@0
(cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))

rewrite158.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
833×prod-diff_binary64
461×log-prod_binary64
403×fma-def_binary64
279×pow2_binary64
194×fma-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01154
124654
2304554
Stop Event
1×node limit
Counts
3 → 70
Calls
Call 1
Inputs
(pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)
(cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))) 2)) (log.f64 (cbrt.f64 (exp.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 +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)))) (log.f64 (sqrt.f64 (exp.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 -.f64 (exp.f64 (log1p.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) (pow.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 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(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) (*.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (*.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (pow.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 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3/2) (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) 1) (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.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)) (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.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))))) (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(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))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.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 log.f64 (+.f64 1 (expm1.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 cbrt.f64 (pow.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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 log1p.f64 (expm1.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 exp.f64 (*.f64 3 (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 (*.f64 3 (log.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 (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 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 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))) 3) 1/3)))) (#(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 (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 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 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 log1p.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 (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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3))))))
((#(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 (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 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 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))) 3) 1/3)))) (#(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 (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 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 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 log1p.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 (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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3))))))

simplify206.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
1274×sqr-pow_binary64
676×cube-prod_binary64
666×pow-sqr_binary64
560×fabs-mul_binary64
374×unpow3_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08432
121432
232432
350432
479432
5166432
6553432
71227432
81319432
91453432
101611432
111845432
122167432
132589432
143091432
153693432
164417432
174738432
185020432
195244432
205422432
215506432
226446432
237420432
247886432
Stop Event
1×node limit
Counts
106 → 51
Calls
Call 1
Inputs
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 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))
(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
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N 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 (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)))
(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)))

localize63.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
✓0.5b
(sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
✓0.6b
(pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)
2.9b
(+.f64 N (-.f64 1 N))
Compiler

Compiled 62 to 33 computations (46.8% saved)

series5.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
N
@inf
(pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)
1.0ms
N
@0
(pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)
1.0ms
N
@-inf
(pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)
0.0ms
N
@0
(sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
0.0ms
N
@-inf
(sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))

rewrite70.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
833×prod-diff_binary64
447×log-prod_binary64
404×fma-def_binary64
273×pow2_binary64
194×fma-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01136
124436
2299336
Stop Event
1×node limit
Counts
2 → 47
Calls
Call 1
Inputs
(pow.f64 (sqrt.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))))
Outputs
((#(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 (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 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 (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 (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 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (*.f64 (cbrt.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 (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 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1/4) (*.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1/4) (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 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1/4) 3) (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (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 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 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 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 log1p.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 (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))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.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 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) 2)) (log.f64 (cbrt.f64 (exp.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 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (log.f64 (sqrt.f64 (exp.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 (exp.f64 (log1p.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.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)))) 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)))) (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 (cbrt.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (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 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1/4) (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)) (sqrt.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 1 1/2) (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1/2)))) (#(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)))) 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))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.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 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.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))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.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 (sqrt.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)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1))))))

simplify55.0ms (0.7%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
07288
112288
218288
327288
435288
539288
651288
764288
869288
970288
Stop Event
1×saturated
Counts
71 → 51
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))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (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)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

localize38.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
✓0.3b
(exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3))
✓0.8b
(log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
2.9b
(+.f64 N (-.f64 1 N))
Compiler

Compiled 98 to 57 computations (41.8% saved)

series91.0ms (1.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
51.0ms
N
@0
(log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
20.0ms
N
@inf
(log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
17.0ms
N
@-inf
(log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
3.0ms
N
@-inf
(exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3))
1.0ms
N
@inf
(exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3))

rewrite75.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
833×prod-diff_binary64
566×log-prod_binary64
424×fma-def_binary64
225×expm1-udef_binary64
224×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01446
129636
2385736
Stop Event
1×node limit
Counts
2 → 55
Calls
Call 1
Inputs
(log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.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 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (*.f64 2 (log.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 (*.f64 2 (log.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (log.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 (log.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (log.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 (exp.f64 (log1p.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.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 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 3 (log.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 (*.f64 (log.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 1/3 (*.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3)) 2) (*.f64 (cbrt.f64 (*.f64 (log.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 (cbrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (pow.f64 (cbrt.f64 (log.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 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2) (cbrt.f64 (log.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 (*.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3)) (*.f64 (sqrt.f64 (*.f64 (log.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 (sqrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (log.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 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (log.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 (*.f64 1/3 (pow.f64 (cbrt.f64 (*.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3)) 2)) (cbrt.f64 (*.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/3 (sqrt.f64 (*.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3))) (sqrt.f64 (*.f64 (log.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 (log.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 (log.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 (log.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 (log.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 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.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 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.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 (log.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 (*.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (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 (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 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 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))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/3) (*.f64 (log.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 (E.f64) (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 3) (log.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(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 pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2)) (cbrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (sqrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(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 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 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 log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))

simplify23.0ms (0.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
07288
112288
218288
327288
435288
539288
651288
764288
869288
970288
Stop Event
1×saturated
Counts
79 → 59
Calls
Call 1
Inputs
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (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))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
Outputs
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(log.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)))

eval294.0ms (3.5%)

Compiler

Compiled 13391 to 8404 computations (37.2% saved)

prune95.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New62512637
Fresh000
Picked101
Done314
Total62913642
Error
0.2b
Counts
642 → 13
Alt Table
Click to see full alt table
StatusErrorProgram
28.1b
(atan2.f64 1 (*.f64 N N))
0.8b
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 2)
13.1b
(*.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (*.f64 (cbrt.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))))))
✓0.2b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶0.5b
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
▶21.9b
(atan2.f64 1 (+.f64 N (/.f64 (-.f64 (pow.f64 N 4) 1) (-.f64 (*.f64 N N) 1))))
1.8b
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
8.4b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3))
▶0.2b
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
▶29.5b
(atan2.f64 1 (+.f64 N 1))
▶30.1b
(atan2.f64 1 1)
1.6b
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)
1.6b
(exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))) 1/3))
Compiler

Compiled 320 to 230 computations (28.1% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 N (fma.f64 N N 1))
✓0.2b
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
Compiler

Compiled 21 to 12 computations (42.9% saved)

series2.0ms (0%)

Counts
2 → 16
Calls

6 calls:

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

rewrite71.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
642×pow1_binary64
596×add-log-exp_binary64
596×log1p-expm1-u_binary64
596×expm1-log1p-u_binary64
583×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0619
112219
2159019
Stop Event
1×node limit
Counts
2 → 49
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(+.f64 N (fma.f64 N N 1))
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 (sqrt.f64 (+.f64 N (fma.f64 N N 1))) (sqrt.f64 (+.f64 N (fma.f64 N N 1))))))) (#(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 (pow.f64 N 3) N))))))) (#(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 (fma.f64 N N 1) 2) (*.f64 N N)) (-.f64 (fma.f64 N N 1) 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 (sqrt.f64 (+.f64 N (fma.f64 N N 1))) 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 N) 2) (cbrt.f64 N) (fma.f64 N N 1))))) (#(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 (sqrt.f64 N) (sqrt.f64 N) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 N N 1)) (sqrt.f64 (fma.f64 N N 1)) N)))))

simplify89.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
993×fma-neg_binary64
532×unswap-sqr_binary64
469×distribute-rgt-neg-in_binary64
353×cancel-sign-sub-inv_binary64
307×neg-sub0_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
014127
135115
257115
3149115
4518115
51584115
63512115
75699115
87551115
Stop Event
1×node limit
Counts
65 → 60
Calls
Call 1
Inputs
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 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 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N (+.f64 N -1) 1))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N (+.f64 N -1) 1))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N (+.f64 N -1) 1))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N (+.f64 N -1) 1))
1
(+.f64 N 1)
(+.f64 1 N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(fma.f64 N (+.f64 N -1) 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(fma.f64 N (+.f64 N -1) 1)
(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 (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(fma.f64 N (+.f64 N -1) 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(fma.f64 N (+.f64 N -1) 1)
(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 (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(fma.f64 N (+.f64 N -1) 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(fma.f64 N (+.f64 N -1) 1)

localize4.0ms (0%)

Compiler

Compiled 5 to 5 computations (0% saved)

localize5.0ms (0.1%)

Compiler

Compiled 11 to 8 computations (27.3% saved)

localize26.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 N (/.f64 (-.f64 (pow.f64 N 4) 1) (-.f64 (*.f64 N N) 1)))
✓0.2b
(atan2.f64 1 (+.f64 N (/.f64 (-.f64 (pow.f64 N 4) 1) (-.f64 (*.f64 N N) 1))))
✓18.7b
(/.f64 (-.f64 (pow.f64 N 4) 1) (-.f64 (*.f64 N N) 1))
Compiler

Compiled 59 to 37 computations (37.3% saved)

series5.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

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

rewrite95.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
558×log-prod_binary64
510×fma-def_binary64
417×fma-neg_binary64
305×pow2_binary64
205×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01151
126124
2373924
Stop Event
1×node limit
Counts
3 → 182
Calls
Call 1
Inputs
(/.f64 (-.f64 (pow.f64 N 4) 1) (-.f64 (*.f64 N N) 1))
(atan2.f64 1 (+.f64 N (/.f64 (-.f64 (pow.f64 N 4) 1) (-.f64 (*.f64 N N) 1))))
(+.f64 N (/.f64 (-.f64 (pow.f64 N 4) 1) (-.f64 (*.f64 N 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 N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (neg.f64 (/.f64 1 (fma.f64 N N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 N N 1))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N 1)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 N N) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 1 (fma.f64 N N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 N 4) -1) (/.f64 1 (fma.f64 N N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 N N 1)) (pow.f64 (cbrt.f64 (fma.f64 N N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N 1)) 2) (cbrt.f64 (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 N 4) -1)) 2) (*.f64 (cbrt.f64 (+.f64 (pow.f64 N 4) -1)) (/.f64 1 (fma.f64 N N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 N) (hypot.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (pow.f64 N 4) -1)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 N 4) -1)) (/.f64 1 (fma.f64 N N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (neg.f64 (pow.f64 N 4)) 1) (/.f64 1 (neg.f64 (fma.f64 N N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 N N -1)) (+.f64 (pow.f64 N 4) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 N 4) -1)) 2) 1) (/.f64 (cbrt.f64 (+.f64 (pow.f64 N 4) -1)) (fma.f64 N N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 (pow.f64 N 4) -1)) 1) (/.f64 (sqrt.f64 (+.f64 (pow.f64 N 4) -1)) (fma.f64 N N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 N N -1)) 2)) (/.f64 (+.f64 (pow.f64 N 4) -1) (cbrt.f64 (fma.f64 N N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 N 4) -1)) 2) (pow.f64 (cbrt.f64 (fma.f64 N N -1)) 2)) (cbrt.f64 (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 (pow.f64 N 4) -1)) (pow.f64 (cbrt.f64 (fma.f64 N N -1)) 2)) (/.f64 (sqrt.f64 (+.f64 (pow.f64 N 4) -1)) (cbrt.f64 (fma.f64 N N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (fma.f64 N N -1))) (/.f64 (+.f64 (pow.f64 N 4) -1) (sqrt.f64 (fma.f64 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N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (+.f64 N 1)) (/.f64 (pow.f64 N 4) (+.f64 N -1)) (neg.f64 (-.f64 (/.f64 1 (fma.f64 N N -1)) N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 N 4) -1)) 2) (+.f64 N 1)) (/.f64 (cbrt.f64 (+.f64 (pow.f64 N 4) -1)) (+.f64 N -1)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 (pow.f64 N 4) -1)) (+.f64 N 1)) (/.f64 (sqrt.f64 (+.f64 (pow.f64 N 4) -1)) (+.f64 N -1)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (*.f64 N N) 1) (/.f64 (*.f64 N N) (fma.f64 N N -1)) (neg.f64 (-.f64 (/.f64 1 (fma.f64 N N -1)) N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 N 8)) 1) (/.f64 (cbrt.f64 (pow.f64 N 4)) (fma.f64 N N -1)) (neg.f64 (-.f64 (/.f64 1 (fma.f64 N N -1)) N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (*.f64 N N) (pow.f64 (cbrt.f64 (fma.f64 N N -1)) 2)) (/.f64 (*.f64 N N) (cbrt.f64 (fma.f64 N N 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simplify65.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
808×unswap-sqr_binary64
500×associate-*l*_binary64
450×associate-*r*_binary64
269×distribute-neg-frac_binary64
254×fma-def_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
022531
150449
2102449
3234449
41099449
55387449
Stop Event
1×node limit
Counts
218 → 195
Calls
Call 1
Inputs
1
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (pow.f64 N 2))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1)) (+.f64 (*.f64 -1 N) (/.f64 1 (-.f64 (pow.f64 N 2) 1)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1)) (+.f64 (*.f64 -1 N) (/.f64 1 (-.f64 (pow.f64 N 2) 1)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1)) (+.f64 (*.f64 -1 N) (/.f64 1 (-.f64 (pow.f64 N 2) 1)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1)) (+.f64 (*.f64 -1 N) (/.f64 1 (-.f64 (pow.f64 N 2) 1)))))
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
1
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (*.f64 N N))
(fma.f64 N N 1)
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (*.f64 N N))
(fma.f64 N N 1)
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (*.f64 N N))
(fma.f64 N N 1)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (*.f64 N N))
(fma.f64 N N 1)
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (*.f64 N N))
(fma.f64 N N 1)
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (*.f64 N N))
(fma.f64 N N 1)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (*.f64 N N))
(fma.f64 N N 1)
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (*.f64 N N))
(fma.f64 N N 1)
(+.f64 1 (pow.f64 N 2))
(+.f64 1 (*.f64 N N))
(fma.f64 N N 1)
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (+.f64 N (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1))) (/.f64 1 (-.f64 (pow.f64 N 2) 1))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1)) (+.f64 (*.f64 -1 N) (/.f64 1 (-.f64 (pow.f64 N 2) 1)))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1)) (+.f64 (*.f64 -1 N) (/.f64 1 (-.f64 (pow.f64 N 2) 1)))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1)) (+.f64 (*.f64 -1 N) (/.f64 1 (-.f64 (pow.f64 N 2) 1)))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (pow.f64 N 2) 1)) (+.f64 (*.f64 -1 N) (/.f64 1 (-.f64 (pow.f64 N 2) 1)))))
(atan2.f64 1 (+.f64 N (-.f64 (/.f64 (pow.f64 N 4) (+.f64 (*.f64 N N) -1)) (/.f64 1 (+.f64 (*.f64 N N) -1)))))
(atan2.f64 1 (+.f64 N (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (/.f64 -1 (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 (+.f64 N (/.f64 (pow.f64 N 4) (fma.f64 N N -1))) (/.f64 -1 (fma.f64 N N -1))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N -1)) (+.f64 N (/.f64 -1 (fma.f64 N N -1)))))
1
(+.f64 N 1)
(+.f64 1 N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.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 (+.f64 1 N) (*.f64 N N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.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 (+.f64 1 N) (*.f64 N N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 1 (fma.f64 N N N))

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 N (fma.f64 N N 1))
✓0.2b
(pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3)
✓0.2b
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
✓15.1b
(cbrt.f64 (+.f64 N (fma.f64 N N 1)))
Compiler

Compiled 41 to 26 computations (36.6% saved)

series7.0ms (0.1%)

Counts
3 → 20
Calls

9 calls:

TimeVariablePointExpression
3.0ms
N
@inf
(pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3)
1.0ms
N
@0
(pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3)
1.0ms
N
@-inf
(pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3)
1.0ms
N
@inf
(cbrt.f64 (+.f64 N (fma.f64 N N 1)))
1.0ms
N
@0
(cbrt.f64 (+.f64 N (fma.f64 N N 1)))

rewrite67.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
803×pow1_binary64
754×add-log-exp_binary64
753×log1p-expm1-u_binary64
753×expm1-log1p-u_binary64
736×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0929
119029
2207429
Stop Event
1×node limit
Counts
3 → 77
Calls
Call 1
Inputs
(cbrt.f64 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))) (pow.f64 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))) 2) (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/6) (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 N (fma.f64 N N 1))) 1/3) (pow.f64 (sqrt.f64 (+.f64 N (fma.f64 N N 1))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N 1) 2))) (cbrt.f64 (-.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3))) (cbrt.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 pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))))))))
((#(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 N (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 N N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) (+.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 N (*.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 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))) 2) (*.f64 (cbrt.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 (sqrt.f64 (+.f64 N (fma.f64 N N 1))) (sqrt.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/6) (*.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/6) (pow.f64 (cbrt.f64 (+.f64 N (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)) (/.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 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))) 2) 3) (cbrt.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/6) 3) (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 2) 1) (cbrt.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))) 2)) (cbrt.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 2) (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/6)) (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/6))))) (#(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 (pow.f64 N 3) N))))))) (#(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 (fma.f64 N N 1) 2) (*.f64 N N)) (-.f64 (fma.f64 N N 1) N))))) (#(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 (cbrt.f64 (*.f64 N N)) (cbrt.f64 N) (fma.f64 N N 1))))) (#(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 (sqrt.f64 N) (sqrt.f64 N) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 N N 1)) (sqrt.f64 (fma.f64 N N 1)) N)))))

simplify82.0ms (1%)

Algorithm
1×egg-herbie
Rules
514×unsub-neg_binary64
393×fma-def_binary64
378×associate-*l*_binary64
343×unswap-sqr_binary64
327×neg-sub0_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033252
195190
2218190
3637184
42566184
55622184
67621184
Stop Event
1×node limit
Counts
97 → 91
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/3 N) 1)
(+.f64 (*.f64 1/3 N) (+.f64 (*.f64 2/9 (pow.f64 N 2)) 1))
(+.f64 (*.f64 1/3 N) (+.f64 (*.f64 2/9 (pow.f64 N 2)) (+.f64 1 (*.f64 -13/81 (pow.f64 N 3)))))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)) 1/3) 3))
1
(+.f64 N 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
Outputs
1
(+.f64 (*.f64 1/3 N) 1)
(fma.f64 1/3 N 1)
(+.f64 (*.f64 1/3 N) (+.f64 (*.f64 2/9 (pow.f64 N 2)) 1))
(fma.f64 1/3 N (fma.f64 2/9 (*.f64 N N) 1))
(fma.f64 N (*.f64 N 2/9) (fma.f64 1/3 N 1))
(fma.f64 N (fma.f64 N 2/9 1/3) 1)
(+.f64 (*.f64 1/3 N) (+.f64 (*.f64 2/9 (pow.f64 N 2)) (+.f64 1 (*.f64 -13/81 (pow.f64 N 3)))))
(fma.f64 1/3 N (+.f64 (fma.f64 2/9 (*.f64 N N) 1) (*.f64 -13/81 (pow.f64 N 3))))
(fma.f64 1/3 N (fma.f64 2/9 (*.f64 N N) (fma.f64 -13/81 (pow.f64 N 3) 1)))
(fma.f64 1/3 N (fma.f64 N (*.f64 N 2/9) (fma.f64 -13/81 (pow.f64 N 3) 1)))
(fma.f64 N (fma.f64 N 2/9 1/3) (fma.f64 -13/81 (pow.f64 N 3) 1))
(fma.f64 (*.f64 N N) (fma.f64 N -13/81 2/9) (fma.f64 1/3 N 1))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(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 (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))

eval171.0ms (2%)

Compiler

Compiled 6412 to 4484 computations (30.1% saved)

prune57.0ms (0.7%)

Pruning

13 alts after pruning (9 fresh and 4 done)

PrunedKeptTotal
New3844388
Fresh257
Picked101
Done145
Total38813401
Error
0.2b
Counts
401 → 13
Alt Table
Click to see full alt table
StatusErrorProgram
28.3b
(atan2.f64 1 (pow.f64 (cbrt.f64 (*.f64 N N)) 3))
✓21.9b
(atan2.f64 1 (+.f64 N (/.f64 (-.f64 (pow.f64 N 4) 1) (-.f64 (*.f64 N N) 1))))
28.1b
(atan2.f64 1 (*.f64 N N))
0.8b
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 2)
13.1b
(*.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (*.f64 (cbrt.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))))))
✓0.2b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.2b
(atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 1 N)))
✓29.5b
(atan2.f64 1 (+.f64 N 1))
1.6b
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)
27.6b
(atan2.f64 1 (+.f64 N (*.f64 N N)))
8.4b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3))
✓30.1b
(atan2.f64 1 1)
1.6b
(exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))) 1/3))
Compiler

Compiled 163 to 117 computations (28.2% saved)

regimes34.0ms (0.4%)

Counts
28 → 1
Calls
Call 1
Inputs
(atan2.f64 1 1)
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N (*.f64 N 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 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (/.f64 (-.f64 (pow.f64 N 4) 1) (-.f64 (*.f64 N N) 1))))
(atan2.f64 1 (pow.f64 (cbrt.f64 (*.f64 N N)) 3))
(log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(-.f64 (expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 2)
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3))
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)
(exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))) 1/3))
(cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))
(pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)
(exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3))
(+.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)))
(*.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (*.f64 (cbrt.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))))))
Outputs
(atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 1 N)))
Calls

3 calls:

13.0ms
N
7.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Results
ErrorSegmentsBranch
0.2b1N
0.2b1(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.2b1(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 339 to 221 computations (34.8% saved)

regimes6.0ms (0.1%)

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

1 calls:

5.0ms
N
Results
ErrorSegmentsBranch
1.8b1N
Compiler

Compiled 30 to 19 computations (36.7% saved)

regimes13.0ms (0.2%)

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

1 calls:

12.0ms
N
Results
ErrorSegmentsBranch
1.1b3N
Compiler

Compiled 23 to 15 computations (34.8% saved)

bsearch53.0ms (0.6%)

Algorithm
2×binary-search
Steps
TimeLeftRight
24.0ms
0.738899494268031
27433382.816363614
29.0ms
-260541.50953744358
-1.1221111430368413e-13
Compiler

Compiled 12 to 9 computations (25% saved)

regimes12.0ms (0.1%)

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

1 calls:

10.0ms
N
Results
ErrorSegmentsBranch
1.6b3N
Compiler

Compiled 16 to 12 computations (25% saved)

bsearch51.0ms (0.6%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
0.738899494268031
27433382.816363614
28.0ms
-260541.50953744358
-1.1221111430368413e-13
Compiler

Compiled 12 to 9 computations (25% saved)

regimes11.0ms (0.1%)

Accuracy

Total -54.6b remaining (-2978.9%)

Threshold costs -54.6b (-2978.9%)

Counts
2 → 3
Calls
Call 1
Inputs
(atan2.f64 1 1)
(atan2.f64 1 (*.f64 N N))
Outputs
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 1)
(atan2.f64 1 (*.f64 N N))
Calls

1 calls:

10.0ms
N
Results
ErrorSegmentsBranch
1.8b3N
Compiler

Compiled 11 to 8 computations (27.3% saved)

bsearch52.0ms (0.6%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
0.738899494268031
27433382.816363614
29.0ms
-260541.50953744358
-1.1221111430368413e-13
Compiler

Compiled 12 to 9 computations (25% saved)

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
026129
132129
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(if (<=.f64 N -4476069050855169/17179869184) (atan2.f64 1 (+.f64 N (*.f64 N N))) (if (<=.f64 N 6655414974099505/9007199254740992) (atan2.f64 1 (+.f64 N 1)) (atan2.f64 1 (+.f64 N (*.f64 N N)))))
(if (<=.f64 N -4476069050855169/17179869184) (atan2.f64 1 (*.f64 N N)) (if (<=.f64 N 6655414974099505/9007199254740992) (atan2.f64 1 (+.f64 N 1)) (atan2.f64 1 (*.f64 N N))))
(if (<=.f64 N -4476069050855169/17179869184) (atan2.f64 1 (*.f64 N N)) (if (<=.f64 N 6655414974099505/9007199254740992) (atan2.f64 1 1) (atan2.f64 1 (*.f64 N N))))
(atan2.f64 1 1)
Outputs
(atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(if (<=.f64 N -4476069050855169/17179869184) (atan2.f64 1 (+.f64 N (*.f64 N N))) (if (<=.f64 N 6655414974099505/9007199254740992) (atan2.f64 1 (+.f64 N 1)) (atan2.f64 1 (+.f64 N (*.f64 N N)))))
(if (<=.f64 N -4476069050855169/17179869184) (atan2.f64 1 (+.f64 N (*.f64 N N))) (if (<=.f64 N 6655414974099505/9007199254740992) (atan2.f64 1 (+.f64 1 N)) (atan2.f64 1 (+.f64 N (*.f64 N N)))))
(if (<=.f64 N -4476069050855169/17179869184) (atan2.f64 1 (*.f64 N N)) (if (<=.f64 N 6655414974099505/9007199254740992) (atan2.f64 1 (+.f64 N 1)) (atan2.f64 1 (*.f64 N N))))
(if (<=.f64 N -4476069050855169/17179869184) (atan2.f64 1 (*.f64 N N)) (if (<=.f64 N 6655414974099505/9007199254740992) (atan2.f64 1 (+.f64 1 N)) (atan2.f64 1 (*.f64 N N))))
(if (<=.f64 N -4476069050855169/17179869184) (atan2.f64 1 (*.f64 N N)) (if (<=.f64 N 6655414974099505/9007199254740992) (atan2.f64 1 1) (atan2.f64 1 (*.f64 N N))))
(atan2.f64 1 1)
Compiler

Compiled 96 to 65 computations (32.3% saved)

soundness0.0ms (0%)

end60.0ms (0.7%)

Compiler

Compiled 91 to 56 computations (38.5% saved)

Profiling

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