Details

Time bar (total: 7.1s)

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)

sample2.6s (36.5%)

Results
1.2s2124×body2048valid
695.0ms4552×body256valid
538.0ms1066×body1024valid
147.0ms514×body512valid

preprocess25.0ms (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)

simplify13.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

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

eval0.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
15.2b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶15.2b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 8 to 6 computations (25% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(atan.f64 (+.f64 N 1))
✓1.0b
(-.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
@0
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms
N
@-inf
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms
N
@inf
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms
N
@-inf
(atan.f64 (+.f64 N 1))
0.0ms
N
@0
(atan.f64 (+.f64 N 1))

rewrite100.0ms (1.4%)

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 (0.4%)

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))

eval49.0ms (0.7%)

Compiler

Compiled 786 to 518 computations (34.1% saved)

prune9.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New53356
Fresh000
Picked011
Done000
Total53457
Error
13.9b
Counts
57 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶28.0b
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
▶14.1b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓15.2b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶29.2b
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
Compiler

Compiled 44 to 34 computations (22.7% saved)

localize24.0ms (0.3%)

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

Compiled 36 to 27 computations (25% saved)

series4.0ms (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
@0
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
0.0ms
N
@inf
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))

rewrite81.0ms (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))))))

simplify179.0ms (2.5%)

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))

localize25.0ms (0.4%)

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)))
✓27.6b
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
Compiler

Compiled 35 to 26 computations (25.7% saved)

series12.0ms (0.2%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
4.0ms
N
@-inf
(-.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))
3.0ms
N
@0
(-.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)))

rewrite81.0ms (1.1%)

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))))))

simplify202.0ms (2.9%)

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))

localize47.0ms (0.7%)

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))))
✓2.7b
(+.f64 N (-.f64 1 N))
Compiler

Compiled 39 to 26 computations (33.3% saved)

series3.0ms (0%)

Counts
3 → 36
Calls

9 calls:

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

rewrite88.0ms (1.2%)

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
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 N (-.f64 1 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 N N) (+.f64 (+.f64 N -1) N)) (/.f64 (pow.f64 (-.f64 1 N) 2) (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 N (-.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 N (-.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (cbrt.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) (sqrt.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (/.f64 1 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2)) (/.f64 1 (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)) (-.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N)) (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 N -1) N) (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (+.f64 (pow.f64 (-.f64 1 N) 2) (-.f64 (*.f64 N N) (*.f64 N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2)) (+.f64 (+.f64 N -1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3))) (neg.f64 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2))) (neg.f64 (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 N 1) 3) (pow.f64 N 3)) (+.f64 (pow.f64 (+.f64 N 1) 2) (fma.f64 N N (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 N 1) 2) (*.f64 N N)) (+.f64 (+.f64 N 1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 1 N) 2) (*.f64 N N)) (-.f64 (-.f64 1 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 N (-.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 N (-.f64 1 N)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 N (-.f64 1 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N)) (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (+.f64 N -1) N) (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 N (-.f64 1 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (+.f64 N 1)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (exp.f64 (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 N) (+.f64 1 (expm1.f64 (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (+.f64 1 (expm1.f64 (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 N))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (-.f64 1 N)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 N))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 N 1)) (exp.f64 (neg.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (exp.f64 (neg.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (/.f64 1 (exp.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 N (-.f64 1 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (-.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (-.f64 N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log1p.f64 (-.f64 N N))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (-.f64 N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (-.f64 N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N 1 (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 N (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 N (-.f64 1 N)) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 N (-.f64 1 N)) (fma.f64 (neg.f64 (cbrt.f64 N)) (cbrt.f64 (*.f64 N N)) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 N (-.f64 1 N)) (fma.f64 -1 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 N 1) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 N) 1 N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 N (-.f64 1 N)) 1 (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 N (-.f64 1 N)) 1 (fma.f64 (neg.f64 (cbrt.f64 N)) (cbrt.f64 (*.f64 N N)) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 N (-.f64 1 N)) 1 (fma.f64 -1 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 N 1) 1 (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (fma.f64 (neg.f64 (cbrt.f64 N)) (cbrt.f64 (*.f64 N N)) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (fma.f64 -1 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (cbrt.f64 (+.f64 N (-.f64 1 N))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (cbrt.f64 (+.f64 N (-.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 N)) (cbrt.f64 (*.f64 N N)) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (cbrt.f64 (+.f64 N (-.f64 1 N))) (fma.f64 -1 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 N) (cbrt.f64 (*.f64 N N)) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (cbrt.f64 N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (*.f64 (cbrt.f64 N) 1) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 N 1)) (pow.f64 (cbrt.f64 (+.f64 N 1)) 2) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 N 1)) 2) (cbrt.f64 (+.f64 N 1)) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 1 N)) (pow.f64 (cbrt.f64 (-.f64 1 N)) 2) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 N)) 2) (cbrt.f64 (-.f64 1 N)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) (sqrt.f64 (+.f64 N (-.f64 1 N))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) (sqrt.f64 (+.f64 N (-.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 N)) (cbrt.f64 (*.f64 N N)) N))))) (#(struct:change #<rule egg-rr> (2) 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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 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(*.f64 (exp.f64 N) (exp.f64 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (exp.f64 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 N N)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 N (sqrt.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x 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(*.f64 N N)) (cbrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (*.f64 (cbrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (*.f64 (cbrt.f64 N) 1) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (sqrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (pow.f64 N 3/2) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) 1) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3)) (/.f64 1 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) 1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (-.f64 1 (fma.f64 N N N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 N) N) (cbrt.f64 (*.f64 N N)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))))

simplify87.0ms (1.2%)

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)

eval418.0ms (5.9%)

Compiler

Compiled 9864 to 6484 computations (34.3% saved)

prune108.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New5733576
Fresh000
Picked101
Done303
Total5773580
Error
0.5b
Counts
580 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
▶27.2b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
▶0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶14.1b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))))
Compiler

Compiled 51 to 35 computations (31.4% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiled 27 to 19 computations (29.6% saved)

series1.0ms (0%)

Counts
1 → 8
Calls

3 calls:

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

rewrite89.0ms (1.3%)

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)))))))))

simplify113.0ms (1.6%)

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)))

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))))
✓0.0b
(*.f64 (fma.f64 N N -1) N)
2.7b
(+.f64 N (-.f64 1 N))
✓5.3b
(/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))
Compiler

Compiled 65 to 41 computations (36.9% saved)

series7.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
3.0ms
N
@0
(/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))
1.0ms
N
@inf
(/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))
1.0ms
N
@-inf
(/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))
0.0ms
N
@-inf
(*.f64 (fma.f64 N N -1) N)
0.0ms
N
@inf
(*.f64 (fma.f64 N N -1) N)

rewrite90.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
654×log-prod_binary64
575×fma-def_binary64
305×fma-neg_binary64
237×expm1-udef_binary64
236×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01248
127330
2413030
Stop Event
1×node limit
Counts
3 → 126
Calls
Call 1
Inputs
(/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))
(*.f64 (fma.f64 N N -1) N)
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N))) (cbrt.f64 (exp.f64 (fma.f64 N N N))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (fma.f64 N N N) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (*.f64 (fma.f64 N N -1) (/.f64 -1 (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N -1) (/.f64 1 (/.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N -1) (*.f64 N (/.f64 -1 (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 N (fma.f64 N N -1)) (/.f64 -1 (-.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 N (fma.f64 N N -1))) 2) (*.f64 (cbrt.f64 (*.f64 N (fma.f64 N N -1))) (/.f64 -1 (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 N N N)) (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 N (fma.f64 N N -1))) (*.f64 (sqrt.f64 (*.f64 N (fma.f64 N N -1))) (/.f64 -1 (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 N (neg.f64 (fma.f64 N N -1))) (/.f64 1 (-.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (-.f64 1 N)) (*.f64 N (fma.f64 N N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 N 1) (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 N N -1) 1) (/.f64 N (+.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 N (fma.f64 N N -1))) 2) 1) (/.f64 (cbrt.f64 (*.f64 N (fma.f64 N N -1))) (+.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 N (fma.f64 N N -1))) 1) (/.f64 (sqrt.f64 (*.f64 N (fma.f64 N N -1))) (+.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 N (pow.f64 (cbrt.f64 (+.f64 N -1)) 2)) (/.f64 (fma.f64 N N -1) (cbrt.f64 (+.f64 N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 N N -1) (pow.f64 (cbrt.f64 (+.f64 N -1)) 2)) (/.f64 N (cbrt.f64 (+.f64 N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 N -1)) 2)) (/.f64 (*.f64 N (fma.f64 N N -1)) (cbrt.f64 (+.f64 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 (+.f64 N -1)) 2)) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 N (fma.f64 N N -1))) (pow.f64 (cbrt.f64 (+.f64 N -1)) 2)) (/.f64 (sqrt.f64 (*.f64 N (fma.f64 N N -1))) (cbrt.f64 (+.f64 N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 N (sqrt.f64 (+.f64 N -1))) (/.f64 (fma.f64 N N -1) (sqrt.f64 (+.f64 N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 N N -1) (sqrt.f64 (+.f64 N -1))) (/.f64 N (sqrt.f64 (+.f64 N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 N -1))) (/.f64 (*.f64 N (fma.f64 N N -1)) (sqrt.f64 (+.f64 N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 N (fma.f64 N N -1))) 2) (sqrt.f64 (+.f64 N -1))) (/.f64 (cbrt.f64 (*.f64 N (fma.f64 N N -1))) (sqrt.f64 (+.f64 N -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 -1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 N (fma.f64 N N -1)) (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 (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 pow.f64 (/.f64 1 (fma.f64 N N N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 1 (fma.f64 N N N)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 1 N)))))) (#(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)) (exp.f64 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 fma.f64 N N N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N 1 (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (fma.f64 N N N) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (fma.f64 N N N) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) (pow.f64 (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) 2) (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 N) (pow.f64 (cbrt.f64 N) 2) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (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) (*.f64 (sqrt.f64 N) 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 (pow.f64 (cbrt.f64 N) 2) (pow.f64 (cbrt.f64 N) 2)) (pow.f64 (cbrt.f64 N) 2) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (sqrt.f64 N)) (sqrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) N)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 N (fma.f64 N N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 N 3) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 N) (fma.f64 N N -1))) (cbrt.f64 (pow.f64 (exp.f64 N) (fma.f64 N N -1))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 N) (fma.f64 N N -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 N) (fma.f64 N N -1)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 N) (fma.f64 N N -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 N (fma.f64 N N -1)))) 1)))) (#(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 (pow.f64 (exp.f64 N) (fma.f64 N N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 N (fma.f64 N N -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (pow.f64 N 3)) (exp.f64 (neg.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (pow.f64 N 3)) (/.f64 1 (exp.f64 N))))))) (#(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 cbrt.f64 (*.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 N N -1) 3) (pow.f64 N 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 exp.f64 (*.f64 (log.f64 (*.f64 N (fma.f64 N N -1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N (*.f64 N N) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 N 3) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N N) N (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (sqrt.f64 N)) (*.f64 N (sqrt.f64 N)) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 N 3)) (sqrt.f64 (pow.f64 N 3)) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 N N) 1) N (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (pow.f64 N 3/2) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 N N) (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 N N) (sqrt.f64 N)) (sqrt.f64 N) (neg.f64 N))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)))) (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)))))) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))) (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))) 2) (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))) (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 (fma.f64 N N N) 1))) 1))))))

simplify130.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
747×associate-/l*_binary64
485×associate-/r*_binary64
423×fma-def_binary64
416×distribute-rgt-in_binary64
391×distribute-lft-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
022395
155356
2108344
3311344
41592260
Stop Event
1×node limit
Counts
162 → 138
Calls
Call 1
Inputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(*.f64 -1 N)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(pow.f64 N 3)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(pow.f64 N 3)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
Outputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(*.f64 -1 N)
(neg.f64 N)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(fma.f64 -1 N (pow.f64 N 3))
(-.f64 (pow.f64 N 3) N)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(fma.f64 -1 N (pow.f64 N 3))
(-.f64 (pow.f64 N 3) N)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(fma.f64 -1 N (pow.f64 N 3))
(-.f64 (pow.f64 N 3) N)
(pow.f64 N 3)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(fma.f64 -1 N (pow.f64 N 3))
(-.f64 (pow.f64 N 3) N)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(fma.f64 -1 N (pow.f64 N 3))
(-.f64 (pow.f64 N 3) N)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(fma.f64 -1 N (pow.f64 N 3))
(-.f64 (pow.f64 N 3) N)
(pow.f64 N 3)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(fma.f64 -1 N (pow.f64 N 3))
(-.f64 (pow.f64 N 3) N)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(fma.f64 -1 N (pow.f64 N 3))
(-.f64 (pow.f64 N 3) N)
(+.f64 (*.f64 -1 N) (pow.f64 N 3))
(fma.f64 -1 N (pow.f64 N 3))
(-.f64 (pow.f64 N 3) N)
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (+.f64 N -1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (+.f64 N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (+.f64 N -1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

localize63.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
2.7b
(+.f64 N (-.f64 1 N))
✓10.8b
(-.f64 (pow.f64 N 4) (*.f64 N N))
✓33.5b
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
Compiler

Compiled 81 to 36 computations (55.6% saved)

series5.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

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

rewrite119.0ms (1.7%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01460
133030
2521430
Stop Event
1×node limit
Counts
3 → 286
Calls
Call 1
Inputs
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N)) (neg.f64 (/.f64 N (/.f64 (fma.f64 N N N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (fma.f64 N N N) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N)) (/.f64 N (/.f64 (fma.f64 N N N) N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 N N 0) N)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (+.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) 2) (/.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) (*.f64 (fma.f64 N N N) (/.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 N N N)) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (neg.f64 (cbrt.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (pow.f64 N 8) (pow.f64 N 4))) (*.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (neg.f64 (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 N N N)) (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 N 8) (pow.f64 N 4)))) (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (/.f64 (pow.f64 (fma.f64 N N N) 2) (cbrt.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 N (sqrt.f64 N))) (/.f64 (pow.f64 (fma.f64 N N N) 2) (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 N 8) (pow.f64 N 4))) 1) (/.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 N 8) (pow.f64 N 4))) (hypot.f64 N (sqrt.f64 N))) (/.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 N N N) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (/.f64 (fma.f64 N N N) (cbrt.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 N N N) 1) (/.f64 (fma.f64 N N N) (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 N) (sqrt.f64 (+.f64 N 1))) (*.f64 (sqrt.f64 N) (sqrt.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (hypot.f64 N (sqrt.f64 N))) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 N (pow.f64 (cbrt.f64 (+.f64 N 1)) 2)) (cbrt.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 N (sqrt.f64 (+.f64 N 1))) (sqrt.f64 (+.f64 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 (fma.f64 N N N) 1)))) (#(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 pow.f64 (/.f64 1 (fma.f64 N N N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (fma.f64 N N N))))) (#(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 1 (exp.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (+.f64 1 (expm1.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (/.f64 1 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (pow.f64 (exp.f64 N) N) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (/.f64 1 (pow.f64 (exp.f64 N) N)) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (pow.f64 (exp.f64 N) N) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (/.f64 1 (pow.f64 (exp.f64 N) N)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 N) (pow.f64 (exp.f64 N) N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (pow.f64 (exp.f64 N) N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 N) (+.f64 1 (expm1.f64 (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (+.f64 1 (expm1.f64 (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 N) (/.f64 1 (pow.f64 (exp.f64 N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (/.f64 1 (pow.f64 (exp.f64 N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (pow.f64 (exp.f64 N) N)) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 N) N) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule 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simplify52.0ms (0.7%)

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

Useful iterations: 4 (0.0ms)

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

eval422.0ms (6%)

Compiler

Compiled 16725 to 9302 computations (44.4% saved)

prune257.0ms (3.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New7117718
Fresh000
Picked101
Done112
Total7138721
Error
0.5b
Counts
721 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
▶5.8b
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))))
20.7b
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
▶1.1b
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
▶2.2b
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
▶20.7b
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
29.9b
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) N)))
✓0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶28.5b
(atan2.f64 1 (+.f64 1 N))
Compiler

Compiled 190 to 140 computations (26.3% saved)

localize51.0ms (0.7%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.5b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓0.6b
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
✓12.3b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
Compiler

Compiled 42 to 22 computations (47.6% saved)

series7.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

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

rewrite178.0ms (2.5%)

Algorithm
1×batch-egg-rewrite
Rules
735×pow1_binary64
684×add-log-exp_binary64
683×log1p-expm1-u_binary64
683×expm1-log1p-u_binary64
669×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0935
118635
2192435
Stop Event
1×node limit
Counts
3 → 58
Calls
Call 1
Inputs
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.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)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (pow.f64 (atan2.f64 1 (+.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 1 (+.f64 1 (fma.f64 N N N)))) 2)) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) 1/2) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.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))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.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))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (*.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4)) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (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 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (*.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4)) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (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 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2) 1/2)))) (#(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 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)))))))))

simplify61.0ms (0.9%)

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
07420
112420
218420
327420
435420
539420
651420
764420
869420
970420
Stop Event
1×saturated
Counts
94 → 45
Calls
Call 1
Inputs
(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)))
(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
(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))))
(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)))

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 11 to 8 computations (27.3% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite43.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
495×pow1_binary64
482×add-sqr-sqrt_binary64
460×add-log-exp_binary64
460×log1p-expm1-u_binary64
460×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11017
212437
Stop Event
1×node limit
Counts
1 → 16
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 N))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 N))) (sqrt.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 N))))))))

simplify50.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
13×fma-def_binary64
11×fma-neg_binary64
7×cancel-sign-sub-inv_binary64
6×associate--r+_binary64
6×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0984
11984
22584
34884
46784
59784
611284
711684
Stop Event
1×saturated
Counts
28 → 19
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
Outputs
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 N))

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 18 to 9 computations (50% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite43.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
563×pow1_binary64
525×add-log-exp_binary64
524×log1p-expm1-u_binary64
524×expm1-log1p-u_binary64
513×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0610
11218
214828
Stop Event
1×node limit
Counts
1 → 16
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (fma.f64 N N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2) (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))) (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (fma.f64 N N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (fma.f64 N N 1))))))))

simplify161.0ms (2.3%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
07120
11496
22196
33296
46196
516096
658196
7144996
8163396
9181796
10202596
11231896
12271396
13319696
14376296
15444896
16528396
17568196
18597196
19625196
20632596
21636196
22730296
Stop Event
1×node limit
Counts
28 → 18
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
Outputs
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))

localize77.0ms (1.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (fma.f64 N N -1) N)
✓0.5b
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))))
5.3b
(/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))
Compiler

Compiled 53 to 34 computations (35.8% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite167.0ms (2.4%)

Algorithm
1×batch-egg-rewrite
Rules
562×prod-diff_binary64
523×log-prod_binary64
335×pow-prod-down_binary64
323×fma-def_binary64
278×pow2_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01020
121413
2298111
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))) (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))) 2) (cbrt.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))) (sqrt.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan2.f64 1 (fma.f64 (+.f64 N 1) N 1))) 1))))))

simplify46.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
734×div-sub_binary64
611×fma-neg_binary64
469×associate-/l/_binary64
397×associate-/r/_binary64
374×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
016240
136240
272216
3209216
4838132
53152132
Stop Event
1×node limit
Counts
34 → 25
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
Outputs
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 N (fma.f64 N N -1)) (-.f64 N 1))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 -1 (/.f64 (*.f64 N (fma.f64 N N -1)) (+.f64 1 (*.f64 -1 N))))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 N 1) (fma.f64 N N -1)))))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (-.f64 N 1)) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (fma.f64 (fma.f64 N N -1) (/.f64 N (-.f64 N 1)) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

localize26.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.5b
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
10.8b
(-.f64 (pow.f64 N 4) (*.f64 N N))
33.5b
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
Compiler

Compiled 69 to 29 computations (58% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite57.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
506×fma-def_binary64
469×log-prod_binary64
339×fma-neg_binary64
256×pow2_binary64
206×pow-unpow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01225
127111
2403011
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 1 (+.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 1 (+.f64 1 (fma.f64 N N N))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (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)))) (cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.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))) 2) 1/2)))) (#(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 log.f64 (+.f64 1 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1))))))

simplify49.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
665×associate-/r*_binary64
532×div-sub_binary64
488×fma-def_binary64
439×associate-*l*_binary64
340×associate-*r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
022408
149408
280408
3205300
41170216
57352216
Stop Event
1×node limit
Counts
34 → 25
Calls
Call 1
Inputs
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
Outputs
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))) (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (*.f64 N (+.f64 N -1))) (/.f64 N (/.f64 (*.f64 N (+.f64 N -1)) N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N))) (*.f64 (/.f64 N (-.f64 (*.f64 N N) N)) N)))
(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 N (*.f64 1 (+.f64 N -1))) (+.f64 (*.f64 N N) -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))

eval195.0ms (2.8%)

Compiler

Compiled 9268 to 5317 computations (42.6% saved)

prune123.0ms (1.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New5176523
Fresh202
Picked101
Done235
Total5229531
Error
0.5b
Counts
531 → 9
Alt Table
Click to see full alt table
StatusErrorProgram
0.6b
(atan2.f64 1 (+.f64 1 (*.f64 (fma.f64 N N -1) (*.f64 N (/.f64 -1 (-.f64 1 N))))))
✓28.5b
(atan2.f64 1 (+.f64 1 N))
29.9b
(atan2.f64 1 (+.f64 1 (*.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) (+.f64 N 1)))))
2.7b
(pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2)
7.1b
(atan2.f64 1 (+.f64 1 (/.f64 (pow.f64 N 3) (+.f64 N -1))))
✓2.2b
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
1.1b
(*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
22.1b
(atan2.f64 1 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))))
✓0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 123 to 91 computations (26% saved)

regimes22.0ms (0.3%)

Counts
20 → 1
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 1 (*.f64 N 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 1 (/.f64 (pow.f64 N 3) (+.f64 N -1))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))))
(atan2.f64 1 (+.f64 1 (*.f64 (fma.f64 N N -1) (*.f64 N (/.f64 -1 (-.f64 1 N))))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (*.f64 (fma.f64 N N -1) N) (+.f64 N -1))))
(atan2.f64 1 (+.f64 1 (*.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) (+.f64 N 1)))))
(atan2.f64 1 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
(pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2)
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) N)))
(*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
Outputs
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Calls

2 calls:

12.0ms
N
3.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Results
ErrorSegmentsBranch
0.5b1N
0.5b1(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 275 to 185 computations (32.7% saved)

regimes75.0ms (1.1%)

Accuracy

Total -26.6b remaining (-1212.9%)

Threshold costs -26.6b (-1212.9%)

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

1 calls:

74.0ms
N
Results
ErrorSegmentsBranch
2.2b1N
Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify7.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01230
11830
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (+.f64 1 N))
Outputs
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (+.f64 1 N))
Compiler

Compiled 24 to 19 computations (20.8% saved)

soundness0.0ms (0%)

end55.0ms (0.8%)

Compiler

Compiled 22 to 17 computations (22.7% saved)

Profiling

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