Details

analyze538.0ms (5.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	37.5%	12.6%	7
50%	37.5%	12.6%	8
50%	31.2%	18.8%	9
50%	31.2%	18.8%	10
50%	28.1%	22%	11
50%	28.1%	22%	12
50%	26.5%	23.5%	13
50%	26.5%	23.5%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample112.0ms (1.1%)

Algorithm

1×

intervals

Results

32.0ms	64×	body	1024	valid
25.0ms	66×	body	1024	invalid
12.0ms	147×	body	128	valid
8.0ms	29×	body	512	valid
7.0ms	28×	body	512	invalid
4.0ms	22×	body	256	invalid
3.0ms	16×	body	256	valid
2.0ms	19×	body	128	invalid

Compiler

Compiled 23 to 23 computations (0% saved)

simplify293.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (160.0ms)

Iter	Nodes	Cost
0	5290	18

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_419` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
4×	`add-log-exp_binary64_458` `associate-r_binary64_359`
3×	`pow-prod-down_binary64_490` `add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `add-sqr-sqrt_binary64_441`
2×	`flip3-+_binary64_422` `distribute-lft-out_binary64_370` `associate-*r/_binary64_361` `flip-+_binary64_393`
1×	`distribute-rgt-in_binary64_369` `sum-log_binary64_510` `distribute-lft-in_binary64_368` `-commutative_binary64_350` `associate-l*_binary64_360` `+-commutative_binary64_349`

Counts

2 → 35

Calls

4 calls:

20.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
10.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

series298.0ms (2.8%)

Counts

2 → 18

Calls

2 calls:

254.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
43.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

Compiler

Compiled 404 to 334 computations (17.3% saved)

simplify137.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4922	964
1	4922	964

prune92.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Error

Counts

54 → 3

Compiler

Compiled 880 to 371 computations (57.8% saved)

localize12.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.0b	(/.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im))
0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im))
0.0b	(+.f64 (/.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im)))
0.0b	(+.f64 (/.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im)))
0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im))
0.0b	(/.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_455`
9×	`add-exp-log_binary64_457`
8×	`pow1_binary64_480`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
5×	`add-log-exp_binary64_458`
4×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`pow-prod-down_binary64_490` `times-frac_binary64_425` `associate-r_binary64_359` `associate-/r*_binary64_363`
2×	`div-inv_binary64_416` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`flip3-+_binary64_422` `clear-num_binary64_418` `sum-log_binary64_510` `distribute-lft-out_binary64_370` `-commutative_binary64_350` `associate-l_binary64_360` `frac-2neg_binary64_430` `flip-+_binary64_393` `+-commutative_binary64_349` `associate-/l_binary64_364`

Counts

3 → 51

Calls

6 calls:

9.0ms	(+.f64 (/.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im)))
8.0ms	(/.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im))
7.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im))
0.0ms	(+.f64 (/.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im)))
0.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im))

series735.0ms (7%)

Counts

3 → 36

Calls

3 calls:

398.0ms	(+.f64 (/.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im)))
201.0ms	(/.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im))
136.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im))

Compiler

Compiled 976 to 722 computations (26% saved)

simplify143.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4947	1618
1	4947	1618

prune137.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	87	3	90

Error

Counts

90 → 3

Compiler

Compiled 1723 to 853 computations (50.5% saved)

localize25.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.6b	(log.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cos.f64 re)))
0.1b	(pow.f64 (sqrt.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cos.f64 re))
0.0b	(exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0b	(exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
0.1b	(pow.f64 (sqrt.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cos.f64 re))
0.6b	(log.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cos.f64 re)))

rewrite55.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_419`
14×	`unpow-prod-down_binary64_498`
12×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
11×	`log-prod_binary64_505`
9×	`add-log-exp_binary64_458`
8×	`exp-prod_binary64_471` `sqrt-prod_binary64_435`
7×	`add-exp-log_binary64_457` `pow-pow_binary64_491`
6×	`pow1_binary64_480`
5×	`sqrt-pow1_binary64_437`
4×	`add-cbrt-cube_binary64_455`
3×	`rem-log-exp_binary64_460` `distribute-lft-out_binary64_370` `exp-sum_binary64_465` `pow-unpow_binary64_496`
2×	`pow-exp_binary64_487` `sqr-pow_binary64_391` `sum-log_binary64_510` `pow-to-exp_binary64_488` `rem-exp-log_binary64_459`
1×	`flip3-+_binary64_422` `pow1/2_binary64_499` `sqrt-pow2_binary64_438` `log-pow_binary64_508` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 76

Calls

8 calls:

19.0ms	(pow.f64 (sqrt.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cos.f64 re))
16.0ms	(log.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cos.f64 re)))
8.0ms	(exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
6.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series1.8s (16.9%)

Counts

4 → 36

Calls

4 calls:

988.0ms	(log.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cos.f64 re)))
695.0ms	(pow.f64 (sqrt.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cos.f64 re))
67.0ms	(exp.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
34.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

Compiler

Compiled 1170 to 822 computations (29.7% saved)

simplify117.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5057	2836

prune156.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	112	3	115

Error

Counts

115 → 3

Compiler

Compiled 2245 to 631 computations (71.9% saved)

localize27.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (exp.f64 im) -2)
0.0b	(/.f64 (.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
0.0b	(pow.f64 (exp.f64 im) 2)
0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2)))
0.0b	(pow.f64 (exp.f64 im) 2)
0.0b	(pow.f64 (exp.f64 im) -2)
6.0b	(-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))
6.0b	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_441`
17×	`*-un-lft-identity_binary64_419`
16×	`unpow-prod-down_binary64_498`
13×	`difference-of-squares_binary64_388` `add-cube-cbrt_binary64_454`
11×	`cancel-sign-sub-inv_binary64_385`
10×	`sqr-pow_binary64_391`
8×	`add-log-exp_binary64_458` `pow-pow_binary64_491`
6×	`exp-prod_binary64_471` `pow-unpow_binary64_496` `pow1_binary64_480`
5×	`unpow2_binary64_484`
4×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
2×	`sub-neg_binary64_412` `pow-exp_binary64_487` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `pow-to-exp_binary64_488` `diff-log_binary64_511` `flip--_binary64_394`

Counts

4 → 89

Calls

8 calls:

17.0ms	(-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))
12.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
6.0ms	(pow.f64 (exp.f64 im) 2)
6.0ms	(pow.f64 (exp.f64 im) -2)
0.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2)))

series280.0ms (2.7%)

Counts

4 → 24

Calls

4 calls:

111.0ms	(-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))
75.0ms	(pow.f64 (exp.f64 im) -2)
51.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
44.0ms	(pow.f64 (exp.f64 im) 2)

Compiler

Compiled 768 to 620 computations (19.3% saved)

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5169	1367

prune158.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	113	3	116

Error

Counts

116 → 3

Compiler

Compiled 2782 to 1223 computations (56% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	134	444
1	134	444

regimes165.0ms (1.6%)

Accuracy

Total 0.0b remaining (88.2%)

Threshold costs 0.0b (88.2%)

Compiler

Compiled 1124 to 924 computations (17.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	24
1	13	24

end0.0ms (0%)

sample5.0s (47.7%)

Algorithm

1×

intervals

Results

1.0s	1962×	body	1024	valid
679.0ms	2037×	body	1024	invalid
391.0ms	4557×	body	128	valid
262.0ms	987×	body	512	valid
247.0ms	1040×	body	512	invalid
82.0ms	487×	body	256	valid
74.0ms	471×	body	256	invalid
65.0ms	712×	body	128	invalid
7.0ms	7×	body	2048	valid

Compiler

Compiled 843 to 688 computations (18.4% saved)

Pareto

0.4146524040015839

Details

analyze538.0ms (5.1%)

sample112.0ms (1.1%)

simplify293.0ms (2.8%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite36.0ms (0.3%)

series298.0ms (2.8%)

simplify137.0ms (1.3%)

prune92.0ms (0.9%)

localize12.0ms (0.1%)

rewrite30.0ms (0.3%)

series735.0ms (7%)

simplify143.0ms (1.4%)

prune137.0ms (1.3%)

localize25.0ms (0.2%)

rewrite55.0ms (0.5%)

series1.8s (16.9%)

simplify117.0ms (1.1%)

prune156.0ms (1.5%)

localize27.0ms (0.3%)

rewrite56.0ms (0.5%)

series280.0ms (2.7%)

simplify90.0ms (0.9%)

prune158.0ms (1.5%)

simplify14.0ms (0.1%)

regimes165.0ms (1.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.0s (47.7%)

Profiling