Details

analyze1.0s (15.9%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample62.0ms (1%)

Algorithm

1×

intervals

Results

34.0ms	116×	body	1024	valid
9.0ms	43×	body	512	valid
5.0ms	68×	body	128	valid
3.0ms	25×	body	256	valid
2.0ms	4×	body	2048	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify103.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 12.5b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
2.2b	(cos.f64 (+.f64 a b))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`add-sqr-sqrt_binary64_441`
7×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
5×	`pow1_binary64_480`
3×	`times-frac_binary64_425` `add-log-exp_binary64_458` `associate-r_binary64_359` `associate-l_binary64_360` `associate-/r*_binary64_363`
2×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `cos-sum_binary64_553` `div-inv_binary64_416` `unswap-sqr_binary64_387` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/l_binary64_364`

Counts

3 → 47

Calls

3 calls:

5.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0ms	(*.f64 r (sin.f64 b))
4.0ms	(cos.f64 (+.f64 a b))

series158.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

111.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
32.0ms	(*.f64 r (sin.f64 b))
15.0ms	(cos.f64 (+.f64 a b))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5418	692

prune52.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Merged error: 0.2b

Counts

57 → 8

Compiler

Compiled 863 to 241 computations (72.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_441`
15×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
12×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
10×	`pow1_binary64_480`
9×	`associate-r_binary64_359` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/r/_binary64_365`
3×	`pow-prod-down_binary64_490` `times-frac_binary64_425` `unswap-sqr_binary64_387` `sin-mult_binary64_574` `cos-mult_binary64_573` `-commutative_binary64_350` `associate-/r_binary64_363`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `div-inv_binary64_416` `flip3--_binary64_423` `frac-2neg_binary64_430` `flip--_binary64_394` `sub-div_binary64_426` `frac-sub_binary64_428` `associate-/l*_binary64_364`

Counts

4 → 81

Calls

4 calls:

9.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
4.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
4.0ms	(*.f64 r (sin.f64 b))

series370.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
42.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
34.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
31.0ms	(*.f64 r (sin.f64 b))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4993	1420
1	4993	1420

prune96.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	84	9	93
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	90	11	101

Merged error: 0.0b

Counts

101 → 11

Compiler

Compiled 2175 to 476 computations (78.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
4.0b	(log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_441`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
11×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`pow1_binary64_480`
6×	`associate-r_binary64_359` `associate-l_binary64_360`
5×	`add-log-exp_binary64_458`
3×	`times-frac_binary64_425` `log-prod_binary64_505` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `log-pow_binary64_508` `associate-/r*_binary64_363`
2×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `associate-/r/_binary64_365` `*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `rem-log-exp_binary64_460` `div-inv_binary64_416` `exp-to-pow_binary64_481` `sin-mult_binary64_574` `exp-prod_binary64_471` `flip3--_binary64_423` `frac-2neg_binary64_430` `flip--_binary64_394` `associate-/l*_binary64_364`

Counts

4 → 74

Calls

4 calls:

9.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
4.0ms	(*.f64 r (sin.f64 b))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))

series457.0ms (7%)

Counts

4 → 12

Calls

4 calls:

304.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))))
87.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))
37.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
29.0ms	(*.f64 r (sin.f64 b))

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4954	1320
1	4954	1320

prune81.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 0.0b

Counts

97 → 10

Compiler

Compiled 2121 to 460 computations (78.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
27.4b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
12×	`add-sqr-sqrt_binary64_441`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`pow1_binary64_480`
8×	`cbrt-prod_binary64_450`
4×	`add-log-exp_binary64_458` `sin-mult_binary64_574`
3×	`times-frac_binary64_425` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `cube-div_binary64_448` `associate-/r/_binary64_365` `associate-l_binary64_360` `pow-unpow_binary64_496` `associate-/r*_binary64_363`
2×	`pow-prod-down_binary64_490` `unpow-prod-down_binary64_498` `cbrt-div_binary64_451` `unpow3_binary64_485` `cube-mult_binary64_449` `rem-cube-cbrt_binary64_442` `pow-exp_binary64_487` `sqr-pow_binary64_391` `cube-prod_binary64_447` `pow-pow_binary64_491` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `pow1/3_binary64_501` `div-inv_binary64_416` `unswap-sqr_binary64_387` `flip3--_binary64_423` `rem-cbrt-cube_binary64_443` `cos-mult_binary64_573` `pow-to-exp_binary64_488` `-commutative_binary64_350` `frac-2neg_binary64_430` `flip--_binary64_394` `frac-sub_binary64_428` `associate-/l_binary64_364`

Counts

4 → 84

Calls

4 calls:

11.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
5.0ms	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
3.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

series398.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

252.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))))
71.0ms	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
38.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))
37.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5309	1574

prune82.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	95	11	106

Merged error: 0.0b

Counts

106 → 11

Compiler

Compiled 2203 to 566 computations (74.3% saved)

regimes311.0ms (4.8%)

Compiler: Compiled 3552 to 2206 computations (37.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	30
1	27	30

end0.0ms (0%)

sample2.9s (44.2%)

Algorithm

1×

intervals

Results

1.2s	3472×	body	1024	valid
291.0ms	1413×	body	512	valid
161.0ms	2313×	body	128	valid
123.0ms	203×	body	2048	valid
83.0ms	599×	body	256	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 910 to 569 computations (37.5% saved)

Details

analyze1.0s (15.9%)

sample62.0ms (1%)

simplify103.0ms (1.6%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite16.0ms (0.2%)

series158.0ms (2.4%)

simplify82.0ms (1.3%)

prune52.0ms (0.8%)

localize13.0ms (0.2%)

rewrite28.0ms (0.4%)

series370.0ms (5.7%)

simplify55.0ms (0.8%)

prune96.0ms (1.5%)

localize15.0ms (0.2%)

rewrite26.0ms (0.4%)

series457.0ms (7%)

simplify69.0ms (1.1%)

prune81.0ms (1.2%)

localize16.0ms (0.2%)

rewrite33.0ms (0.5%)

series398.0ms (6.1%)

simplify59.0ms (0.9%)

prune82.0ms (1.3%)

regimes311.0ms (4.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.9s (44.2%)

Profiling