Details

analyze1.3s (11.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	56
1	66	56
0	3	3
1	3	3

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)

sample68.0ms (0.6%)

Algorithm

1×

intervals

Results

35.0ms	105×	body	1024	valid
9.0ms	46×	body	512	valid
5.0ms	75×	body	128	valid
4.0ms	26×	body	256	valid
2.0ms	4×	body	2048	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune2.0ms (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

Error

15.4b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (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)))
4.0b	(cos.f64 (+.f64 a b))

rewrite62.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`add-sqr-sqrt_binary64_441`
7×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
5×	`pow1_binary64_480`
3×	`add-log-exp_binary64_458` `times-frac_binary64_425` `associate-/r_binary64_363` `associate-l_binary64_360` `associate-r*_binary64_359`
2×	`prod-exp_binary64_468` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `cbrt-unprod_binary64_452`
1×	`cos-sum_binary64_553` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l_binary64_364` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `-commutative_binary64_350`

Counts

3 → 47

Calls

3 calls:

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

Compiler

Compiled 725 to 158 computations (78.2% saved)

series428.0ms (3.9%)

Error

14.0b

Counts

3 → 36

Calls

3 calls:

274.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
72.0ms	(*.f64 r (sin.f64 b))
43.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1504 to 908 computations (39.6% saved)

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5030	1447

prune88.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	76	7	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	7	84

Error

0.2b

Counts

84 → 7

Compiler

Compiled 1373 to 436 computations (68.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.1b	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))

rewrite118.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`add-sqr-sqrt_binary64_441`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
10×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
8×	`pow1_binary64_480`
6×	`add-log-exp_binary64_458` `associate-l_binary64_360` `associate-r_binary64_359`
5×	`sin-mult_binary64_574`
4×	`cos-mult_binary64_573` `associate-/r/_binary64_365`
3×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `times-frac_binary64_425` `associate-/r*_binary64_363`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `frac-sub_binary64_428` `sub-div_binary64_426` `flip3--_binary64_423` `flip--_binary64_394` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `*-commutative_binary64_350`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l*_binary64_364` `diff-log_binary64_511` `sub-neg_binary64_412` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 76

Calls

4 calls:

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

Compiler

Compiled 1946 to 307 computations (84.2% saved)

series954.0ms (8.6%)

Error

0.2b

Counts

4 → 48

Calls

4 calls:

577.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
145.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
110.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
78.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 2544 to 1409 computations (44.6% saved)

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5014	2573

prune129.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	115	9	124
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	119	12	131

Error

0.0b

Counts

131 → 12

Compiler

Compiled 2997 to 772 computations (74.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))
0.2b	(/.f64 1 (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
0.2b	(.f64 r (/.f64 1 (-.f64 (/.f64 (.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))))
0.2b	(/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b))

rewrite169.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

50×	`add-sqr-sqrt_binary64_441`
44×	`*-un-lft-identity_binary64_419`
35×	`times-frac_binary64_425`
27×	`add-cube-cbrt_binary64_454`
22×	`add-exp-log_binary64_457`
21×	`associate-r_binary64_359`
16×	`add-cbrt-cube_binary64_455`
8×	`associate-/r*_binary64_363` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371`
7×	`pow1_binary64_480`
6×	`div-exp_binary64_470` `add-log-exp_binary64_458`
5×	`prod-exp_binary64_468`
4×	`cbrt-undiv_binary64_453` `associate-/l*_binary64_364` `associate-/r/_binary64_365`
3×	`cbrt-unprod_binary64_452` `div-inv_binary64_416` `unswap-sqr_binary64_387` `associate-l_binary64_360` `flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `1-exp_binary64_463` `rec-exp_binary64_469`
1×	`cos-mult_binary64_573` `associate-/l/_binary64_366` `pow-prod-down_binary64_490` `un-div-inv_binary64_417` `associate-r/_binary64_361` `-commutative_binary64_350` `inv-pow_binary64_504` `pow-flip_binary64_493` `diff-log_binary64_511` `sub-neg_binary64_412`

Counts

4 → 123

Calls

4 calls:

15.0ms	(.f64 r (/.f64 1 (-.f64 (/.f64 (.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))))
9.0ms	(/.f64 1 (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
8.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))
5.0ms	(/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b))

Compiler

Compiled 3294 to 874 computations (73.5% saved)

series1.2s (10.6%)

Error

0.0b

Counts

4 → 51

Calls

4 calls:

498.0ms	(.f64 r (/.f64 1 (-.f64 (/.f64 (.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))))
271.0ms	(/.f64 1 (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
190.0ms	(/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b))
162.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))

Compiler

Compiled 2701 to 1670 computations (38.2% saved)

simplify90.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4991	4594
1	4991	4594

prune179.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	171	3	174
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	175	11	186

Error

0.0b

Counts

186 → 11

Compiler

Compiled 4345 to 1277 computations (70.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sin.f64 a)) (cbrt.f64 (sin.f64 a)))
0.6b	(cbrt.f64 (sin.f64 a))
0.6b	(cbrt.f64 (sin.f64 a))
0.6b	(cbrt.f64 (sin.f64 a))

rewrite86.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`cbrt-prod_binary64_450`
23×	`add-sqr-sqrt_binary64_441`
15×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
11×	`pow1_binary64_480`
9×	`pow1/3_binary64_501`
6×	`add-exp-log_binary64_457` `swap-sqr_binary64_386` `associate-l_binary64_360` `associate-r_binary64_359`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `unswap-sqr_binary64_387`
2×	`pow-prod-down_binary64_490` `pow-prod-up_binary64_489` `pow-sqr_binary64_392`
1×	`pow2_binary64_500` `pow-plus_binary64_482` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350`

Counts

4 → 73

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 (sin.f64 a)) (cbrt.f64 (sin.f64 a)))
1.0ms	(cbrt.f64 (sin.f64 a))
1.0ms	(cbrt.f64 (sin.f64 a))
1.0ms	(cbrt.f64 (sin.f64 a))

Compiler

Compiled 2241 to 440 computations (80.4% saved)

series333.0ms (3%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

105.0ms	(*.f64 (cbrt.f64 (sin.f64 a)) (cbrt.f64 (sin.f64 a)))
72.0ms	(cbrt.f64 (sin.f64 a))
69.0ms	(cbrt.f64 (sin.f64 a))
67.0ms	(cbrt.f64 (sin.f64 a))

Compiler

Compiled 1363 to 805 computations (40.9% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5013	837

prune88.0ms (0.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	91	11	102

Error

0.0b

Counts

102 → 11

Compiler

Compiled 2523 to 565 computations (77.6% saved)

regimes1.0s (9.1%)

Accuracy

Total 0.4b remaining (96.6%)

Threshold costs 0.4b (96.6%)

Compiler

Compiled 11943 to 7517 computations (37.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	39
1	65	39

end0.0ms (0%)

sample4.5s (40.9%)

Algorithm

1×

intervals

Results

1.1s	3507×	body	1024	valid
286.0ms	1365×	body	512	valid
165.0ms	2300×	body	128	valid
124.0ms	192×	body	2048	valid
96.0ms	636×	body	256	valid
1.0ms	2×	body	1024	invalid

Compiler

Compiled 2991 to 1887 computations (36.9% saved)

Details

analyze1.3s (11.7%)

sample68.0ms (0.6%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite62.0ms (0.6%)

series428.0ms (3.9%)

simplify75.0ms (0.7%)

prune88.0ms (0.8%)

localize15.0ms (0.1%)

rewrite118.0ms (1.1%)

series954.0ms (8.6%)

simplify75.0ms (0.7%)

prune129.0ms (1.2%)

localize16.0ms (0.1%)

rewrite169.0ms (1.5%)

series1.2s (10.6%)

simplify90.0ms (0.8%)

prune179.0ms (1.6%)

localize18.0ms (0.2%)

rewrite86.0ms (0.8%)

series333.0ms (3%)

simplify66.0ms (0.6%)

prune88.0ms (0.8%)

regimes1.0s (9.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.5s (40.9%)

Profiling