Details

analyze1.0s (12.8%)

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)

sample84.0ms (1%)

Algorithm

1×

intervals

Results

49.0ms	125×	body	1024	valid
9.0ms	38×	body	512	valid
8.0ms	9×	body	2048	valid
4.0ms	65×	body	128	valid
3.0ms	19×	body	256	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify167.0ms (2.1%)

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

Merged error: 17.3b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize10.0ms (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)))
2.4b	(cos.f64 (+.f64 a b))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
9×	`add-sqr-sqrt_binary64_445`
7×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
5×	`pow1_binary64_484`
3×	`times-frac_binary64_429` `associate-l_binary64_364` `associate-r_binary64_363` `add-log-exp_binary64_462` `associate-/r*_binary64_367`
2×	`prod-exp_binary64_472` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `cos-sum_binary64_557` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `unswap-sqr_binary64_391` `associate-/l_binary64_368`

Counts

3 → 47

Calls

3 calls:

6.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
5.0ms	(*.f64 r (sin.f64 b))
5.0ms	(cos.f64 (+.f64 a b))

series315.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

229.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
58.0ms	(*.f64 r (sin.f64 b))
28.0ms	(cos.f64 (+.f64 a b))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4847	692
1	4847	692

prune137.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 0.2b

Counts

57 → 7

Compiler

Compiled 2250 to 1140 computations (49.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_445`
13×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
10×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
8×	`pow1_binary64_484`
6×	`associate-l_binary64_364` `associate-r_binary64_363` `add-log-exp_binary64_462`
5×	`sin-mult_binary64_578` `cos-mult_binary64_577`
4×	`associate-/r/_binary64_369`
3×	`times-frac_binary64_429` `prod-exp_binary64_472` `associate-/r*_binary64_367` `cbrt-unprod_binary64_456`
2×	`pow-prod-down_binary64_494` `flip3--_binary64_427` `*-commutative_binary64_354` `flip--_binary64_398` `unswap-sqr_binary64_391` `sub-div_binary64_430` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `frac-sub_binary64_432`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `associate-/l*_binary64_368`

Counts

4 → 77

Calls

4 calls:

10.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
7.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series807.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

516.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
150.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
74.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
67.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4990	1631
1	4990	1631

prune277.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	87	9	96

Merged error: 0.0b

Counts

96 → 9

Compiler

Compiled 5645 to 2424 computations (57.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_445`
29×	`*-un-lft-identity_binary64_423`
19×	`add-cube-cbrt_binary64_458`
18×	`times-frac_binary64_429`
13×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`associate-/r*_binary64_367`
6×	`pow1_binary64_484` `add-log-exp_binary64_462`
5×	`distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392`
4×	`associate-/l*_binary64_368`
3×	`associate-l_binary64_364` `cancel-sign-sub-inv_binary64_389` `associate-r_binary64_363` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
2×	`prod-exp_binary64_472` `flip3--_binary64_427` `cos-mult_binary64_577` `associate-/r/_binary64_369` `clear-num_binary64_422` `frac-2neg_binary64_434` `flip--_binary64_398` `div-inv_binary64_420` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `sub-neg_binary64_416` `diff-log_binary64_515` `associate-/l/_binary64_370` `*-commutative_binary64_354` `unswap-sqr_binary64_391`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
9.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
6.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series848.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

450.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
185.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
152.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
60.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4929	2353
1	4929	2353

prune258.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	106	9	115

Merged error: 0.0b

Counts

115 → 9

Compiler

Compiled 5352 to 2288 computations (57.2% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3)) (*.f64 (sin.f64 a) (sin.f64 b))))
0.5b	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3))
0.5b	(pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3)

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
12×	`add-sqr-sqrt_binary64_445`
10×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
9×	`pow1_binary64_484`
8×	`cbrt-prod_binary64_454`
4×	`add-log-exp_binary64_462`
3×	`times-frac_binary64_429` `associate-l_binary64_364` `prod-exp_binary64_472` `cos-mult_binary64_577` `associate-/r/_binary64_369` `associate-r_binary64_363` `pow-unpow_binary64_500` `associate-/r*_binary64_367` `cube-div_binary64_452` `cbrt-unprod_binary64_456`
2×	`pow-prod-down_binary64_494` `cbrt-div_binary64_455` `unpow3_binary64_489` `sin-mult_binary64_578` `pow-exp_binary64_491` `pow-pow_binary64_495` `cube-prod_binary64_451` `cube-mult_binary64_453` `rem-cube-cbrt_binary64_446` `cbrt-undiv_binary64_457` `sqr-pow_binary64_395` `unpow-prod-down_binary64_502` `div-exp_binary64_474`
1×	`pow-to-exp_binary64_492` `pow1/3_binary64_505` `flip3--_binary64_427` `-commutative_binary64_354` `rem-cbrt-cube_binary64_447` `clear-num_binary64_422` `frac-2neg_binary64_434` `flip--_binary64_398` `div-inv_binary64_420` `unswap-sqr_binary64_391` `associate-/l_binary64_368` `frac-sub_binary64_432`

Counts

4 → 84

Calls

4 calls:

12.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3)) (*.f64 (sin.f64 a) (sin.f64 b))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
5.0ms	(pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3)
3.0ms	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3))

series768.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

490.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3)) (*.f64 (sin.f64 a) (sin.f64 b))))
139.0ms	(pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3)
70.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
69.0ms	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3))

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4937	1563
1	4937	1563

prune100.0ms (1.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	96	9	105

Merged error: 0.0b

Counts

105 → 9

Compiler

Compiled 2435 to 712 computations (70.8% saved)

regimes67.0ms (0.8%)

Compiler: Compiled 591 to 402 computations (32% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms (0%)

sample2.7s (33.2%)

Algorithm

1×

intervals

Results

1.4s	3542×	body	1024	valid
305.0ms	1334×	body	512	valid
174.0ms	2364×	body	128	valid
164.0ms	189×	body	2048	valid
92.0ms	571×	body	256	valid
1.0ms	2×	body	1024	invalid

Compiler

Compiled 221 to 152 computations (31.2% saved)

Details

analyze1.0s (12.8%)

sample84.0ms (1%)

simplify167.0ms (2.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite18.0ms (0.2%)

series315.0ms (3.9%)

simplify82.0ms (1%)

prune137.0ms (1.7%)

localize16.0ms (0.2%)

rewrite34.0ms (0.4%)

series807.0ms (10.1%)

simplify57.0ms (0.7%)

prune277.0ms (3.5%)

localize14.0ms (0.2%)

rewrite40.0ms (0.5%)

series848.0ms (10.6%)

simplify80.0ms (1%)

prune258.0ms (3.2%)

localize21.0ms (0.3%)

rewrite34.0ms (0.4%)

series768.0ms (9.6%)

simplify74.0ms (0.9%)

prune100.0ms (1.2%)

regimes67.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (33.2%)

Profiling