Details

analyze1.0s (13.5%)

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)

sample83.0ms (1.1%)

Algorithm

1×

intervals

Results

49.0ms	125×	body	1024	valid
8.0ms	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)

simplify158.0ms (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)

localize13.0ms (0.2%)

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))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
9×	`add-sqr-sqrt_binary64_435`
7×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
5×	`pow1_binary64_472`
3×	`times-frac_binary64_420` `associate-l_binary64_357` `add-log-exp_binary64_450` `associate-r_binary64_356` `associate-/r*_binary64_360`
2×	`cbrt-undiv_binary64_445` `prod-exp_binary64_460` `cbrt-unprod_binary64_444` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `-commutative_binary64_347` `cos-sum_binary64_545` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `unswap-sqr_binary64_382` `associate-/l_binary64_361`

Counts

3 → 47

Calls

3 calls:

6.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))
4.0ms	(*.f64 r (sin.f64 b))

series315.0ms (4.2%)

Counts

3 → 9

Calls

3 calls:

232.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
54.0ms	(*.f64 r (sin.f64 b))
29.0ms	(cos.f64 (+.f64 a b))

simplify78.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4866	692
1	4866	692

prune50.0ms (0.7%)

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 836 to 225 computations (73.1% saved)

localize15.0ms (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))))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_435`
13×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
10×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
8×	`pow1_binary64_472`
6×	`associate-l_binary64_357` `add-log-exp_binary64_450` `associate-r_binary64_356`
5×	`cos-mult_binary64_565` `sin-mult_binary64_566`
4×	`associate-/r/_binary64_362`
3×	`times-frac_binary64_420` `prod-exp_binary64_460` `cbrt-unprod_binary64_444` `associate-/r*_binary64_360`
2×	`flip3--_binary64_418` `*-commutative_binary64_347` `frac-sub_binary64_423` `cbrt-undiv_binary64_445` `pow-prod-down_binary64_482` `flip--_binary64_389` `unswap-sqr_binary64_382` `sub-div_binary64_421` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `div-inv_binary64_411` `sub-neg_binary64_407` `frac-2neg_binary64_425` `associate-/l*_binary64_361`

Counts

4 → 76

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

series796.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

507.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
148.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
74.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
66.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4918	1621
1	4918	1621

prune90.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	86	9	95

Merged error: 0.0b

Counts

95 → 9

Compiler

Compiled 2061 to 436 computations (78.8% saved)

localize17.0ms (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)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_435`
28×	`*-un-lft-identity_binary64_414`
18×	`times-frac_binary64_420` `add-cube-cbrt_binary64_446`
13×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`associate-/r*_binary64_360`
6×	`pow1_binary64_472` `add-log-exp_binary64_450`
5×	`distribute-lft-out--_binary64_368` `difference-of-squares_binary64_383`
4×	`associate-/l*_binary64_361`
3×	`cbrt-undiv_binary64_445` `associate-l_binary64_357` `associate-r_binary64_356` `div-exp_binary64_462`
2×	`associate-/r/_binary64_362` `flip3--_binary64_418` `clear-num_binary64_413` `cos-mult_binary64_565` `div-inv_binary64_411` `prod-exp_binary64_460` `frac-2neg_binary64_425` `flip--_binary64_389` `cbrt-unprod_binary64_444`
1×	`diff-log_binary64_503` `*-commutative_binary64_347` `pow-prod-down_binary64_482` `sub-neg_binary64_407` `unswap-sqr_binary64_382` `associate-/l/_binary64_363`

Counts

4 → 91

Calls

4 calls:

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

series809.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

439.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
178.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
132.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
61.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify104.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4917	2329
1	4917	2329

prune95.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	103	9	112

Merged error: 0.0b

Counts

112 → 9

Compiler

Compiled 2284 to 475 computations (79.2% saved)

localize18.0ms (0.2%)

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 (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
12×	`add-sqr-sqrt_binary64_435`
10×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
9×	`pow1_binary64_472`
8×	`cbrt-prod_binary64_442`
4×	`add-log-exp_binary64_450`
3×	`associate-/r/_binary64_362` `times-frac_binary64_420` `cos-mult_binary64_565` `pow-unpow_binary64_488` `prod-exp_binary64_460` `associate-l_binary64_357` `associate-r_binary64_356` `cbrt-unprod_binary64_444` `cube-div_binary64_440` `associate-/r*_binary64_360`
2×	`cbrt-div_binary64_443` `cube-prod_binary64_439` `cube-mult_binary64_441` `sqr-pow_binary64_386` `cbrt-undiv_binary64_445` `pow-pow_binary64_483` `pow-exp_binary64_479` `pow-prod-down_binary64_482` `unpow3_binary64_477` `unpow-prod-down_binary64_490` `rem-cube-cbrt_binary64_436` `sin-mult_binary64_566` `div-exp_binary64_462`
1×	`flip3--_binary64_418` `clear-num_binary64_413` `div-inv_binary64_411` `-commutative_binary64_347` `frac-sub_binary64_423` `rem-cbrt-cube_binary64_437` `pow-to-exp_binary64_480` `frac-2neg_binary64_425` `flip--_binary64_389` `pow1/3_binary64_493` `unswap-sqr_binary64_382` `associate-/l_binary64_361`

Counts

4 → 84

Calls

4 calls:

14.0ms	(/.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))

series735.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

475.0ms	(/.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))))
128.0ms	(pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3)
66.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
65.0ms	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3))

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4945	1563
1	4945	1563

prune83.0ms (1.1%)

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 2196 to 570 computations (74% saved)

regimes67.0ms (0.9%)

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%)

sample2.6s (35.5%)

Algorithm

1×

intervals

Results

1.4s	3542×	body	1024	valid
300.0ms	1334×	body	512	valid
171.0ms	2364×	body	128	valid
160.0ms	189×	body	2048	valid
94.0ms	571×	body	256	valid
1.0ms	2×	body	1024	invalid

Compiler

Compiled 221 to 152 computations (31.2% saved)

Details

analyze1.0s (13.5%)

sample83.0ms (1.1%)

simplify158.0ms (2.1%)

prune2.0ms (0%)

localize13.0ms (0.2%)

rewrite17.0ms (0.2%)

series315.0ms (4.2%)

simplify78.0ms (1.1%)

prune50.0ms (0.7%)

localize15.0ms (0.2%)

rewrite32.0ms (0.4%)

series796.0ms (10.7%)

simplify69.0ms (0.9%)

prune90.0ms (1.2%)

localize17.0ms (0.2%)

rewrite36.0ms (0.5%)

series809.0ms (10.9%)

simplify104.0ms (1.4%)

prune95.0ms (1.3%)

localize18.0ms (0.2%)

rewrite34.0ms (0.5%)

series735.0ms (9.9%)

simplify72.0ms (1%)

prune83.0ms (1.1%)

regimes67.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (35.5%)

Profiling