Details

analyze2.0s (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)

sample136.0ms (0.9%)

Algorithm

1×

intervals

Results

79.0ms	112×	body	1024	valid
15.0ms	39×	body	512	valid
12.0ms	8×	body	2048	valid
9.0ms	78×	body	128	valid
5.0ms	19×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify301.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune5.0ms (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: 15.3b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize21.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
3.0b	(cos.f64 (+.f64 a b))

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_435`
19×	`times-frac_binary64_420` `add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
13×	`associate-r_binary64_356`
10×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
5×	`pow1_binary64_472`
3×	`associate-l_binary64_357` `add-log-exp_binary64_450` `associate-/l_binary64_361` `associate-/r_binary64_360`
2×	`div-inv_binary64_411` `cbrt-undiv_binary64_445` `prod-exp_binary64_460` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `-commutative_binary64_347` `cos-sum_binary64_545` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `associate-r/_binary64_358`

Counts

3 → 67

Calls

3 calls:

16.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
10.0ms	(cos.f64 (+.f64 a b))
9.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))

series602.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

399.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
154.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
49.0ms	(cos.f64 (+.f64 a b))

simplify138.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4887	1258
1	4887	1258

prune144.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 0.2b

Counts

77 → 8

Compiler

Compiled 1296 to 304 computations (76.5% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite88.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_435`
22×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
20×	`associate-r_binary64_356`
19×	`times-frac_binary64_420`
13×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`associate-/r/_binary64_362` `pow1_binary64_472`
7×	`sin-mult_binary64_566`
6×	`cos-mult_binary64_565` `associate-l_binary64_357` `add-log-exp_binary64_450`
3×	`flip3--_binary64_418` `frac-sub_binary64_423` `prod-exp_binary64_460` `flip--_binary64_389` `unswap-sqr_binary64_382` `associate-/l_binary64_361` `cbrt-unprod_binary64_444` `sub-div_binary64_421` `associate-/r_binary64_360`
2×	`div-inv_binary64_411` `*-commutative_binary64_347` `cbrt-undiv_binary64_445` `pow-prod-down_binary64_482` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `sub-neg_binary64_407` `frac-2neg_binary64_425` `associate-*r/_binary64_358`

Counts

4 → 99

Calls

4 calls:

26.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
18.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
11.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
10.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series1.8s (12.4%)

Counts

4 → 12

Calls

4 calls:

921.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
491.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
286.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
127.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify152.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4915	2742
1	4915	2742

prune238.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	111	8	119

Merged error: 0.0b

Counts

119 → 8

Compiler

Compiled 2923 to 545 computations (81.4% saved)

localize29.0ms (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)))

rewrite78.0ms (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:

20.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
17.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
11.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
9.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series1.6s (10.6%)

Counts

4 → 12

Calls

4 calls:

842.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
332.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
271.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
121.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify185.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4917	2329
1	4917	2329

prune184.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	104	7	111

Merged error: 0.0b

Counts

111 → 7

Compiler

Compiled 2296 to 482 computations (79% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))))
0.3b	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
26.7b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))

rewrite87.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_435`
22×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
19×	`times-frac_binary64_420`
16×	`associate-r_binary64_356`
14×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
9×	`pow1_binary64_472`
8×	`cbrt-prod_binary64_442`
6×	`associate-/r/_binary64_362`
4×	`add-log-exp_binary64_450` `cube-div_binary64_440` `sin-mult_binary64_566`
3×	`cbrt-div_binary64_443` `pow-unpow_binary64_488` `prod-exp_binary64_460` `associate-l_binary64_357` `associate-/l_binary64_361` `cbrt-unprod_binary64_444` `associate-/r_binary64_360`
2×	`flip3--_binary64_418` `cube-prod_binary64_439` `cos-mult_binary64_565` `div-inv_binary64_411` `cube-mult_binary64_441` `sqr-pow_binary64_386` `frac-sub_binary64_423` `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` `flip--_binary64_389` `unswap-sqr_binary64_382` `rem-cube-cbrt_binary64_436` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `-commutative_binary64_347` `rem-cbrt-cube_binary64_437` `pow-to-exp_binary64_480` `frac-2neg_binary64_425` `pow1/3_binary64_493` `associate-r/_binary64_358`

Counts

4 → 106

Calls

4 calls:

28.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
22.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))))
10.0ms	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
6.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))

series1.8s (12.5%)

Counts

4 → 12

Calls

4 calls:

914.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
513.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))))
262.0ms	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
156.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5207	2715

prune200.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	117	8	125

Merged error: 0.0b

Counts

125 → 8

Compiler

Compiled 3014 to 724 computations (76% saved)

regimes137.0ms (0.9%)

Compiler: Compiled 789 to 438 computations (44.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	31
1	29	31

end0.0ms (0%)

sample4.6s (31%)

Algorithm

1×

intervals

Results

2.3s	3496×	body	1024	valid
546.0ms	1309×	body	512	valid
328.0ms	2392×	body	128	valid
322.0ms	200×	body	2048	valid
169.0ms	603×	body	256	valid

Compiler

Compiled 290 to 167 computations (42.4% saved)

Details

analyze2.0s (13.5%)

sample136.0ms (0.9%)

simplify301.0ms (2%)

prune5.0ms (0%)

localize21.0ms (0.1%)

rewrite46.0ms (0.3%)

series602.0ms (4.1%)

simplify138.0ms (0.9%)

prune144.0ms (1%)

localize33.0ms (0.2%)

rewrite88.0ms (0.6%)

series1.8s (12.4%)

simplify152.0ms (1%)

prune238.0ms (1.6%)

localize29.0ms (0.2%)

rewrite78.0ms (0.5%)

series1.6s (10.6%)

simplify185.0ms (1.3%)

prune184.0ms (1.3%)

localize35.0ms (0.2%)

rewrite87.0ms (0.6%)

series1.8s (12.5%)

simplify119.0ms (0.8%)

prune200.0ms (1.4%)

regimes137.0ms (0.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.6s (31%)

Profiling