Details

analyze2.1s (14.4%)

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
0%	99.9%	0.1%	7
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

Compiler

Compiled 26 to 22 computations (15.4% saved)

sample122.0ms (0.8%)

Algorithm

1×

intervals

Results

68.0ms	100×	body	1024	valid
14.0ms	108×	body	128	valid
12.0ms	29×	body	512	valid
5.0ms	41×	body	128	invalid
5.0ms	19×	body	256	valid
2.0ms	3×	body	1024	invalid
2.0ms	5×	body	512	invalid
1.0ms	4×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify216.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4928	35
1	4928	35

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 32.7b

Counts

2 → 1

Compiler

Compiled 46 to 38 computations (17.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.2b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
14.3b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
17.5b	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite78.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-exp-log_binary64_449`
58×	`prod-exp_binary64_460`
52×	`add-cbrt-cube_binary64_447`
28×	`times-frac_binary64_420`
26×	`cbrt-unprod_binary64_444` `add-sqr-sqrt_binary64_435`
24×	`div-exp_binary64_462`
20×	`pow1_binary64_472`
19×	`*-un-lft-identity_binary64_414`
18×	`associate-l_binary64_357`
17×	`add-cube-cbrt_binary64_446`
16×	`associate-*l/_binary64_359`
12×	`associate-/l*_binary64_361`
10×	`cube-prod_binary64_439` `pow-prod-down_binary64_482` `unpow-prod-down_binary64_490` `associate-r_binary64_356` `frac-times_binary64_424`
8×	`cbrt-undiv_binary64_445` `pow-exp_binary64_479` `pow-to-exp_binary64_480` `tan-quot_binary64_570`
6×	`associate-*r/_binary64_358`
5×	`unswap-sqr_binary64_382`
4×	`flip3-+_binary64_417` `sqr-pow_binary64_386` `add-log-exp_binary64_450` `flip-+_binary64_388`
3×	`cube-mult_binary64_441` `*-commutative_binary64_347` `unpow3_binary64_477`
2×	`div-inv_binary64_411`
1×	`distribute-lft-in_binary64_365` `clear-num_binary64_413` `distribute-rgt-in_binary64_366` `frac-2neg_binary64_425` `distribute-lft-out_binary64_367` `associate-/r*_binary64_360`

Counts

4 → 159

Calls

4 calls:

24.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
13.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
11.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
8.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.2s (8.3%)

Counts

4 → 12

Calls

4 calls:

730.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
333.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
117.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
44.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5586	3677

prune276.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	9	172

Merged error: 16.3b

Counts

172 → 9

Compiler

Compiled 5012 to 2750 computations (45.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
4.6b	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
9.0b	(/.f64 (*.f64 t t) l)
14.3b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite82.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
65×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
44×	`associate-*l/_binary64_359`
34×	`frac-times_binary64_424`
29×	`pow1_binary64_472`
20×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
17×	`pow-prod-down_binary64_482`
16×	`tan-quot_binary64_570`
15×	`add-sqr-sqrt_binary64_435`
14×	`associate-*r/_binary64_358`
13×	`*-un-lft-identity_binary64_414`
11×	`add-cube-cbrt_binary64_446`
10×	`associate-r_binary64_356`
9×	`associate-l_binary64_357`
8×	`flip3-+_binary64_417` `flip-+_binary64_388`
7×	`times-frac_binary64_420`
4×	`add-log-exp_binary64_450`
3×	`-commutative_binary64_347` `associate-/r_binary64_360`
2×	`div-inv_binary64_411` `unswap-sqr_binary64_382`
1×	`distribute-lft-in_binary64_365` `clear-num_binary64_413` `distribute-rgt-in_binary64_366` `frac-2neg_binary64_425` `distribute-lft-out_binary64_367` `associate-/l*_binary64_361`

Counts

4 → 151

Calls

4 calls:

29.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
16.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
8.0ms	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
5.0ms	(/.f64 (*.f64 t t) l)

series1.2s (8.3%)

Counts

4 → 12

Calls

4 calls:

733.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
346.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
109.0ms	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
24.0ms	(/.f64 (*.f64 t t) l)

simplify104.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5000	4012

prune243.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	161	11	172

Merged error: 10.9b

Counts

172 → 11

Compiler

Compiled 4983 to 2493 computations (50% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
3.0b	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
3.3b	(*.f64 (/.f64 t l) (sin.f64 k))
14.3b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite172.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

421×	`add-exp-log_binary64_449`
304×	`add-cbrt-cube_binary64_447`
259×	`prod-exp_binary64_460`
181×	`cbrt-unprod_binary64_444`
179×	`frac-times_binary64_424`
178×	`associate-*l/_binary64_359`
108×	`div-exp_binary64_462`
81×	`associate-*r/_binary64_358`
69×	`cbrt-undiv_binary64_445`
56×	`tan-quot_binary64_570`
47×	`associate-/r/_binary64_362`
40×	`pow1_binary64_472`
32×	`flip3-+_binary64_417` `flip-+_binary64_388`
26×	`pow-prod-down_binary64_482`
21×	`add-sqr-sqrt_binary64_435`
18×	`1-exp_binary64_455` `*-un-lft-identity_binary64_414`
16×	`add-cube-cbrt_binary64_446`
15×	`associate-l_binary64_357`
13×	`times-frac_binary64_420`
10×	`associate-r_binary64_356`
4×	`add-log-exp_binary64_450`
3×	`-commutative_binary64_347` `associate-/l_binary64_361`
2×	`div-inv_binary64_411` `unswap-sqr_binary64_382`
1×	`distribute-lft-in_binary64_365` `clear-num_binary64_413` `distribute-rgt-in_binary64_366` `frac-2neg_binary64_425` `distribute-lft-out_binary64_367` `associate-/r*_binary64_360`

Counts

4 → 308

Calls

4 calls:

39.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
39.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
20.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

series1.7s (11.7%)

Counts

4 → 12

Calls

4 calls:

738.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
525.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
342.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
108.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

simplify155.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4977	9870
1	4977	9870

prune534.0ms (3.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	310	10	320
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	317	14	331

Merged error: 7.8b

Counts

331 → 14

Compiler

Compiled 9952 to 5291 computations (46.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.4b	(.f64 (/.f64 t l) (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
2.5b	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.3b	(*.f64 (/.f64 t l) (sin.f64 k))
14.3b	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite96.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

125×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
78×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
49×	`pow1_binary64_472`
41×	`associate-*r/_binary64_358`
39×	`associate-*l/_binary64_359`
35×	`frac-times_binary64_424`
32×	`pow-prod-down_binary64_482`
28×	`associate-l_binary64_357`
26×	`add-sqr-sqrt_binary64_435`
23×	`*-un-lft-identity_binary64_414`
21×	`add-cube-cbrt_binary64_446`
19×	`times-frac_binary64_420`
18×	`tan-quot_binary64_570`
16×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
11×	`associate-r_binary64_356`
8×	`flip3-+_binary64_417` `flip-+_binary64_388`
4×	`*-commutative_binary64_347` `add-log-exp_binary64_450`
2×	`div-inv_binary64_411` `unswap-sqr_binary64_382`
1×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366` `distribute-lft-out_binary64_367`

Counts

4 → 176

Calls

4 calls:

30.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
17.0ms	(.f64 (/.f64 t l) (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
12.0ms	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
8.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

series1.5s (10.1%)

Counts

4 → 12

Calls

4 calls:

730.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
337.0ms	(.f64 (/.f64 t l) (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
313.0ms	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
106.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5082	5129

prune226.0ms (1.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	184	4	188
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	187	15	202

Merged error: 7.8b

Counts

202 → 15

Compiler

Compiled 5720 to 2045 computations (64.2% saved)

regimes264.0ms (1.8%)

Compiler: Compiled 1772 to 1299 computations (26.7% saved)

bsearch191.0ms (1.3%)

Steps

Iters	Range		Point
6	9.163044128556979e-116	3.8584035694833476e-115	1.8975220742021813e-115
9	-1.2690279208306966e-235	-7.367777990015376e-245	-3.0717970846058635e-240

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	148
1	60	148

end0.0ms (0%)

sample3.9s (26.7%)

Algorithm

1×

intervals

Results

1.7s	2715×	body	1024	valid
529.0ms	1248×	body	512	valid
452.0ms	3404×	body	128	valid
174.0ms	626×	body	256	valid
172.0ms	1334×	body	128	invalid
62.0ms	154×	body	512	invalid
34.0ms	56×	body	1024	invalid
25.0ms	93×	body	256	invalid
8.0ms	7×	body	2048	valid

Compiler

Compiled 547 to 387 computations (29.3% saved)

Details

analyze2.1s (14.4%)

sample122.0ms (0.8%)

simplify216.0ms (1.5%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite78.0ms (0.5%)

series1.2s (8.3%)

simplify70.0ms (0.5%)

prune276.0ms (1.9%)

localize20.0ms (0.1%)

rewrite82.0ms (0.6%)

series1.2s (8.3%)

simplify104.0ms (0.7%)

prune243.0ms (1.7%)

localize20.0ms (0.1%)

rewrite172.0ms (1.2%)

series1.7s (11.7%)

simplify155.0ms (1.1%)

prune534.0ms (3.6%)

localize18.0ms (0.1%)

rewrite96.0ms (0.7%)

series1.5s (10.1%)

simplify87.0ms (0.6%)

prune226.0ms (1.5%)

regimes264.0ms (1.8%)

bsearch191.0ms (1.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.9s (26.7%)

Profiling