Details

analyze524.0ms (5.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample25.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

27.3b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
0.3b	(+.f64 (.f64 a c) (.f64 b d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.3b	(+.f64 (.f64 a c) (.f64 b d))
26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829` `add-sqr-sqrt_binary64_3851`
9×	`times-frac_binary64_3835`
7×	`add-log-exp_binary64_3868`
5×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
4×	`flip3-+_binary64_3832` `flip-+_binary64_3803`
3×	`pow1_binary64_3890` `associate-/l_binary64_3774` `associate-/r_binary64_3773`
2×	`sum-log_binary64_3920` `associate-/l/_binary64_3776` `associate-/r/_binary64_3775` `+-commutative_binary64_3759`
1×	`div-inv_binary64_3826` `div-exp_binary64_3880` `clear-num_binary64_3828` `cbrt-undiv_binary64_3863` `frac-2neg_binary64_3840`

Counts

3 → 53

Calls

6 calls:

11.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
5.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
3.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
0.0ms	(+.f64 (.f64 c c) (.f64 d d))

series519.0ms (5.4%)

Counts

3 → 60

Calls

3 calls:

294.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
139.0ms	(+.f64 (.f64 a c) (.f64 b d))
85.0ms	(+.f64 (.f64 c c) (.f64 d d))

Compiler

Compiled 1290 to 1074 computations (16.7% saved)

simplify95.0ms (1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5047	2038

prune153.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Error

5.0b

Counts

114 → 8

Compiler

Compiled 2231 to 286 computations (87.2% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(+.f64 (.f64 a c) (.f64 b d))
0.1b	(/.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.3b	(+.f64 (.f64 a c) (.f64 b d))
16.5b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_3851`
21×	`add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829`
18×	`times-frac_binary64_3835` `sqrt-prod_binary64_3845`
6×	`add-log-exp_binary64_3868` `add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865` `pow1_binary64_3890` `sqrt-div_binary64_3846` `associate-/r*_binary64_3773`
5×	`flip3-+_binary64_3832` `flip-+_binary64_3803`
3×	`associate-/l*_binary64_3774`
2×	`rem-sqrt-square_binary64_3842` `associate-/l/_binary64_3776` `associate-/r/_binary64_3775` `pow1/2_binary64_3909` `sqrt-pow1_binary64_3847`
1×	`div-inv_binary64_3826` `div-exp_binary64_3880` `sum-log_binary64_3920` `clear-num_binary64_3828` `cbrt-undiv_binary64_3863` `+-commutative_binary64_3759` `frac-2neg_binary64_3840`

Counts

4 → 84

Calls

8 calls:

10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
0.0ms	(+.f64 (.f64 c c) (.f64 d d))

series816.0ms (8.5%)

Counts

4 → 92

Calls

4 calls:

403.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
148.0ms	(+.f64 (.f64 a c) (.f64 b d))
134.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
130.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 3500 to 2466 computations (29.5% saved)

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4967	3592
1	4967	3592

prune145.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	176	8	184

Error

5.0b

Counts

184 → 8

Compiler

Compiled 5303 to 744 computations (86% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

26.2b	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
0.7b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
0.3b	(+.f64 (.f64 a c) (.f64 b d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.3b	(+.f64 (.f64 a c) (.f64 b d))
0.7b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
26.2b	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_3851`
21×	`*-un-lft-identity_binary64_3829`
20×	`times-frac_binary64_3835` `add-cube-cbrt_binary64_3864`
17×	`add-exp-log_binary64_3867`
15×	`associate-r_binary64_3769`
11×	`add-cbrt-cube_binary64_3865`
8×	`add-log-exp_binary64_3868`
7×	`pow1_binary64_3890`
6×	`flip3-+_binary64_3832` `flip-+_binary64_3803`
4×	`div-exp_binary64_3880` `prod-exp_binary64_3878` `associate-/r/_binary64_3775`
3×	`unswap-sqr_binary64_3797` `associate-/l_binary64_3774` `associate-/r_binary64_3773` `associate-l_binary64_3770`
2×	`div-inv_binary64_3826` `sum-log_binary64_3920` `1-exp_binary64_3873` `frac-times_binary64_3839` `associate-*l/_binary64_3772` `rec-exp_binary64_3879` `cbrt-undiv_binary64_3863` `+-commutative_binary64_3759` `cbrt-unprod_binary64_3862`
1×	`pow-prod-down_binary64_3900` `clear-num_binary64_3828` `associate-r/_binary64_3771` `-commutative_binary64_3760` `frac-2neg_binary64_3840` `un-div-inv_binary64_3827` `inv-pow_binary64_3914` `pow-flip_binary64_3903`

Counts

4 → 97

Calls

8 calls:

15.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
6.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
0.0ms	(+.f64 (.f64 c c) (.f64 d d))

series581.0ms (6%)

Counts

4 → 69

Calls

4 calls:

296.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
142.0ms	(+.f64 (.f64 a c) (.f64 b d))
83.0ms	(+.f64 (.f64 c c) (.f64 d d))
60.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 1689 to 1434 computations (15.1% saved)

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5276	2811

prune118.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	166	8	174

Error

5.0b

Counts

174 → 8

Compiler

Compiled 3449 to 711 computations (79.4% saved)

localize17.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(+.f64 (.f64 a c) (.f64 b d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
22.9b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
31.2b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
31.2b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
31.2b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-div_binary64_3861`
10×	`flip3-+_binary64_3832` `flip-+_binary64_3803`
9×	`add-exp-log_binary64_3867` `add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829` `cbrt-prod_binary64_3860` `add-sqr-sqrt_binary64_3851`
8×	`associate-/r/_binary64_3775`
7×	`add-cbrt-cube_binary64_3865`
4×	`add-log-exp_binary64_3868` `pow1_binary64_3890` `frac-times_binary64_3839`
3×	`times-frac_binary64_3835` `pow1/3_binary64_3911` `associate-/l*_binary64_3774`
2×	`div-exp_binary64_3880` `associate-/l/_binary64_3776` `associate-l/_binary64_3772` `cbrt-undiv_binary64_3863` `associate-r/_binary64_3771`
1×	`div-inv_binary64_3826` `prod-exp_binary64_3878` `clear-num_binary64_3828` `associate-/r*_binary64_3773` `frac-2neg_binary64_3840` `cbrt-unprod_binary64_3862`

Counts

4 → 70

Calls

8 calls:

15.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
5.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
0.0ms	(+.f64 (.f64 c c) (.f64 d d))

series1.5s (15.3%)

Counts

4 → 60

Calls

4 calls:

956.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
175.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
172.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
169.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 3642 to 2622 computations (28% saved)

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5073	2905

prune134.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	130	8	138

Error

5.0b

Counts

138 → 8

Compiler

Compiled 4819 to 891 computations (81.5% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	178	1194
1	178	1194

regimes667.0ms (6.9%)

Compiler: Compiled 4157 to 2403 computations (42.2% saved)

bsearch83.0ms (0.9%)

Steps

Iters	Range		Point
9	5.261012177257102e+79	9.232655022452831e+86	1.315316451044619e+86
6	1.4455124447971334e-123	7.993289479926725e-123	2.1472644582174967e-123
10	-1.5447351947110331e-100	-1.2451099552022908e-113	-8.849808015292707e-110
8	-4.362551450141799e+80	-1.5989624956840602e+77	-2.7839182926984815e+79

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes403.0ms (4.2%)

Compiler: Compiled 1554 to 1331 computations (14.4% saved)

bsearch77.0ms (0.8%)

Steps

Iters	Range		Point
9	5.261012177257102e+79	9.232655022452831e+86	4.534169458994563e+85
6	1.4455124447971334e-123	7.993289479926725e-123	4.231028026572649e-123
10	-1.5447351947110331e-100	-1.2451099552022908e-113	-3.697868456727824e-105
8	-4.362551450141799e+80	-1.5989624956840602e+77	-3.88489195189713e+80

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes261.0ms (2.7%)

Compiler: Compiled 611 to 617 computations (-1% saved)

bsearch76.0ms (0.8%)

Steps

Iters	Range		Point
9	5.261012177257102e+79	9.232655022452831e+86	7.627044215435255e+80
6	1.4455124447971334e-123	7.993289479926725e-123	2.7738332462896228e-123
10	-1.5447351947110331e-100	-1.2451099552022908e-113	-2.5452377900992097e-111
8	-4.362551450141799e+80	-1.5989624956840602e+77	-3.067174421205907e+78

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes271.0ms (2.8%)

Compiler: Compiled 368 to 400 computations (-8.7% saved)

bsearch97.0ms (1%)

Steps

Iters	Range		Point
9	5.261012177257102e+79	9.232655022452831e+86	9.194438870773511e+79
9	4.782406745779112e+39	6.3437690306833865e+44	1.8421711922152538e+44
9	3.721174892280916e-55	1.4967404820226354e-47	4.851168696310362e-53
4	-1.4759290785408983e-74	-8.624414968021159e-75	-1.4560731490103253e-74
9	-4000405.996115119	-1.6834101773030716	-933.8271277034492
4	-1.1605460571496514e+42	-6.640815571476473e+41	-6.7235157637121674e+41

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes228.0ms (2.4%)

Compiler: Compiled 220 to 276 computations (-25.5% saved)

bsearch113.0ms (1.2%)

Steps

Iters	Range		Point
7	3.894663791927708e-30	1.578449942376281e-28	3.477343742624138e-29
10	-9.864761793523553e-144	-1.8159786411367057e-155	-9.76721819496008e-144
9	-3.9670558149534753e-92	-3.598098152088858e-100	-3.6577455230706303e-100
7	-0.03564989410319676	-0.00037766704431149587	-0.0023436085176820323
9	-3.152961435058467e+64	-1.5703142594340002e+59	-2.3261484249870466e+64
8	-1.3697805213111073e+87	-1.4008730392468882e+84	-1.5705045420008371e+84

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes185.0ms (1.9%)

Compiler: Compiled 132 to 204 computations (-54.5% saved)

bsearch106.0ms (1.1%)

Steps

Iters	Range		Point
7	3.894663791927708e-30	1.578449942376281e-28	1.3472407996180275e-28
9	-1.7527997884207948e-170	-4.4879088877496736e-178	-1.711980249881788e-170
9	-3.9670558149534753e-92	-3.598098152088858e-100	-3.6577455230706303e-100
7	-0.03564989410319676	-0.00037766704431149587	-0.003450368105936221
9	-3.152961435058467e+64	-1.5703142594340002e+59	-1.2310890621845736e+63
8	-1.3697805213111073e+87	-1.4008730392468882e+84	-1.4197209839973271e+84

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes174.0ms (1.8%)

Compiler: Compiled 88 to 168 computations (-90.9% saved)

bsearch55.0ms (0.6%)

Steps

Iters	Range		Point
9	5.261012177257102e+79	9.232655022452831e+86	5.330723836123918e+79
4	-1.4759290785408983e-74	-8.624414968021159e-75	-1.4560731490103253e-74
9	-4000405.996115119	-1.6834101773030716	-26.275331922204646
7	-2.5571681320258447e+43	-1.1605460571496514e+42	-1.73245955427787e+42

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes52.0ms (0.5%)

Compiler: Compiled 32 to 112 computations (-250% saved)

bsearch11.0ms (0.1%)

Steps

Iters	Range		Point
6	-1.6934845283067424e+131	-1.5117820023391907e+130	-7.8654638730470845e+130

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes35.0ms (0.4%)

Accuracy

Total 9.5b remaining (66.1%)

Threshold costs 0b (0%)

Compiler

Compiled 20 to 92 computations (-360% saved)

bsearch14.0ms (0.1%)

Compiler: Compiled 531 to 223 computations (58% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	218	670
1	218	670

end0.0ms (0%)

sample1.6s (16.2%)

Algorithm

1×

intervals

Results

496.0ms	8000×	body	128	valid
19.0ms	443×	body	128	invalid

Compiler

Compiled 1300 to 718 computations (44.8% saved)

Pareto

0.8338473633352704

Details

analyze524.0ms (5.4%)

sample25.0ms (0.3%)

simplify91.0ms (0.9%)

prune3.0ms (0%)

localize11.0ms (0.1%)

rewrite28.0ms (0.3%)

series519.0ms (5.4%)

simplify95.0ms (1%)

prune153.0ms (1.6%)

localize13.0ms (0.1%)

rewrite32.0ms (0.3%)

series816.0ms (8.5%)

simplify92.0ms (1%)

prune145.0ms (1.5%)

localize15.0ms (0.2%)

rewrite39.0ms (0.4%)

series581.0ms (6%)

simplify87.0ms (0.9%)

prune118.0ms (1.2%)

localize17.0ms (0.2%)

rewrite37.0ms (0.4%)

series1.5s (15.3%)

simplify83.0ms (0.9%)

prune134.0ms (1.4%)

simplify18.0ms (0.2%)

regimes667.0ms (6.9%)

bsearch83.0ms (0.9%)

regimes403.0ms (4.2%)

bsearch77.0ms (0.8%)

regimes261.0ms (2.7%)

bsearch76.0ms (0.8%)

regimes271.0ms (2.8%)

bsearch97.0ms (1%)

regimes228.0ms (2.4%)

bsearch113.0ms (1.2%)

regimes185.0ms (1.9%)

bsearch106.0ms (1.1%)

regimes174.0ms (1.8%)

bsearch55.0ms (0.6%)

regimes52.0ms (0.5%)

bsearch11.0ms (0.1%)

regimes35.0ms (0.4%)

bsearch14.0ms (0.1%)

simplify12.0ms (0.1%)

end0.0ms (0%)

sample1.6s (16.2%)

Profiling