Details

analyze777.0ms (8.1%)

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
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample55.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	184×	body	128	valid
10.0ms	32×	body	1024	valid
6.0ms	23×	body	1024	nan
5.0ms	24×	body	512	valid
3.0ms	47×	body	128	nan
3.0ms	14×	body	512	nan
2.0ms	14×	body	256	valid
1.0ms	7×	body	256	nan
1.0ms	2×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify215.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5009	41

prune6.0ms (0.1%)

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

Merged error: 42.2b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
14.1b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
22.4b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite69.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_101`
13×	`sqrt-prod_binary64_95`
12×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
11×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
7×	`pow1_binary64_140`
6×	`associate-/r_binary64_23` `associate-l*_binary64_20` `times-frac_binary64_85` `add-log-exp_binary64_118`
4×	`sqrt-div_binary64_96`
3×	`flip--_binary64_54` `flip3--_binary64_83` `associate-r_binary64_19`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `associate--l+_binary64_16` `unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `associate-/r/_binary64_25`
1×	`div-inv_binary64_76` `distribute-lft-in_binary64_28` `associate-/l_binary64_24` `rem-sqrt-square_binary64_92` `-commutative_binary64_10` `pow-prod-down_binary64_150` `sqrt-pow1_binary64_97` `diff-log_binary64_171` `clear-num_binary64_78` `pow1/2_binary64_159` `cancel-sign-sub-inv_binary64_45` `distribute-rgt-in_binary64_29` `sub-neg_binary64_72` `frac-2neg_binary64_90`

Counts

4 → 80

Calls

4 calls:

21.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
16.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
16.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
5.0ms	(*.f64 (sqrt.f64 2) t)

series2.8s (28.7%)

Counts

4 → 12

Calls

4 calls:

1.6s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
818.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
319.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
46.0ms	(*.f64 (sqrt.f64 2) t)

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4955	3058
1	4955	3058

prune638.0ms (6.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 7.5b

Counts

93 → 7

Compiler

Compiled 14902 to 9835 computations (34% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.6b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
6.9b	(/.f64 (*.f64 l l) x)
8.4b	(/.f64 (*.f64 t t) x)
27.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
10×	`add-sqr-sqrt_binary64_101`
9×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
8×	`associate-*r/_binary64_21`
6×	`associate-/r*_binary64_23` `times-frac_binary64_85` `add-log-exp_binary64_118`
5×	`pow1_binary64_140`
4×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `flip-+_binary64_53` `frac-add_binary64_87` `sqrt-div_binary64_96` `flip3-+_binary64_82`
3×	`sqrt-prod_binary64_95`
2×	`div-inv_binary64_76` `associate-/l*_binary64_24` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `associate-+r+_binary64_11` `clear-num_binary64_78` `frac-2neg_binary64_90`
1×	`sum-log_binary64_170` `distribute-lft-in_binary64_28` `+-commutative_binary64_9` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29`

Counts

4 → 74

Calls

4 calls:

9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)

series315.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
91.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
27.0ms	(/.f64 (*.f64 t t) x)
23.0ms	(/.f64 (*.f64 l l) x)

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5003	1976

prune324.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 3.8b

Counts

93 → 10

Compiler

Compiled 7701 to 4697 computations (39% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
3.6b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
8.4b	(/.f64 (*.f64 t t) x)
27.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-sqr-sqrt_binary64_101` `associate-*r/_binary64_21` `add-log-exp_binary64_118`
7×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
5×	`flip-+_binary64_53` `flip3-+_binary64_82` `pow1_binary64_140`
4×	`frac-add_binary64_87` `sqrt-div_binary64_96`
3×	`sqrt-prod_binary64_95` `associate-/r*_binary64_23` `times-frac_binary64_85`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `sum-log_binary64_170` `+-commutative_binary64_9` `associate-+r+_binary64_11`
1×	`div-inv_binary64_76` `distribute-lft-in_binary64_28` `associate-/l*_binary64_24` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

Counts

4 → 64

Calls

4 calls:

13.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
5.0ms	(/.f64 (*.f64 t t) x)

series350.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
91.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
51.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
23.0ms	(/.f64 (*.f64 t t) x)

simplify42.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5206	2011

prune225.0ms (2.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	73	13	86

Merged error: 3.8b

Counts

86 → 13

Compiler

Compiled 5790 to 3232 computations (44.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
3.6b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
8.4b	(/.f64 (*.f64 t t) x)
27.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-sqr-sqrt_binary64_101` `associate-*r/_binary64_21` `add-log-exp_binary64_118`
7×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
5×	`flip-+_binary64_53` `flip3-+_binary64_82` `pow1_binary64_140`
4×	`frac-add_binary64_87` `sqrt-div_binary64_96`
3×	`sqrt-prod_binary64_95` `associate-/r*_binary64_23` `times-frac_binary64_85`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `sum-log_binary64_170` `+-commutative_binary64_9` `associate-+r+_binary64_11`
1×	`div-inv_binary64_76` `distribute-lft-in_binary64_28` `associate-/l*_binary64_24` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

Counts

4 → 64

Calls

4 calls:

9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))
5.0ms	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
5.0ms	(/.f64 (*.f64 t t) x)

series423.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))
109.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
86.0ms	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
23.0ms	(/.f64 (*.f64 t t) x)

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5015	2016

prune99.0ms (1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	76	13	89

Merged error: 3.8b

Counts

89 → 13

Compiler

Compiled 2807 to 1073 computations (61.8% saved)

regimes330.0ms (3.4%)

Compiler: Compiled 2967 to 1948 computations (34.3% saved)

bsearch529.0ms (5.5%)

Steps

Iters	Range		Point
5	9.066701080462736e+104	3.6239322138541783e+105	3.552303323015909e+105
9	2.9356296320339956e-167	9.393450140931853e-158	2.9878933277788783e-167
6	5.808436522777279e-270	5.36640949457357e-269	5.289804017494565e-269
9	-9.688054288276612e-263	-4.842710277104906e-270	-9.537665178779285e-263
8	-2.9407021909694715e-192	-7.216082082978438e-197	-7.376286544804047e-197
9	-4.522081167183284e+107	-8.191308943204796e+99	-4.448494623502798e+107

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	163	267
1	163	267

end0.0ms (0%)

sample2.1s (21.7%)

Algorithm

1×

intervals

Results

375.0ms	5322×	body	128	valid
316.0ms	1176×	body	1024	valid
199.0ms	775×	body	1024	nan
174.0ms	878×	body	512	valid
99.0ms	1502×	body	128	nan
97.0ms	502×	body	512	nan
73.0ms	553×	body	256	valid
38.0ms	269×	body	256	nan
24.0ms	71×	body	2048	valid

Compiler

Compiled 719 to 456 computations (36.6% saved)

Details

analyze777.0ms (8.1%)

sample55.0ms (0.6%)

simplify215.0ms (2.2%)

prune6.0ms (0.1%)

localize16.0ms (0.2%)

rewrite69.0ms (0.7%)

series2.8s (28.7%)

simplify69.0ms (0.7%)

prune638.0ms (6.6%)

localize15.0ms (0.2%)

rewrite36.0ms (0.4%)

series315.0ms (3.3%)

simplify62.0ms (0.6%)

prune324.0ms (3.4%)

localize15.0ms (0.2%)

rewrite44.0ms (0.5%)

series350.0ms (3.6%)

simplify42.0ms (0.4%)

prune225.0ms (2.3%)

localize22.0ms (0.2%)

rewrite38.0ms (0.4%)

series423.0ms (4.4%)

simplify62.0ms (0.6%)

prune99.0ms (1%)

regimes330.0ms (3.4%)

bsearch529.0ms (5.5%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample2.1s (21.7%)

Profiling