Details

analyze808.0ms (8.6%)

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)

sample60.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms	174×	body	128	valid
9.0ms	32×	body	1024	valid
7.0ms	26×	body	1024	nan
6.0ms	29×	body	512	valid
5.0ms	23×	body	512	nan
3.0ms	47×	body	128	nan
3.0ms	21×	body	256	valid
1.0ms	8×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify237.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5155	41

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

Merged error: 43.3b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.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)
14.3b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
20.6b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite71.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_98`
13×	`sqrt-prod_binary64_92`
12×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
11×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
7×	`pow1_binary64_135`
6×	`associate-/r_binary64_23` `associate-l*_binary64_20` `add-log-exp_binary64_113` `times-frac_binary64_83`
4×	`sqrt-div_binary64_93`
3×	`flip--_binary64_52` `flip3--_binary64_81` `associate-r_binary64_19`
2×	`cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `associate--l+_binary64_16` `div-exp_binary64_125` `unswap-sqr_binary64_45` `associate-/r/_binary64_25` `prod-exp_binary64_123`
1×	`pow-prod-down_binary64_145` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `sub-neg_binary64_70` `distribute-lft-in_binary64_28` `associate-/l_binary64_24` `-commutative_binary64_10` `pow1/2_binary64_154` `clear-num_binary64_76` `diff-log_binary64_166` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

4 → 79

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))))
17.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
17.0ms	(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)

series2.9s (30.6%)

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)))
852.0ms	(/.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))))
330.0ms	(-.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)

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4950	3052
1	4950	3052

prune204.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	7	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Merged error: 6.7b

Counts

92 → 7

Compiler

Compiled 3728 to 2190 computations (41.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.7b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.7b	(/.f64 (*.f64 l l) x)
7.8b	(/.f64 (*.f64 t t) x)
26.8b	(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_112` `add-cbrt-cube_binary64_110`
10×	`add-sqr-sqrt_binary64_98`
9×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
8×	`associate-*r/_binary64_21`
6×	`associate-/r*_binary64_23` `add-log-exp_binary64_113` `times-frac_binary64_83`
5×	`pow1_binary64_135`
4×	`frac-add_binary64_85` `flip-+_binary64_51` `cbrt-undiv_binary64_108` `sqrt-div_binary64_93` `flip3-+_binary64_80` `div-exp_binary64_125`
3×	`sqrt-prod_binary64_92`
2×	`cbrt-unprod_binary64_107` `associate-/l*_binary64_24` `prod-exp_binary64_123` `associate-+r+_binary64_11` `clear-num_binary64_76` `frac-2neg_binary64_88` `div-inv_binary64_74`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `distribute-lft-in_binary64_28` `+-commutative_binary64_9` `pow1/2_binary64_154` `distribute-rgt-in_binary64_29` `sum-log_binary64_165`

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)

series333.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

195.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
89.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
25.0ms	(/.f64 (*.f64 t t) x)
24.0ms	(/.f64 (*.f64 l l) x)

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5516	1977

prune138.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	80	13	93

Merged error: 5.2b

Counts

93 → 13

Compiler

Compiled 3376 to 1582 computations (53.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
4.7b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
7.8b	(/.f64 (*.f64 t t) x)
26.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
8×	`add-log-exp_binary64_113` `associate-*r/_binary64_21` `add-sqr-sqrt_binary64_98`
7×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
5×	`flip-+_binary64_51` `flip3-+_binary64_80` `pow1_binary64_135`
4×	`frac-add_binary64_85` `sqrt-div_binary64_93`
3×	`sqrt-prod_binary64_92` `associate-/r*_binary64_23` `times-frac_binary64_83`
2×	`cbrt-undiv_binary64_108` `+-commutative_binary64_9` `div-exp_binary64_125` `associate-+r+_binary64_11` `sum-log_binary64_165`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `distribute-lft-in_binary64_28` `associate-/l*_binary64_24` `prod-exp_binary64_123` `pow1/2_binary64_154` `clear-num_binary64_76` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

4 → 64

Calls

4 calls:

15.0ms	(+.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)

series347.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
85.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
58.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
28.0ms	(/.f64 (*.f64 t t) x)

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5034	2011

prune121.0ms (1.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	75	14	89

Merged error: 5.2b

Counts

89 → 14

Compiler

Compiled 3166 to 1464 computations (53.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.8b	(/.f64 (*.f64 t t) x)
26.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))) (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))))
27.2b	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))
27.2b	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-div_binary64_93`
18×	`associate-*r/_binary64_21`
12×	`add-sqr-sqrt_binary64_98`
9×	`add-exp-log_binary64_112` `sqrt-prod_binary64_92` `add-cbrt-cube_binary64_110` `flip-+_binary64_51` `flip3-+_binary64_80` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
8×	`frac-add_binary64_85`
7×	`pow1_binary64_135`
4×	`add-log-exp_binary64_113` `frac-times_binary64_87`
3×	`associate-/r*_binary64_23` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `times-frac_binary64_83` `pow1/2_binary64_154`
2×	`cbrt-undiv_binary64_108` `associate-*l/_binary64_22` `div-exp_binary64_125`
1×	`cbrt-unprod_binary64_107` `associate-/l*_binary64_24` `prod-exp_binary64_123` `clear-num_binary64_76` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

4 → 74

Calls

4 calls:

14.0ms	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))
13.0ms	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))
12.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))) (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))))
5.0ms	(/.f64 (*.f64 t t) x)

series478.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))) (sqrt.f64 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))))
128.0ms	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))
127.0ms	(sqrt.f64 (+.f64 (*.f64 t t) (/.f64 l (/.f64 x l))))
25.0ms	(/.f64 (*.f64 t t) x)

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5005	2430

prune124.0ms (1.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	86	14	100

Merged error: 5.2b

Counts

100 → 14

Compiler

Compiled 3830 to 1310 computations (65.8% saved)

regimes364.0ms (3.9%)

Compiler: Compiled 4067 to 2553 computations (37.2% saved)

bsearch359.0ms (3.8%)

Steps

Iters	Range		Point
4	5.3758349208426694e+113	9.877787290889992e+113	9.712703512221514e+113
9	7.340996980453347e-157	1.6707997971669048e-150	7.461103816305763e-157
10	8.129140683311145e-213	8.406421684544448e-203	8.323497236838193e-203
6	-1.1016096422962694e+108	-2.4737141056931664e+107	-4.775489866798947e+107

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	161	244
1	161	244

end0.0ms (0%)

sample2.4s (26.1%)

Algorithm

1×

intervals

Results

403.0ms	5333×	body	128	valid
332.0ms	1158×	body	1024	valid
240.0ms	873×	body	1024	nan
188.0ms	889×	body	512	valid
112.0ms	532×	body	512	nan
108.0ms	1536×	body	128	nan
81.0ms	550×	body	256	valid
37.0ms	273×	body	256	nan
25.0ms	70×	body	2048	valid

Compiler

Compiled 859 to 519 computations (39.6% saved)

Details

analyze808.0ms (8.6%)

sample60.0ms (0.6%)

simplify237.0ms (2.5%)

prune3.0ms (0%)

localize20.0ms (0.2%)

rewrite71.0ms (0.8%)

series2.9s (30.6%)

simplify70.0ms (0.7%)

prune204.0ms (2.2%)

localize15.0ms (0.2%)

rewrite36.0ms (0.4%)

series333.0ms (3.6%)

simplify46.0ms (0.5%)

prune138.0ms (1.5%)

localize16.0ms (0.2%)

rewrite46.0ms (0.5%)

series347.0ms (3.7%)

simplify40.0ms (0.4%)

prune121.0ms (1.3%)

localize21.0ms (0.2%)

rewrite57.0ms (0.6%)

series478.0ms (5.1%)

simplify45.0ms (0.5%)

prune124.0ms (1.3%)

regimes364.0ms (3.9%)

bsearch359.0ms (3.8%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.4s (26.1%)

Profiling