Details

analyze504.0ms (9.3%)

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample35.0ms (0.7%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
2.0ms	24×	body	128	nan
1.0ms	15×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify240.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune5.0ms (0.1%)

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: 20.7b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_98`
8×	`add-log-exp_binary64_113` `*-un-lft-identity_binary64_77`
7×	`sqrt-prod_binary64_92`
6×	`pow1_binary64_135` `add-cube-cbrt_binary64_109`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `sqrt-div_binary64_93` `flip--_binary64_52` `flip3--_binary64_81`
2×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `sub-neg_binary64_70` `difference-of-squares_binary64_46` `pow1/2_binary64_154` `diff-log_binary64_166`
1×	`distribute-lft-out--_binary64_31`

Counts

4 → 55

Calls

4 calls:

11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series433.0ms (8%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4880	1379
1	4880	1379

prune138.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	5	68

Merged error: 7.5b

Counts

68 → 5

Compiler

Compiled 3069 to 1848 computations (39.8% saved)

localize30.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
2.4b	(/.f64 (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 a c) b)))) a)
6.0b	(/.f64 (*.f64 a c) b)
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_77`
21×	`add-sqr-sqrt_binary64_98`
16×	`add-cube-cbrt_binary64_109`
15×	`times-frac_binary64_83`
11×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
6×	`associate-/r*_binary64_23` `add-log-exp_binary64_113`
5×	`pow1_binary64_135` `associate-/l*_binary64_24`
4×	`sqrt-prod_binary64_92` `distribute-lft-out_binary64_30`
3×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
2×	`sqrt-div_binary64_93` `flip--_binary64_52` `difference-of-squares_binary64_46` `clear-num_binary64_76` `flip3--_binary64_81` `associate-/l/_binary64_26` `frac-2neg_binary64_88` `div-inv_binary64_74`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `flip-+_binary64_51` `cbrt-unprod_binary64_107` `distribute-lft-out--_binary64_31` `div-sub_binary64_82` `flip3-+_binary64_80` `sub-neg_binary64_70` `associate-+r-_binary64_13` `prod-exp_binary64_123` `pow1/2_binary64_154` `diff-log_binary64_166`

Counts

4 → 84

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(/.f64 (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 a c) b)))) a)
5.0ms	(/.f64 (*.f64 a c) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series351.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
84.0ms	(/.f64 (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 a c) b)))) a)
33.0ms	(/.f64 (*.f64 a c) b)

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4967	1838
1	4967	1838

prune183.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	92	9	101

Merged error: 6.6b

Counts

101 → 9

Compiler

Compiled 4308 to 2371 computations (45% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_98`
10×	`pow1_binary64_135`
9×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
8×	`add-log-exp_binary64_113` `*-un-lft-identity_binary64_77`
6×	`sub-neg_binary64_70` `associate-*r/_binary64_21` `add-cube-cbrt_binary64_109`
4×	`sqrt-prod_binary64_92` `distribute-lft-in_binary64_28` `flip--_binary64_52` `flip3--_binary64_81` `distribute-rgt-in_binary64_29`
3×	`associate-l_binary64_20` `pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123`
2×	`sqrt-div_binary64_93` `difference-of-squares_binary64_46` `diff-log_binary64_166`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `distribute-lft-out--_binary64_31` `frac-sub_binary64_86` `-commutative_binary64_10` `pow1/2_binary64_154` `associate-r*_binary64_19`

Counts

4 → 65

Calls

4 calls:

19.0ms	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series353.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
58.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
49.0ms	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4854	1362
1	4854	1362

prune127.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	77	9	86

Merged error: 5.1b

Counts

86 → 9

Compiler

Compiled 3118 to 1666 computations (46.6% saved)

localize33.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
2.4b	(/.f64 (+.f64 b (-.f64 b (.f64 2 (.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))))) a)
4.0b	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_98`
40×	`times-frac_binary64_83`
39×	`*-un-lft-identity_binary64_77`
29×	`add-cube-cbrt_binary64_109`
27×	`add-exp-log_binary64_112`
22×	`associate-r_binary64_19`
20×	`add-cbrt-cube_binary64_110`
11×	`cbrt-prod_binary64_105`
8×	`cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `div-exp_binary64_125` `prod-exp_binary64_123`
7×	`associate-l_binary64_20` `pow1_binary64_135`
6×	`add-log-exp_binary64_113` `unswap-sqr_binary64_45`
4×	`sqrt-prod_binary64_92` `associate-/l*_binary64_24` `distribute-lft-out_binary64_30`
3×	`associate-/r*_binary64_23` `div-inv_binary64_74`
2×	`sqrt-div_binary64_93` `flip--_binary64_52` `difference-of-squares_binary64_46` `flip3--_binary64_81` `associate-/l/_binary64_26`
1×	`pow-prod-down_binary64_145` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `flip-+_binary64_51` `distribute-lft-out--_binary64_31` `div-sub_binary64_82` `frac-times_binary64_87` `flip3-+_binary64_80` `sub-neg_binary64_70` `associate-l/_binary64_22` `associate-+r-_binary64_13` `associate-r/_binary64_21` `*-commutative_binary64_10` `pow1/2_binary64_154` `clear-num_binary64_76` `diff-log_binary64_166` `frac-2neg_binary64_88`

Counts

4 → 122

Calls

4 calls:

18.0ms	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
9.0ms	(/.f64 (+.f64 b (-.f64 b (.f64 2 (.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))))) a)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series445.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
116.0ms	(/.f64 (+.f64 b (-.f64 b (.f64 2 (.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))))) a)
107.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
104.0ms	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5109	2767

prune240.0ms (4.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	132	11	143

Merged error: 5.1b

Counts

143 → 11

Compiler

Compiled 6152 to 2953 computations (52% saved)

regimes212.0ms (3.9%)

Compiler: Compiled 1536 to 993 computations (35.4% saved)

bsearch136.0ms (2.5%)

Steps

Iters	Range	Point
8	4.128312546146331e+96	1.9135304727080364e+99	4.084166787237329e+98
8	-1.5927448472007976e-279	-2.222355501379704e-283	-2.276046310772245e-283
8	-6.389863478315464e+104	-1.2853371392720047e+101	-6.252365262196174e+104

Iters

Range

Point

4.128312546146331e+96

1.9135304727080364e+99

4.084166787237329e+98

-1.5927448472007976e-279

-2.222355501379704e-283

-2.276046310772245e-283

-6.389863478315464e+104

-1.2853371392720047e+101

-6.252365262196174e+104

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	292	310
1	292	310

end0.0ms (0%)

sample1.5s (27%)

Algorithm

1×

intervals

Results

690.0ms	8000×	body	128	valid
58.0ms	704×	body	128	nan
31.0ms	375×	body	128	invalid

Compiler

Compiled 752 to 472 computations (37.2% saved)

Details

analyze504.0ms (9.3%)

sample35.0ms (0.7%)

simplify240.0ms (4.4%)

prune5.0ms (0.1%)

localize23.0ms (0.4%)

rewrite28.0ms (0.5%)

series433.0ms (8%)

simplify63.0ms (1.2%)

prune138.0ms (2.6%)

localize30.0ms (0.6%)

rewrite30.0ms (0.6%)

series351.0ms (6.5%)

simplify58.0ms (1.1%)

prune183.0ms (3.4%)

localize26.0ms (0.5%)

rewrite40.0ms (0.7%)

series353.0ms (6.5%)

simplify82.0ms (1.5%)

prune127.0ms (2.3%)

localize33.0ms (0.6%)

rewrite47.0ms (0.9%)

series445.0ms (8.2%)

simplify77.0ms (1.4%)

prune240.0ms (4.4%)

regimes212.0ms (3.9%)

bsearch136.0ms (2.5%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample1.5s (27%)

Profiling