Details

analyze2.9s (9.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4978	427
1	4978	427
0	4	4
1	4	4

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%	98.2%	1.8%	7
0%	92%	8%	8
0%	91.2%	8.8%	9
0.4%	89.3%	10.3%	10
7.1%	79.2%	13.6%	11
11.9%	70.2%	17.9%	12
13.8%	67.4%	18.7%	13
16.6%	63.3%	20.1%	14

Symmetry

(sort A C)

Compiler

Compiled 41 to 33 computations (19.5% saved)

sample149.0ms (0.5%)

Algorithm

1×

intervals

Results

26.0ms	188×	body	128	valid
20.0ms	20×	body	2048	valid
19.0ms	27×	body	1024	valid
13.0ms	24×	body	1024	nan
13.0ms	18×	body	2048	nan
11.0ms	84×	body	128	nan
6.0ms	14×	body	512	valid
5.0ms	12×	body	512	nan
2.0ms	9×	body	256	nan
2.0ms	7×	body	256	valid

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify56.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5390	61

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

52.5b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
17.0b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
20.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
36.8b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite796.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

52.0b

Rules

66×	`sqrt-div_binary64_5551`
40×	`associate-*r/_binary64_5476`
39×	`*-un-lft-identity_binary64_5534`
36×	`times-frac_binary64_5540`
35×	`add-sqr-sqrt_binary64_5556`
34×	`associate-*l/_binary64_5477`
32×	`add-cube-cbrt_binary64_5569`
25×	`flip3-+_binary64_5537` `flip-+_binary64_5508`
24×	`frac-sub_binary64_5543` `frac-times_binary64_5544`
22×	`flip3--_binary64_5538` `flip--_binary64_5509`
20×	`distribute-neg-frac_binary64_5498` `associate-/l/_binary64_5481`
17×	`pow1_binary64_5595`
16×	`distribute-rgt-neg-in_binary64_5492` `distribute-lft-neg-in_binary64_5491`
15×	`sqrt-prod_binary64_5550`
12×	`associate-/l*_binary64_5479`
8×	`add-exp-log_binary64_5572` `add-cbrt-cube_binary64_5570`
7×	`pow-prod-down_binary64_5605`
5×	`sqrt-pow1_binary64_5552`
4×	`add-log-exp_binary64_5573` `unpow-prod-down_binary64_5613` `neg-mul-1_binary64_5530`
3×	`distribute-lft-out_binary64_5485` `associate-/r_binary64_5478` `associate-l_binary64_5475` `associate-r*_binary64_5474`
2×	`pow1/2_binary64_5614` `associate-/r/_binary64_5480`
1×	`distribute-lft-out--_binary64_5486` `rem-sqrt-square_binary64_5547` `div-exp_binary64_5585` `cbrt-undiv_binary64_5568` `frac-2neg_binary64_5545` `neg-sub0_binary64_5529` `div-sub_binary64_5539` `clear-num_binary64_5533` `div-inv_binary64_5531` `distribute-frac-neg_binary64_5497` `prod-exp_binary64_5583` `cbrt-unprod_binary64_5567` `unswap-sqr_binary64_5502` `*-commutative_binary64_5465`

Counts

4 → 158

Calls

4 calls:

34.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
18.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
12.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
9.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

Compiler

Compiled 11876 to 7641 computations (35.7% saved)

series5.1s (17.6%)

Error

27.9b

Counts

4 → 75

Calls

4 calls:

3.2s	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
1.2s	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
302.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
270.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

Compiler

Compiled 16542 to 12311 computations (25.6% saved)

simplify132.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5075	14827

prune910.0ms (3.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	212	21	233
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	213	21	234

Error

27.6b

Counts

234 → 21

Compiler

Compiled 15922 to 8450 computations (46.9% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
13.1b	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

rewrite64.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

25.8b

Rules

12×	`pow1_binary64_5595`
9×	`add-sqr-sqrt_binary64_5556`
6×	`pow-prod-down_binary64_5605` `sqrt-pow1_binary64_5552` `sqrt-prod_binary64_5550` `associate-l_binary64_5475`
5×	`add-cube-cbrt_binary64_5569` `*-un-lft-identity_binary64_5534`
4×	`add-exp-log_binary64_5572` `add-cbrt-cube_binary64_5570` `associate-r_binary64_5474`
3×	`pow1/2_binary64_5614` `associate-*r/_binary64_5476`
2×	`add-log-exp_binary64_5573` `sqrt-div_binary64_5551` `unswap-sqr_binary64_5502`
1×	`prod-exp_binary64_5583` `cbrt-unprod_binary64_5567` `sqrt-unprod_binary64_5554` `*-commutative_binary64_5465`

Counts

2 → 40

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
4.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

Compiler

Compiled 641 to 475 computations (25.9% saved)

series108.0ms (0.4%)

Error

27.6b

Counts

2 → 12

Calls

2 calls:

57.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
44.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

Compiler

Compiled 494 to 489 computations (1% saved)

simplify117.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4850	676
1	4850	676

prune106.0ms (0.4%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	42	10	52
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	44	29	73

Error

25.8b

Counts

73 → 29

Compiler

Compiled 1801 to 1339 computations (25.7% saved)

localize11.0ms (0%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C))
0.3b	(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 F -1/2)) (sqrt.f64 C)))

rewrite157.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

25.7b

Rules

52×	`add-sqr-sqrt_binary64_5556` `times-frac_binary64_5540`
48×	`sqrt-prod_binary64_5550`
36×	`add-cube-cbrt_binary64_5569` `*-un-lft-identity_binary64_5534`
28×	`associate-r_binary64_5474`
9×	`add-exp-log_binary64_5572` `add-cbrt-cube_binary64_5570`
6×	`unswap-sqr_binary64_5502` `associate-l_binary64_5475` `associate-/r*_binary64_5478`
4×	`pow1_binary64_5595` `associate-/l*_binary64_5479`
2×	`div-exp_binary64_5585` `prod-exp_binary64_5583` `add-log-exp_binary64_5573` `cbrt-unprod_binary64_5567` `cbrt-undiv_binary64_5568` `sqrt-undiv_binary64_5555` `div-inv_binary64_5531`
1×	`pow-prod-down_binary64_5605` `sqrt-unprod_binary64_5554` `associate-r/_binary64_5476` `-commutative_binary64_5465` `frac-2neg_binary64_5545` `clear-num_binary64_5533`

Counts

2 → 102

Calls

2 calls:

15.0ms	(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 F -1/2)) (sqrt.f64 C)))
6.0ms	(/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C))

Compiler

Compiled 2073 to 1432 computations (30.9% saved)

series134.0ms (0.5%)

Error

25.8b

Counts

2 → 12

Calls

2 calls:

72.0ms	(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 F -1/2)) (sqrt.f64 C)))
54.0ms	(/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C))

Compiler

Compiled 542 to 547 computations (-0.9% saved)

simplify90.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5025	2172

prune189.0ms (0.6%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	106	8	114
Fresh	5	23	28
Picked	0	1	1
Done	0	0	0
Total	111	32	143

Error

25.7b

Counts

143 → 32

Compiler

Compiled 3247 to 2346 computations (27.7% saved)

localize11.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b

(*.f64 (/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C)) (sqrt.f64 (sqrt.f64 2)))

0.3b

(/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C))

0.3b

(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C)) (sqrt.f64 (sqrt.f64 2))))

rewrite264.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

25.7b

Rules

70×	`sqrt-prod_binary64_5550`
65×	`add-sqr-sqrt_binary64_5556`
54×	`times-frac_binary64_5540`
41×	`add-cube-cbrt_binary64_5569` `*-un-lft-identity_binary64_5534`
37×	`associate-l_binary64_5475`
19×	`add-exp-log_binary64_5572` `add-cbrt-cube_binary64_5570`
10×	`pow1_binary64_5595` `associate-r_binary64_5474`
9×	`unswap-sqr_binary64_5502`
7×	`prod-exp_binary64_5583` `cbrt-unprod_binary64_5567`
6×	`associate-/r*_binary64_5478`
4×	`pow-prod-down_binary64_5605` `associate-/l*_binary64_5479`
3×	`div-exp_binary64_5585` `add-log-exp_binary64_5573` `cbrt-undiv_binary64_5568` `sqrt-undiv_binary64_5555` `sqrt-unprod_binary64_5554`
2×	`associate-l/_binary64_5477` `-commutative_binary64_5465` `div-inv_binary64_5531`
1×	`associate-*r/_binary64_5476` `frac-2neg_binary64_5545` `clear-num_binary64_5533`

Counts

3 → 136

Calls

3 calls:

16.0ms

(*.f64 (/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C)) (sqrt.f64 (sqrt.f64 2)))

15.0ms

(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C)) (sqrt.f64 (sqrt.f64 2))))

6.0ms

(/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C))

Compiler

Compiled 3482 to 2691 computations (22.7% saved)

series231.0ms (0.8%)

Error

25.7b

Counts

3 → 18

Calls

3 calls:

79.0ms

(*.f64 (/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C)) (sqrt.f64 (sqrt.f64 2)))

76.0ms

(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C)) (sqrt.f64 (sqrt.f64 2))))

59.0ms

(/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C))

Compiler

Compiled 978 to 982 computations (-0.4% saved)

simplify101.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5070	3107

prune215.0ms (0.7%)

Pruning

32 alts after pruning (30 fresh and 2 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	4	26	30
Picked	0	1	1
Done	0	1	1
Total	154	32	186

Error

25.7b

Counts

186 → 32

Compiler

Compiled 3337 to 2581 computations (22.7% saved)

regimes5.9s (19.9%)

Accuracy

Total 3.7b remaining (12%)

Threshold costs 0b (0%)

Compiler

Compiled 61029 to 46907 computations (23.1% saved)

bsearch18.0ms (0.1%)

Compiler: Compiled 40 to 32 computations (20% saved)

simplify67.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	1114	464
1	1114	464

Compiler

Compiled 598 to 410 computations (31.4% saved)

end0.0ms (0%)

sample11.5s (39.3%)

Algorithm

1×

intervals

Results

789.0ms	5476×	body	128	valid
555.0ms	940×	body	1024	valid
490.0ms	645×	body	2048	valid
460.0ms	810×	body	1024	nan
458.0ms	605×	body	2048	nan
358.0ms	2459×	body	128	nan
264.0ms	603×	body	512	valid
237.0ms	564×	body	512	nan
97.0ms	341×	body	256	nan
91.0ms	332×	body	256	valid
8.0ms	4×	body	4096	valid

Compiler

Compiled 9512 to 7234 computations (23.9% saved)

Details

analyze2.9s (9.7%)

sample149.0ms (0.5%)

simplify56.0ms (0.2%)

prune4.0ms (0%)

localize20.0ms (0.1%)

rewrite796.0ms (2.7%)

series5.1s (17.6%)

simplify132.0ms (0.4%)

prune910.0ms (3.1%)

localize7.0ms (0%)

rewrite64.0ms (0.2%)

series108.0ms (0.4%)

simplify117.0ms (0.4%)

prune106.0ms (0.4%)

localize11.0ms (0%)

rewrite157.0ms (0.5%)

series134.0ms (0.5%)

simplify90.0ms (0.3%)

prune189.0ms (0.6%)

localize11.0ms (0%)

rewrite264.0ms (0.9%)

series231.0ms (0.8%)

simplify101.0ms (0.3%)

prune215.0ms (0.7%)

regimes5.9s (19.9%)

bsearch18.0ms (0.1%)

simplify67.0ms (0.2%)

end0.0ms (0%)

sample11.5s (39.3%)

Profiling