Details

analyze926.0ms (7.8%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample85.0ms (0.7%)

Algorithm

1×

intervals

Results

26.0ms	46×	body	2048	valid
16.0ms	153×	body	128	valid
12.0ms	30×	body	1024	valid
4.0ms	13×	body	512	valid
4.0ms	6×	body	4096	valid
2.0ms	25×	body	128	nan
2.0ms	8×	body	256	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify415.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune7.0ms (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: 35.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_414`
15×	`add-sqr-sqrt_binary64_435`
14×	`add-cube-cbrt_binary64_446`
12×	`times-frac_binary64_420`
8×	`add-log-exp_binary64_450`
6×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
5×	`pow1_binary64_472` `distribute-lft-out_binary64_367`
4×	`associate-/l*_binary64_361`
3×	`sqrt-prod_binary64_429` `associate-/r*_binary64_360`
2×	`flip3--_binary64_418` `sqrt-div_binary64_430` `flip3-+_binary64_417` `flip-+_binary64_388` `flip--_binary64_389` `associate-/l/_binary64_363`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `frac-2neg_binary64_425` `pow1/2_binary64_491` `sum-log_binary64_502` `div-exp_binary64_462` `rem-sqrt-square_binary64_427`

Counts

4 → 71

Calls

4 calls:

18.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series892.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

289.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
242.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
238.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
123.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify129.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5412	2012

prune233.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Merged error: 3.8b

Counts

84 → 8

Compiler

Compiled 2130 to 1159 computations (45.6% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.9b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
9.8b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite108.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_420`
53×	`add-sqr-sqrt_binary64_435`
40×	`*-un-lft-identity_binary64_414`
28×	`add-cube-cbrt_binary64_446`
27×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
13×	`associate-/l*_binary64_361`
12×	`difference-of-squares_binary64_383`
10×	`associate-/r/_binary64_362` `cbrt-undiv_binary64_445` `div-exp_binary64_462`
9×	`sqrt-prod_binary64_429` `associate-/r*_binary64_360`
7×	`flip3--_binary64_418` `flip--_binary64_389`
6×	`distribute-lft-out--_binary64_368` `div-inv_binary64_411` `prod-exp_binary64_460` `add-log-exp_binary64_450` `cbrt-unprod_binary64_444`
5×	`pow1_binary64_472`
2×	`clear-num_binary64_413` `sqrt-div_binary64_430` `frac-2neg_binary64_425`
1×	`diff-log_binary64_503` `sqrt-pow1_binary64_431` `sub-neg_binary64_407` `pow1/2_binary64_491` `associate-/l/_binary64_363` `rem-sqrt-square_binary64_427`

Counts

4 → 127

Calls

4 calls:

31.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
26.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series1.8s (15.1%)

Counts

4 → 12

Calls

4 calls:

794.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
634.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
235.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
124.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify130.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5440	4678

prune362.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	140	7	147

Merged error: 3.7b

Counts

147 → 7

Compiler

Compiled 4520 to 2395 computations (47% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite72.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_435`
26×	`*-un-lft-identity_binary64_414`
18×	`times-frac_binary64_420`
16×	`add-cube-cbrt_binary64_446`
10×	`difference-of-squares_binary64_383`
8×	`sqrt-prod_binary64_429` `add-log-exp_binary64_450`
6×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `associate-/r*_binary64_360`
5×	`distribute-lft-out--_binary64_368` `pow1_binary64_472`
4×	`flip3--_binary64_418` `flip--_binary64_389`
3×	`associate-/l*_binary64_361`
2×	`associate-/r/_binary64_362` `sqrt-div_binary64_430` `diff-log_binary64_503` `sub-neg_binary64_407`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `cbrt-undiv_binary64_445` `frac-2neg_binary64_425` `pow1/2_binary64_491` `div-exp_binary64_462` `rem-sqrt-square_binary64_427`

Counts

4 → 81

Calls

4 calls:

18.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
18.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series1.2s (10.3%)

Counts

4 → 12

Calls

4 calls:

669.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
223.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
212.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
114.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify130.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5183	2447

prune217.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Merged error: 3.7b

Counts

100 → 7

Compiler

Compiled 2793 to 1653 computations (40.8% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite102.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_420`
121×	`add-sqr-sqrt_binary64_435`
94×	`*-un-lft-identity_binary64_414`
68×	`add-cube-cbrt_binary64_446`
26×	`difference-of-squares_binary64_383`
22×	`associate-/r*_binary64_360`
16×	`sqrt-prod_binary64_429`
13×	`distribute-lft-out--_binary64_368`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
5×	`pow1_binary64_472` `div-inv_binary64_411`
3×	`flip3--_binary64_418` `cbrt-undiv_binary64_445` `flip--_binary64_389` `associate-/l*_binary64_361` `div-exp_binary64_462`
2×	`sqrt-div_binary64_430` `diff-log_binary64_503` `sub-neg_binary64_407`
1×	`associate-/r/_binary64_362` `clear-num_binary64_413` `sqrt-pow1_binary64_431` `frac-2neg_binary64_425` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 146

Calls

4 calls:

29.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
14.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series1.0s (8.5%)

Counts

4 → 12

Calls

4 calls:

469.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
214.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
201.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
118.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify188.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5045	5651

prune396.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	158	7	165

Merged error: 3.7b

Counts

165 → 7

Compiler

Compiled 5181 to 3004 computations (42% saved)

regimes389.0ms (3.3%)

Compiler: Compiled 396 to 327 computations (17.4% saved)

bsearch171.0ms (1.4%)

Steps

Iters	Range	Point
10	1.442481943309455e+100	4.8347581356643973e+117	1.9271617357234682e+116
3	5.942762572340772e-255	7.897146787474367e-255	6.55350763957002e-255
9	-1.5038904548886159e+158	-1.2031326694220234e+152	-4.630605456274428e+153

Iters

Range

Point

1.442481943309455e+100

4.8347581356643973e+117

1.9271617357234682e+116

5.942762572340772e-255

7.897146787474367e-255

6.55350763957002e-255

-1.5038904548886159e+158

-1.2031326694220234e+152

-4.630605456274428e+153

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	116	95
1	116	95

end0.0ms (0%)

sample2.7s (22.7%)

Algorithm

1×

intervals

Results

576.0ms	1173×	body	2048	valid
514.0ms	5111×	body	128	valid
295.0ms	754×	body	1024	valid
234.0ms	378×	body	4096	valid
112.0ms	394×	body	512	valid
62.0ms	658×	body	128	nan
36.0ms	190×	body	256	valid
35.0ms	360×	body	128	invalid

Compiler

Compiled 254 to 192 computations (24.4% saved)

Details

analyze926.0ms (7.8%)

sample85.0ms (0.7%)

simplify415.0ms (3.5%)

prune7.0ms (0.1%)

localize22.0ms (0.2%)

rewrite62.0ms (0.5%)

series892.0ms (7.6%)

simplify129.0ms (1.1%)

prune233.0ms (2%)

localize25.0ms (0.2%)

rewrite108.0ms (0.9%)

series1.8s (15.1%)

simplify130.0ms (1.1%)

prune362.0ms (3.1%)

localize27.0ms (0.2%)

rewrite72.0ms (0.6%)

series1.2s (10.3%)

simplify130.0ms (1.1%)

prune217.0ms (1.8%)

localize26.0ms (0.2%)

rewrite102.0ms (0.9%)

series1.0s (8.5%)

simplify188.0ms (1.6%)

prune396.0ms (3.4%)

regimes389.0ms (3.3%)

bsearch171.0ms (1.4%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample2.7s (22.7%)

Profiling