Details

analyze460.0ms (7%)

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)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	172×	body	128	valid
6.0ms	26×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	18×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify233.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune8.0ms (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: 35.0b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_445`
14×	`*-un-lft-identity_binary64_423`
9×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`add-cube-cbrt_binary64_458` `add-log-exp_binary64_462`
6×	`times-frac_binary64_429` `sqrt-prod_binary64_439` `difference-of-squares_binary64_392` `associate-/l*_binary64_368`
5×	`pow1_binary64_484`
4×	`cancel-sign-sub-inv_binary64_389` `flip3--_binary64_427` `flip--_binary64_398`
3×	`distribute-lft-out--_binary64_375`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `diff-log_binary64_515` `associate-/l/_binary64_370` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`prod-exp_binary64_472` `rem-sqrt-square_binary64_436` `div-sub_binary64_428` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `associate-/r*_binary64_367` `cbrt-unprod_binary64_456`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.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	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series516.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
123.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5031	1979

prune483.0ms (7.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	9	87

Merged error: 7.0b

Counts

87 → 9

Compiler

Compiled 9255 to 6459 computations (30.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.5b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
9.7b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
22×	`times-frac_binary64_429`
21×	`*-un-lft-identity_binary64_423`
17×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
13×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
12×	`add-sqr-sqrt_binary64_445`
11×	`add-cube-cbrt_binary64_458` `associate-/l*_binary64_368`
6×	`associate-/r/_binary64_369` `add-log-exp_binary64_462`
5×	`distribute-lft-out_binary64_374` `pow1_binary64_484` `associate-/r*_binary64_367`
4×	`flip-+_binary64_397` `flip3-+_binary64_426` `div-inv_binary64_420`
3×	`sqrt-prod_binary64_439`
2×	`sqrt-div_binary64_440` `clear-num_binary64_422` `frac-2neg_binary64_434`
1×	`+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `flip3--_binary64_427` `associate-/l/_binary64_370` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `flip--_binary64_398` `sum-log_binary64_514`

Counts

4 → 102

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series923.0ms (14.1%)

Counts

4 → 12

Calls

4 calls:

376.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
297.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
130.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5005	3121

prune268.0ms (4.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	115	8	123

Merged error: 6.9b

Counts

123 → 8

Compiler

Compiled 5639 to 3725 computations (33.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_423`
15×	`add-sqr-sqrt_binary64_445`
14×	`add-cube-cbrt_binary64_458`
12×	`times-frac_binary64_429`
8×	`add-log-exp_binary64_462`
6×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
5×	`distribute-lft-out_binary64_374` `pow1_binary64_484`
4×	`associate-/r*_binary64_367`
3×	`sqrt-prod_binary64_439` `associate-/l*_binary64_368`
2×	`sqrt-div_binary64_440` `flip-+_binary64_397` `flip3--_binary64_427` `associate-/r/_binary64_369` `flip3-+_binary64_426` `flip--_binary64_398`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `sum-log_binary64_514`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series607.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

314.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
121.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5099	1969

prune111.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	85	7	92

Merged error: 6.9b

Counts

92 → 7

Compiler

Compiled 2405 to 1517 computations (36.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) c))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64_429`
80×	`*-un-lft-identity_binary64_423`
55×	`add-sqr-sqrt_binary64_445`
54×	`add-cube-cbrt_binary64_458`
16×	`associate-/r*_binary64_367`
15×	`add-exp-log_binary64_461`
13×	`distribute-lft-out_binary64_374`
9×	`add-cbrt-cube_binary64_459`
8×	`add-log-exp_binary64_462`
7×	`div-exp_binary64_474`
6×	`pow1_binary64_484`
5×	`div-inv_binary64_420`
3×	`sqrt-prod_binary64_439` `associate-/l*_binary64_368` `cbrt-undiv_binary64_457`
2×	`rec-exp_binary64_473` `1-exp_binary64_467` `sqrt-div_binary64_440` `flip3--_binary64_427` `flip--_binary64_398`
1×	`sub-neg_binary64_416` `flip-+_binary64_397` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `associate-/r/_binary64_369` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434` `pow-flip_binary64_497` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `inv-pow_binary64_508` `sum-log_binary64_514`

Counts

4 → 127

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) c))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series574.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) c))
126.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5286	4178

prune192.0ms (2.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	139	7	146

Merged error: 6.9b

Counts

146 → 7

Compiler

Compiled 4092 to 2569 computations (37.2% saved)

regimes142.0ms (2.2%)

Compiler: Compiled 372 to 312 computations (16.1% saved)

bsearch114.0ms (1.7%)

Steps

Iters	Range		Point
8	5.047843856159705e+79	3.275486995190224e+82	9.885898561182225e+81
11	-3.290852731649204e-307	2.1876641165742222e-285	-2.112715670541307e-307
9	-3.141987374119816e+97	-1.5578411367101382e+89	-2.3585860632819396e+97

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample1.4s (20.8%)

Algorithm

1×

intervals

Results

281.0ms	1134×	body	2048	valid
273.0ms	5060×	body	128	valid
156.0ms	792×	body	1024	valid
129.0ms	417×	body	4096	valid
57.0ms	403×	body	512	valid
33.0ms	666×	body	128	nan
23.0ms	194×	body	256	valid
20.0ms	380×	body	128	invalid

Compiler

Compiled 195 to 151 computations (22.6% saved)

Details

analyze460.0ms (7%)

sample41.0ms (0.6%)

simplify233.0ms (3.5%)

prune8.0ms (0.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.6%)

series516.0ms (7.9%)

simplify75.0ms (1.1%)

prune483.0ms (7.4%)

localize15.0ms (0.2%)

rewrite55.0ms (0.8%)

series923.0ms (14.1%)

simplify74.0ms (1.1%)

prune268.0ms (4.1%)

localize15.0ms (0.2%)

rewrite32.0ms (0.5%)

series607.0ms (9.2%)

simplify71.0ms (1.1%)

prune111.0ms (1.7%)

localize14.0ms (0.2%)

rewrite43.0ms (0.7%)

series574.0ms (8.8%)

simplify78.0ms (1.2%)

prune192.0ms (2.9%)

regimes142.0ms (2.2%)

bsearch114.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (20.8%)

Profiling