Details

analyze811.0ms (11.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4810	96
1	4810	96
0	3	3
1	3	3

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)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	42×	body	2048	valid
8.0ms	157×	body	128	valid
5.0ms	26×	body	1024	valid
3.0ms	9×	body	4096	valid
2.0ms	16×	body	512	valid
1.0ms	20×	body	128	nan
1.0ms	6×	body	256	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify329.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (323.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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: 32.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_419`
15×	`add-sqr-sqrt_binary64_441`
14×	`add-cube-cbrt_binary64_454`
12×	`times-frac_binary64_425`
8×	`add-log-exp_binary64_458`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`distribute-lft-out_binary64_370` `pow1_binary64_480`
4×	`associate-/l*_binary64_364`
3×	`sqrt-prod_binary64_435` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `pow1/2_binary64_499` `div-inv_binary64_416` `sum-log_binary64_510` `frac-2neg_binary64_430` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
7.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series231.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
31.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify94.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4970	2025
1	4970	2025

prune123.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Merged error: 3.7b

Counts

85 → 8

Compiler

Compiled 2128 to 1151 computations (45.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.5b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
8.0b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
20.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite52.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_425`
59×	`add-sqr-sqrt_binary64_441`
44×	`*-un-lft-identity_binary64_419`
30×	`add-cube-cbrt_binary64_454`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
14×	`difference-of-squares_binary64_388`
13×	`sqrt-prod_binary64_435` `associate-/l*_binary64_364`
10×	`associate-/r/_binary64_365` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
9×	`associate-/r*_binary64_363`
7×	`flip3--_binary64_423` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
6×	`add-log-exp_binary64_458` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `cancel-sign-sub-inv_binary64_385`
5×	`pow1_binary64_480`
2×	`sqrt-div_binary64_436` `clear-num_binary64_418` `frac-2neg_binary64_430`
1×	`sub-neg_binary64_412` `pow1/2_binary64_499` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`

Counts

4 → 136

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series506.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
168.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
59.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

simplify111.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5011	5032

prune205.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	149	7	156

Merged error: 3.6b

Counts

156 → 7

Compiler

Compiled 4788 to 2542 computations (46.9% saved)

localize13.0ms (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))))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.5b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_441`
28×	`*-un-lft-identity_binary64_419`
18×	`times-frac_binary64_425` `add-cube-cbrt_binary64_454`
11×	`sqrt-prod_binary64_435`
10×	`difference-of-squares_binary64_388`
8×	`add-log-exp_binary64_458`
7×	`cancel-sign-sub-inv_binary64_385`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `associate-/r*_binary64_363`
5×	`distribute-lft-out--_binary64_371` `pow1_binary64_480`
4×	`flip3--_binary64_423` `flip--_binary64_394`
3×	`associate-/l*_binary64_364`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `associate-/r/_binary64_365` `diff-log_binary64_511`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 88

Calls

4 calls:

10.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series333.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
60.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
34.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4882	2580
1	4882	2580

prune123.0ms (1.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	100	7	107

Merged error: 3.6b

Counts

107 → 7

Compiler

Compiled 2929 to 1732 computations (40.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_458` `add-sqr-sqrt_binary64_441`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `sqrt-prod_binary64_435` `pow1_binary64_480`
4×	`sqrt-div_binary64_436` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394`
2×	`sub-neg_binary64_412` `pow1/2_binary64_499` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385` `rem-sqrt-square_binary64_432`

Counts

4 → 54

Calls

4 calls:

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

series179.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
31.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4915	1236
1	4915	1236

prune97.0ms (1.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	66	7	73

Merged error: 3.6b

Counts

73 → 7

Compiler

Compiled 2448 to 1315 computations (46.3% saved)

regimes992.0ms (14.6%)

Compiler: Compiled 5322 to 3818 computations (28.3% saved)

bsearch64.0ms (0.9%)

Steps

Iters	Range	Point
4	2.38944338590728e+47	4.771398576646484e+47	4.65745276732901e+47
7	-3.4289192520051356e-240	-1.5893605367589336e-242	-1.8441922009769164e-242
4	-1.9544929856771155e+136	-1.0262434930020884e+136	-1.8546541145634366e+136

Iters

Range

Point

2.38944338590728e+47

4.771398576646484e+47

4.65745276732901e+47

-3.4289192520051356e-240

-1.5893605367589336e-242

-1.8441922009769164e-242

-1.9544929856771155e+136

-1.0262434930020884e+136

-1.8546541145634366e+136

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	131	97
1	131	97

end0.0ms (0%)

sample2.2s (32.9%)

Algorithm

1×

intervals

Results

281.0ms	1147×	body	2048	valid
271.0ms	5170×	body	128	valid
150.0ms	756×	body	1024	valid
116.0ms	377×	body	4096	valid
53.0ms	375×	body	512	valid
34.0ms	700×	body	128	nan
20.0ms	394×	body	128	invalid
17.0ms	175×	body	256	valid

Compiler

Compiled 1432 to 1020 computations (28.8% saved)

Details

analyze811.0ms (11.9%)

sample40.0ms (0.6%)

simplify329.0ms (4.8%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite31.0ms (0.5%)

series231.0ms (3.4%)

simplify94.0ms (1.4%)

prune123.0ms (1.8%)

localize12.0ms (0.2%)

rewrite52.0ms (0.8%)

series506.0ms (7.4%)

simplify111.0ms (1.6%)

prune205.0ms (3%)

localize13.0ms (0.2%)

rewrite34.0ms (0.5%)

series333.0ms (4.9%)

simplify81.0ms (1.2%)

prune123.0ms (1.8%)

localize14.0ms (0.2%)

rewrite22.0ms (0.3%)

series179.0ms (2.6%)

simplify58.0ms (0.9%)

prune97.0ms (1.4%)

regimes992.0ms (14.6%)

bsearch64.0ms (0.9%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (32.9%)

Profiling