Details

analyze605.0ms (11.6%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample44.0ms (0.8%)

Algorithm

1×

intervals

Results

14.0ms	186×	body	128	valid
4.0ms	15×	body	4096	valid
4.0ms	16×	body	2048	valid
4.0ms	19×	body	1024	valid
2.0ms	12×	body	512	valid
1.0ms	30×	body	128	nan
1.0ms	8×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify174.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

29.9b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
2.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
20.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
11×	`sqrt-prod_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 96

Calls

4 calls:

20.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
11.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series225.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
64.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
60.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
28.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4941	2578
1	4941	2578

prune115.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	100	9	109

Error

5.3b

Counts

109 → 9

Compiler

Compiled 2377 to 450 computations (81.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
2.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
20.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite60.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
132×	`add-sqr-sqrt_binary64`
131×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
19×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 182

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
11.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series241.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
61.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
47.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
25.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify102.0ms (2%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5030	5933

prune166.0ms (3.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	193	10	203

Error

5.3b

Counts

203 → 10

Compiler

Compiled 5027 to 996 computations (80.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
20.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`cancel-sign-sub-inv_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
1×	`sub-neg_binary64` `associate--l-_binary64` `neg-sub0_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`

Counts

4 → 68

Calls

4 calls:

10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series205.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
53.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
48.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
48.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5133	1397

prune99.0ms (1.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	80	10	90

Error

5.3b

Counts

90 → 10

Compiler

Compiled 4039 to 539 computations (86.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
14.4b	(/.f64 (*.f64 a c) a)
20.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 63

Calls

4 calls:

9.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(/.f64 (*.f64 a c) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series150.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
26.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(/.f64 (*.f64 a c) a)

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4840	973
1	4840	973

prune54.0ms (1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	1	5	6
Picked	1	0	1
Done	0	3	3
Total	75	10	85

Error

5.3b

Counts

85 → 10

Compiler

Compiled 1541 to 295 computations (80.9% saved)

regimes718.0ms (13.8%)

Accuracy

Total 0.9b remaining (14.6%)

Threshold costs 0.9b (14.6%)

Compiler

Compiled 3815 to 2322 computations (39.1% saved)

bsearch106.0ms (2%)

Steps

Iters	Range	Point
7	8.631274828116202e+97	4.456590487523489e+99	3.086691257664919e+98
9	-7.903257010419409e-230	-6.005878130469408e-235	-6.058114844713645e-235
9	-9.874403039960465e+155	-1.1014546475208706e+148	-1.121424513812188e+154

Iters

Range

Point

8.631274828116202e+97

4.456590487523489e+99

3.086691257664919e+98

-7.903257010419409e-230

-6.005878130469408e-235

-6.058114844713645e-235

-9.874403039960465e+155

-1.1014546475208706e+148

-1.121424513812188e+154

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	118	79
1	118	79

end0.0ms (0%)

sample1.8s (33.7%)

Algorithm

1×

intervals

Results

245.0ms	5245×	body	128	valid
238.0ms	1102×	body	2048	valid
131.0ms	734×	body	1024	valid
104.0ms	387×	body	4096	valid
45.0ms	359×	body	512	valid
33.0ms	769×	body	128	nan
15.0ms	173×	body	256	valid
11.0ms	247×	body	128	invalid

Compiler

Compiled 977 to 595 computations (39.1% saved)

Details

analyze605.0ms (11.6%)

sample44.0ms (0.8%)

simplify174.0ms (3.3%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite50.0ms (1%)

series225.0ms (4.3%)

simplify75.0ms (1.4%)

prune115.0ms (2.2%)

localize11.0ms (0.2%)

rewrite60.0ms (1.2%)

series241.0ms (4.6%)

simplify102.0ms (2%)

prune166.0ms (3.2%)

localize14.0ms (0.3%)

rewrite31.0ms (0.6%)

series205.0ms (3.9%)

simplify71.0ms (1.4%)

prune99.0ms (1.9%)

localize10.0ms (0.2%)

rewrite26.0ms (0.5%)

series150.0ms (2.9%)

simplify76.0ms (1.5%)

prune54.0ms (1%)

regimes718.0ms (13.8%)

bsearch106.0ms (2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.8s (33.7%)

Profiling