Details

analyze623.0ms (10.1%)

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)

sample36.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	172×	body	128	valid
7.0ms	31×	body	2048	valid
4.0ms	22×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	15×	body	512	valid
1.0ms	18×	body	128	nan
0.0ms	10×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify196.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	309	20
1	309	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

Merged error: 32.9b

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)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.3b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
20.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite52.0ms (0.8%)

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:

19.0ms	(/.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))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series459.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
127.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
120.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4959	2578
1	4959	2578

prune433.0ms (7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	11	109

Merged error: 6.0b

Counts

109 → 11

Compiler

Compiled 8707 to 4134 computations (52.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.5b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
10.2b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
20.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite54.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
58×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`associate-/r/_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 129

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
12.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series875.0ms (14.1%)

Counts

4 → 12

Calls

4 calls:

357.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
293.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
114.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
112.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4955	4034
1	4955	4034

prune230.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	5	4	9
Picked	0	1	1
Done	0	1	1
Total	143	9	152

Merged error: 5.9b

Counts

152 → 9

Compiler

Compiled 5648 to 1837 computations (67.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.5b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
20.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
122×	`add-sqr-sqrt_binary64`
95×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
22×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
13×	`distribute-lft-out--_binary64`
12×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64` `div-exp_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 154

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series494.0ms (8%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
107.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
55.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5206	4824

prune180.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	2	4	6
Picked	1	0	1
Done	1	1	2
Total	168	7	175

Merged error: 5.9b

Counts

175 → 7

Compiler

Compiled 4728 to 1231 computations (74% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
20.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 85

Calls

4 calls:

11.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series633.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

352.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
105.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
54.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4926	2126
1	4926	2126

prune78.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	97	7	104

Merged error: 5.9b

Counts

104 → 7

Compiler

Compiled 2111 to 523 computations (75.2% saved)

regimes104.0ms (1.7%)

Compiler: Compiled 468 to 318 computations (32.1% saved)

bsearch89.0ms (1.4%)

Steps

Iters	Range	Point
8	8.0016144163214175e+99	4.786710960447229e+103	5.306662329996804e+102
10	-2.4195381281169627e-269	-2.0230317018985908e-280	-4.419827363071725e-280
6	-3.3286808707062796e+98	-2.902580959504667e+97	-2.392490559006445e+98

Iters

Range

Point

8.0016144163214175e+99

4.786710960447229e+103

5.306662329996804e+102

-2.4195381281169627e-269

-2.0230317018985908e-280

-4.419827363071725e-280

-3.3286808707062796e+98

-2.902580959504667e+97

-2.392490559006445e+98

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	70
1	92	70

end0.0ms (0%)

sample1.2s (19.3%)

Algorithm

1×

intervals

Results

245.0ms	1141×	body	2048	valid
244.0ms	5241×	body	128	valid
125.0ms	723×	body	1024	valid
100.0ms	379×	body	4096	valid
44.0ms	339×	body	512	valid
38.0ms	836×	body	128	nan
15.0ms	177×	body	256	valid
11.0ms	242×	body	128	invalid

Compiler

Compiled 170 to 111 computations (34.7% saved)

Details

analyze623.0ms (10.1%)

sample36.0ms (0.6%)

simplify196.0ms (3.2%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite52.0ms (0.8%)

series459.0ms (7.4%)

simplify86.0ms (1.4%)

prune433.0ms (7%)

localize9.0ms (0.1%)

rewrite54.0ms (0.9%)

series875.0ms (14.1%)

simplify61.0ms (1%)

prune230.0ms (3.7%)

localize10.0ms (0.2%)

rewrite53.0ms (0.9%)

series494.0ms (8%)

simplify100.0ms (1.6%)

prune180.0ms (2.9%)

localize10.0ms (0.2%)

rewrite38.0ms (0.6%)

series633.0ms (10.2%)

simplify72.0ms (1.2%)

prune78.0ms (1.3%)

regimes104.0ms (1.7%)

bsearch89.0ms (1.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.2s (19.3%)

Profiling