Details

analyze603.0ms (10.3%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	164×	body	128	valid
6.0ms	28×	body	2048	valid
6.0ms	29×	body	1024	valid
4.0ms	15×	body	4096	valid
1.0ms	11×	body	512	valid
1.0ms	21×	body	128	nan
1.0ms	9×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify194.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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: 35.2b

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))
2.1b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`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 → 89

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

series469.0ms (8%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
131.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
127.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
53.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4922	2470
1	4922	2470

prune116.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	90	11	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	12	102

Merged error: 6.1b

Counts

102 → 12

Compiler

Compiled 2331 to 483 computations (79.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.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)
10.4b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
28×	`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`
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 → 126

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
13.0ms	(/.f64 (.f64 a 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)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series905.0ms (15.5%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
297.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
119.0ms	(-.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)))

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4936	4018
1	4936	4018

prune124.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	132	6	138
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	139	11	150

Merged error: 6.0b

Counts

150 → 11

Compiler

Compiled 3642 to 629 computations (82.7% saved)

localize13.0ms (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))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`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` `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 → 81

Calls

4 calls:

12.0ms	(/.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)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series652.0ms (11.1%)

Counts

4 → 12

Calls

4 calls:

382.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
118.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
100.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
51.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5200	2111

prune89.0ms (1.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	93	11	104

Merged error: 6.0b

Counts

104 → 11

Compiler

Compiled 2373 to 794 computations (66.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.4b	(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`
121×	`add-sqr-sqrt_binary64`
94×	`*-un-lft-identity_binary64`
68×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
22×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`div-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_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 → 152

Calls

4 calls:

16.0ms	(/.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)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series478.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
95.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
54.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4895	4846
1	4895	4846

prune133.0ms (2.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	164	11	175

Merged error: 6.0b

Counts

175 → 11

Compiler

Compiled 3985 to 762 computations (80.9% saved)

regimes157.0ms (2.7%)

Compiler: Compiled 676 to 498 computations (26.3% saved)

bsearch89.0ms (1.5%)

Steps

Iters	Range	Point
7	1.3458593302197346e+101	1.7253578096583875e+103	1.3577439535016504e+103
9	1.1899857569594048e-253	4.952441610662435e-245	9.072727894507963e-250
7	-4.169266455093426e+154	-3.026978260297388e+152	-1.2845873895350852e+154

Iters

Range

Point

1.3458593302197346e+101

1.7253578096583875e+103

1.3577439535016504e+103

1.1899857569594048e-253

4.952441610662435e-245

9.072727894507963e-250

-4.169266455093426e+154

-3.026978260297388e+152

-1.2845873895350852e+154

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	121	79
1	121	79

end0.0ms (0%)

sample1.2s (21%)

Algorithm

1×

intervals

Results

236.0ms	1104×	body	2048	valid
229.0ms	5226×	body	128	valid
126.0ms	731×	body	1024	valid
107.0ms	413×	body	4096	valid
42.0ms	343×	body	512	valid
33.0ms	797×	body	128	nan
21.0ms	183×	body	256	valid
11.0ms	263×	body	128	invalid

Compiler

Compiled 228 to 159 computations (30.3% saved)

Details

analyze603.0ms (10.3%)

sample38.0ms (0.6%)

simplify194.0ms (3.3%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite53.0ms (0.9%)

series469.0ms (8%)

simplify79.0ms (1.4%)

prune116.0ms (2%)

localize9.0ms (0.2%)

rewrite56.0ms (1%)

series905.0ms (15.5%)

simplify93.0ms (1.6%)

prune124.0ms (2.1%)

localize13.0ms (0.2%)

rewrite38.0ms (0.6%)

series652.0ms (11.1%)

simplify68.0ms (1.2%)

prune89.0ms (1.5%)

localize9.0ms (0.2%)

rewrite53.0ms (0.9%)

series478.0ms (8.2%)

simplify80.0ms (1.4%)

prune133.0ms (2.3%)

regimes157.0ms (2.7%)

bsearch89.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (21%)

Profiling