Details

analyze619.0ms (9.6%)

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)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	162×	body	128	valid
7.0ms	33×	body	2048	valid
4.0ms	27×	body	1024	valid
4.0ms	15×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	10×	body	256	valid
1.0ms	20×	body	128	nan
0.0ms	9×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify171.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

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

34.2b

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)
1.2b	(-.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))))
22.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite51.0ms (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:

20.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(-.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)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series480.0ms (7.4%)

Counts

4 → 54

Calls

4 calls:

148.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
126.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
113.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
93.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1353 to 1121 computations (17.1% saved)

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5790	2975

prune135.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	139	11	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	11	151

Error

5.6b

Counts

151 → 11

Compiler

Compiled 2864 to 530 computations (81.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
3.7b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
10.1b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
22.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`difference-of-squares_binary64`
10×	`associate-/r/_binary64`
9×	`associate-/r*_binary64` `sqrt-prod_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_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` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 124

Calls

4 calls:

13.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
11.0ms	(/.f64 (.f64 a c) (-.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))

series601.0ms (9.3%)

Counts

4 → 58

Calls

4 calls:

189.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
158.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
128.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
126.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1825 to 1308 computations (28.3% saved)

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4995	4330
1	4995	4330

prune132.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	7	3	10
Picked	0	1	1
Done	0	0	0
Total	187	6	193

Error

5.6b

Counts

193 → 6

Compiler

Compiled 4060 to 647 computations (84.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
22.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite35.0ms (0.5%)

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:

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

series568.0ms (8.8%)

Counts

4 → 63

Calls

4 calls:

162.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
149.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
129.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
127.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1886 to 1544 computations (18.1% saved)

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5117	2774

prune105.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	148	6	154

Error

5.6b

Counts

154 → 6

Compiler

Compiled 2855 to 794 computations (72.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
7.4b	(-.f64 (/.f64 b_2 (neg.f64 a)) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))
22.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite69.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

43.0ms	(-.f64 (/.f64 b_2 (neg.f64 a)) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))
6.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series501.0ms (7.7%)

Counts

4 → 54

Calls

4 calls:

159.0ms	(-.f64 (/.f64 b_2 (neg.f64 a)) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))
130.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
124.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
87.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1488 to 1186 computations (20.3% saved)

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4956	3357
1	4956	3357

prune111.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	167	6	173

Error

5.6b

Counts

173 → 6

Compiler

Compiled 3304 to 476 computations (85.6% saved)

regimes626.0ms (9.7%)

Accuracy

Total 1.0b remaining (14.5%)

Threshold costs 1.0b (14.5%)

Compiler

Compiled 3992 to 2253 computations (43.6% saved)

bsearch101.0ms (1.6%)

Steps

Iters	Range	Point
8	3.329121997534982e+111	2.824689334732582e+115	8.501638784003518e+114
10	-8.126101094582806e-215	-2.6289303014612727e-226	-2.6604198772285348e-226
8	-1.4681035978426096e+156	-4.6727719348856836e+153	-1.3437071385932138e+154

Iters

Range

Point

3.329121997534982e+111

2.824689334732582e+115

8.501638784003518e+114

-8.126101094582806e-215

-2.6289303014612727e-226

-2.6604198772285348e-226

-1.4681035978426096e+156

-4.6727719348856836e+153

-1.3437071385932138e+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	100	72
1	100	72

end0.0ms (0%)

sample1.7s (26.4%)

Algorithm

1×

intervals

Results

232.0ms	5234×	body	128	valid
223.0ms	1101×	body	2048	valid
120.0ms	739×	body	1024	valid
102.0ms	373×	body	4096	valid
47.0ms	359×	body	512	valid
32.0ms	793×	body	128	nan
16.0ms	194×	body	256	valid
10.0ms	240×	body	128	invalid

Compiler

Compiled 1024 to 580 computations (43.4% saved)

Details

analyze619.0ms (9.6%)

sample41.0ms (0.6%)

simplify171.0ms (2.6%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite51.0ms (0.8%)

series480.0ms (7.4%)

simplify80.0ms (1.2%)

prune135.0ms (2.1%)

localize10.0ms (0.1%)

rewrite44.0ms (0.7%)

series601.0ms (9.3%)

simplify96.0ms (1.5%)

prune132.0ms (2%)

localize9.0ms (0.1%)

rewrite35.0ms (0.5%)

series568.0ms (8.8%)

simplify72.0ms (1.1%)

prune105.0ms (1.6%)

localize10.0ms (0.2%)

rewrite69.0ms (1.1%)

series501.0ms (7.7%)

simplify78.0ms (1.2%)

prune111.0ms (1.7%)

regimes626.0ms (9.7%)

bsearch101.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.7s (26.4%)

Profiling