Details

analyze1.0s (11.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1992	80
1	1992	80
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
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 (0.5%)

Algorithm

1×

intervals

Results

8.0ms	170×	body	128	valid
7.0ms	31×	body	2048	valid
4.0ms	24×	body	1024	valid
3.0ms	12×	body	4096	valid
2.0ms	15×	body	512	valid
1.0ms	22×	body	128	nan
0.0ms	6×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify72.0ms (0.8%)

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%)

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

31.6b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize16.0ms (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)
0.9b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
20.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite152.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

31.4b

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×	`diff-log_binary64` `associate-/r*_binary64`
2×	`sqrt-div_binary64` `sub-neg_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `neg-sub0_binary64` `associate--l-_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 96

Calls

4 calls:

13.0ms	(/.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))

Compiler

Compiled 2360 to 368 computations (84.4% saved)

series579.0ms (6.5%)

Error

5.4b

Counts

4 → 60

Calls

4 calls:

201.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
130.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
105.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
96.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2221 to 1578 computations (29% saved)

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5827	3125

prune125.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	147	9	156
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	147	10	157

Error

5.3b

Counts

157 → 10

Compiler

Compiled 2883 to 546 computations (81.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.9b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
20.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite244.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

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` `flip--_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sqrt-div_binary64` `sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `neg-sub0_binary64` `associate--l-_binary64` `inv-pow_binary64` `pow-flip_binary64` `frac-2neg_binary64` `clear-num_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))))))
10.0ms	(-.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	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 5552 to 1312 computations (76.4% saved)

series575.0ms (6.5%)

Error

5.3b

Counts

4 → 60

Calls

4 calls:

208.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
130.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
108.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
86.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2443 to 1800 computations (26.3% saved)

simplify119.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4991	6494
1	4991	6494

prune197.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	240	2	242
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	243	9	252

Error

5.3b

Counts

252 → 9

Compiler

Compiled 5556 to 1140 computations (79.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.4b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
9.0b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
20.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite165.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

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×	`sqrt-prod_binary64` `associate-/r/_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `flip--_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`sqrt-div_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l/_binary64` `diff-log_binary64` `sub-neg_binary64`

Counts

4 → 129

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)
11.0ms	(/.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)))

Compiler

Compiled 3886 to 521 computations (86.6% saved)

series860.0ms (9.7%)

Error

5.3b

Counts

4 → 70

Calls

4 calls:

261.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
220.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
195.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
129.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3724 to 2339 computations (37.2% saved)

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5280	5172

prune151.0ms (1.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	199	9	208

Error

5.3b

Counts

208 → 9

Compiler

Compiled 4625 to 879 computations (81% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
12.5b	(/.f64 (*.f64 a c) a)
20.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite81.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

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

Counts

4 → 65

Calls

4 calls:

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)))
4.0ms	(/.f64 (*.f64 a c) a)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1706 to 433 computations (74.6% saved)

series520.0ms (5.9%)

Error

5.3b

Counts

4 → 64

Calls

4 calls:

184.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
130.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
124.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
26.0ms	(/.f64 (*.f64 a c) a)

Compiler

Compiled 3460 to 2221 computations (35.8% saved)

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4947	1854
1	4947	1854

prune102.0ms (1.2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	129	9	138

Error

5.3b

Counts

138 → 9

Compiler

Compiled 2774 to 817 computations (70.5% saved)

regimes1.2s (13.5%)

Accuracy

Total 1.0b remaining (15.3%)

Threshold costs 1.0b (15.3%)

Compiler

Compiled 6465 to 3719 computations (42.5% saved)

bsearch94.0ms (1.1%)

Steps

Iters	Range	Point
5	2.4582065864223775e+86	9.291532526416511e+86	6.79328400373391e+86
8	-1.262858342039236e-276	-2.3317726789561077e-281	-2.45851834527593e-281
8	-8.957592937832097e+134	-1.3683314138471575e+131	-1.3907884444731015e+134

Iters

Range

Point

2.4582065864223775e+86

9.291532526416511e+86

6.79328400373391e+86

-1.262858342039236e-276

-2.3317726789561077e-281

-2.45851834527593e-281

-8.957592937832097e+134

-1.3683314138471575e+131

-1.3907884444731015e+134

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	97	82
1	97	82

end0.0ms (0%)

sample2.3s (25.9%)

Algorithm

1×

intervals

Results

263.0ms	1200×	body	2048	valid
234.0ms	5152×	body	128	valid
112.0ms	675×	body	1024	valid
107.0ms	402×	body	4096	valid
52.0ms	384×	body	512	valid
32.0ms	789×	body	128	nan
16.0ms	187×	body	256	valid
10.0ms	238×	body	128	invalid

Compiler

Compiled 1642 to 949 computations (42.2% saved)

Details

analyze1.0s (11.5%)

sample41.0ms (0.5%)

simplify72.0ms (0.8%)

prune4.0ms (0%)

localize16.0ms (0.2%)

rewrite152.0ms (1.7%)

series579.0ms (6.5%)

simplify78.0ms (0.9%)

prune125.0ms (1.4%)

localize11.0ms (0.1%)

rewrite244.0ms (2.8%)

series575.0ms (6.5%)

simplify119.0ms (1.3%)

prune197.0ms (2.2%)

localize10.0ms (0.1%)

rewrite165.0ms (1.9%)

series860.0ms (9.7%)

simplify75.0ms (0.9%)

prune151.0ms (1.7%)

localize11.0ms (0.1%)

rewrite81.0ms (0.9%)

series520.0ms (5.9%)

simplify66.0ms (0.7%)

prune102.0ms (1.2%)

regimes1.2s (13.5%)

bsearch94.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.3s (25.9%)

Profiling