Details

analyze992.0ms (11.2%)

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)

sample45.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	44×	body	2048	valid
7.0ms	163×	body	128	valid
4.0ms	15×	body	4096	valid
4.0ms	21×	body	1024	valid
1.0ms	17×	body	128	nan
1.0ms	9×	body	512	valid
0.0ms	10×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

prune5.0ms (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

35.1b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize11.0ms (0.1%)

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)
0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite147.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

34.9b

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:

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

Compiler

Compiled 2360 to 368 computations (84.4% saved)

series676.0ms (7.6%)

Error

5.6b

Counts

4 → 74

Calls

4 calls:

200.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
146.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
143.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
128.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2982 to 2078 computations (30.3% saved)

simplify87.0ms (1%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6067	3563

prune134.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	162	8	170
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	162	9	171

Error

5.5b

Counts

171 → 9

Compiler

Compiled 3222 to 677 computations (79% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
3.5b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
8.9b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite148.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

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×	`sqrt-prod_binary64` `associate-/r*_binary64`
7×	`flip3--_binary64` `flip--_binary64` `div-exp_binary64` `cbrt-undiv_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
5×	`pow1_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` `cancel-sign-sub-inv_binary64`

Counts

4 → 124

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)
11.0ms	(/.f64 (.f64 a 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)))

Compiler

Compiled 3729 to 526 computations (85.9% saved)

series839.0ms (9.5%)

Error

5.5b

Counts

4 → 76

Calls

4 calls:

279.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
235.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
140.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
127.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3672 to 2268 computations (38.2% saved)

simplify105.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4957	5030
1	4957	5030

prune144.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	202	7	209

Error

5.5b

Counts

209 → 7

Compiler

Compiled 4544 to 831 computations (81.7% saved)

localize9.0ms (0.1%)

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))
0.9b	(-.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))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite107.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

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×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64`
3×	`associate-/l*_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `associate-/r/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 85

Calls

4 calls:

10.0ms	(/.f64 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)
6.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2170 to 502 computations (76.9% saved)

series711.0ms (8%)

Error

5.5b

Counts

4 → 74

Calls

4 calls:

237.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
147.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
141.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
128.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3368 to 2392 computations (29% saved)

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5133	3221

prune116.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	159	7	166

Error

5.5b

Counts

166 → 7

Compiler

Compiled 3169 to 931 computations (70.6% saved)

localize11.0ms (0.1%)

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))))))
0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite235.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

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))))))
9.0ms	(-.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))

Compiler

Compiled 5552 to 1312 computations (76.4% saved)

series651.0ms (7.4%)

Error

5.5b

Counts

4 → 74

Calls

4 calls:

195.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
146.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
127.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
126.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3256 to 2352 computations (27.8% saved)

simplify112.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5023	6932

prune201.0ms (2.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	256	7	263

Error

5.5b

Counts

263 → 7

Compiler

Compiled 5846 to 1242 computations (78.8% saved)

regimes896.0ms (10.1%)

Accuracy

Total 1.0b remaining (16.7%)

Threshold costs 0b (0%)

Compiler

Compiled 5495 to 3395 computations (38.2% saved)

bsearch83.0ms (0.9%)

Steps

Iters	Range	Point
8	6.76140281917348e+86	1.298558282499754e+90	1.2768443745798854e+90
7	1.9133004274740636e-293	1.3977096778937352e-291	8.703437390764477e-293
6	-9.926481871620837e+110	-2.1860443976093696e+110	-6.521592839866794e+110

Iters

Range

Point

6.76140281917348e+86

1.298558282499754e+90

1.2768443745798854e+90

1.9133004274740636e-293

1.3977096778937352e-291

8.703437390764477e-293

-9.926481871620837e+110

-2.1860443976093696e+110

-6.521592839866794e+110

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	97	79
1	97	79

end0.0ms (0%)

sample2.2s (25.2%)

Algorithm

1×

intervals

Results

254.0ms	1114×	body	2048	valid
246.0ms	5184×	body	128	valid
130.0ms	745×	body	1024	valid
113.0ms	402×	body	4096	valid
53.0ms	359×	body	512	valid
36.0ms	764×	body	128	nan
17.0ms	196×	body	256	valid
10.0ms	225×	body	128	invalid

Compiler

Compiled 1390 to 860 computations (38.1% saved)

Details

analyze992.0ms (11.2%)

sample45.0ms (0.5%)

simplify74.0ms (0.8%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

rewrite147.0ms (1.7%)

series676.0ms (7.6%)

simplify87.0ms (1%)

prune134.0ms (1.5%)

localize10.0ms (0.1%)

rewrite148.0ms (1.7%)

series839.0ms (9.5%)

simplify105.0ms (1.2%)

prune144.0ms (1.6%)

localize9.0ms (0.1%)

rewrite107.0ms (1.2%)

series711.0ms (8%)

simplify56.0ms (0.6%)

prune116.0ms (1.3%)

localize11.0ms (0.1%)

rewrite235.0ms (2.7%)

series651.0ms (7.4%)

simplify112.0ms (1.3%)

prune201.0ms (2.3%)

regimes896.0ms (10.1%)

bsearch83.0ms (0.9%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample2.2s (25.2%)

Profiling