Details

analyze1.0s (8.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1992	72
1	1992	72
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 (0.4%)

Algorithm

1×

intervals

Results

7.0ms	159×	body	128	valid
7.0ms	35×	body	2048	valid
5.0ms	32×	body	1024	valid
4.0ms	16×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	25×	body	128	nan
0.0ms	5×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

35.1b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite152.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

34.9b

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-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64`
3×	`associate-/r*_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 86

Calls

4 calls:

14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
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 2014 to 333 computations (83.5% saved)

series839.0ms (7.3%)

Error

5.0b

Counts

4 → 64

Calls

4 calls:

261.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
185.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
173.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
165.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2403 to 1692 computations (29.6% saved)

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4989	2834
1	4989	2834

prune139.0ms (1.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	137	13	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	13	151

Error

4.8b

Counts

151 → 13

Compiler

Compiled 2774 to 617 computations (77.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite132.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

30×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `associate-r_binary64`
11×	`times-frac_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`difference-of-squares_binary64` `cancel-sign-sub-inv_binary64` `prod-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64` `un-div-inv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

17.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
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 b_2 b_2) (.f64 a c))

Compiler

Compiled 2156 to 599 computations (72.2% saved)

series831.0ms (7.3%)

Error

4.8b

Counts

4 → 64

Calls

4 calls:

262.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
190.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
178.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
151.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2649 to 1950 computations (26.4% saved)

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5015	2586

prune138.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	147	4	151
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	152	12	164

Error

4.8b

Counts

164 → 12

Compiler

Compiled 2825 to 879 computations (68.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.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))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite244.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

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

Counts

4 → 164

Calls

4 calls:

16.0ms	(/.f64 1 (/.f64 a (-.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)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 4825 to 1174 computations (75.7% saved)

series813.0ms (7.1%)

Error

4.8b

Counts

4 → 64

Calls

4 calls:

261.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
183.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
166.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
153.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2649 to 1941 computations (26.7% saved)

simplify110.0ms (1%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4966	5825
1	4966	5825

prune221.0ms (1.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	228	12	240

Error

4.8b

Counts

240 → 12

Compiler

Compiled 5130 to 1158 computations (77.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (-.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))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite919.0ms (8%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

789×	`times-frac_binary64`
494×	`add-sqr-sqrt_binary64`
407×	`*-un-lft-identity_binary64`
321×	`add-cube-cbrt_binary64`
86×	`difference-of-squares_binary64`
46×	`sqrt-prod_binary64`
44×	`add-exp-log_binary64`
43×	`distribute-lft-out--_binary64`
40×	`div-inv_binary64`
32×	`div-exp_binary64`
29×	`associate-/r/_binary64`
24×	`associate-/r*_binary64`
17×	`flip3--_binary64` `flip--_binary64`
16×	`add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
8×	`add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64`
5×	`pow1_binary64`
4×	`cancel-sign-sub-inv_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l/_binary64`

Counts

4 → 425

Calls

4 calls:

24.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.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)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 15609 to 5920 computations (62.1% saved)

series830.0ms (7.3%)

Error

4.8b

Counts

4 → 64

Calls

4 calls:

262.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
188.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
172.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
154.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2895 to 2196 computations (24.1% saved)

simplify191.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

489 → 489

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5210	18453

prune582.0ms (5.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	489	0	489
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	489	12	501

Error

4.8b

Counts

501 → 12

Compiler

Compiled 13528 to 3564 computations (73.7% saved)

regimes1.4s (12.6%)

Accuracy

Total 5.1b remaining (47.3%)

Threshold costs 0b (0%)

Compiler

Compiled 7388 to 4586 computations (37.9% saved)

bsearch69.0ms (0.6%)

Steps

Iters	Range		Point
8	2.3841998069328035e-138	3.613937283710691e-135	5.70304349446422e-136
9	-5.161312729204704e+69	-5.09033273845581e+63	-4.9596295979872694e+69

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	65	53
1	65	53

end0.0ms (0%)

sample2.5s (21.7%)

Algorithm

1×

intervals

Results

232.0ms	1120×	body	2048	valid
227.0ms	5241×	body	128	valid
118.0ms	715×	body	1024	valid
106.0ms	410×	body	4096	valid
43.0ms	344×	body	512	valid
30.0ms	764×	body	128	nan
13.0ms	170×	body	256	valid
10.0ms	240×	body	128	invalid

Compiler

Compiled 1889 to 1175 computations (37.8% saved)

Details

analyze1.0s (8.9%)

sample41.0ms (0.4%)

simplify68.0ms (0.6%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite152.0ms (1.3%)

series839.0ms (7.3%)

simplify72.0ms (0.6%)

prune139.0ms (1.2%)

localize9.0ms (0.1%)

rewrite132.0ms (1.2%)

series831.0ms (7.3%)

simplify64.0ms (0.6%)

prune138.0ms (1.2%)

localize9.0ms (0.1%)

rewrite244.0ms (2.1%)

series813.0ms (7.1%)

simplify110.0ms (1%)

prune221.0ms (1.9%)

localize11.0ms (0.1%)

rewrite919.0ms (8%)

series830.0ms (7.3%)

simplify191.0ms (1.7%)

prune582.0ms (5.1%)

regimes1.4s (12.6%)

bsearch69.0ms (0.6%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.5s (21.7%)

Profiling