Details

analyze1.2s (9.8%)

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)

sample48.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	35×	body	2048	valid
8.0ms	160×	body	128	valid
5.0ms	16×	body	4096	valid
4.0ms	24×	body	1024	valid
3.0ms	14×	body	512	valid
1.0ms	15×	body	128	nan
1.0ms	12×	body	128	invalid
1.0ms	7×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune11.0ms (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

37.0b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize19.0ms (0.2%)

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))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite177.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

36.8b

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:

17.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
10.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
9.0ms	(-.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))

Compiler

Compiled 2014 to 333 computations (83.5% saved)

series797.0ms (6.6%)

Error

6.7b

Counts

4 → 68

Calls

4 calls:

204.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
180.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
167.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
157.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2612 to 1794 computations (31.3% saved)

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5209	3070

prune197.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	143	11	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	11	155

Error

6.6b

Counts

155 → 11

Compiler

Compiled 2872 to 635 computations (77.9% 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))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite141.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

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:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
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 2156 to 599 computations (72.2% saved)

series744.0ms (6.1%)

Error

6.6b

Counts

4 → 68

Calls

4 calls:

230.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
153.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
148.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
140.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2866 to 2060 computations (28.1% saved)

simplify52.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4961	2822
1	4961	2822

prune141.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	155	11	166

Error

6.6b

Counts

166 → 11

Compiler

Compiled 2960 to 914 computations (69.1% saved)

localize10.0ms (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))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite238.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

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:

22.0ms	(/.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)

series791.0ms (6.5%)

Error

6.6b

Counts

4 → 68

Calls

4 calls:

242.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
182.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
154.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
143.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)

Compiler

Compiled 2866 to 2051 computations (28.4% saved)

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5045	6061

prune203.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	2	7	9
Picked	0	1	1
Done	1	0	1
Total	233	10	243

Error

6.5b

Counts

243 → 10

Compiler

Compiled 5281 to 1200 computations (77.3% saved)

localize16.0ms (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))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite906.0ms (7.5%)

Algorithm

1×	rewrite-expression-head

Error

6.5b

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)))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
7.0ms	(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)

series776.0ms (6.4%)

Error

6.5b

Counts

4 → 68

Calls

4 calls:

220.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
178.0ms	(sqrt.f64 (-.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)
149.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3120 to 2314 computations (25.8% saved)

simplify264.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

493 → 493

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4984	18731
1	4984	18731

prune568.0ms (4.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	492	1	493
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	492	11	503

Error

6.5b

Counts

503 → 11

Compiler

Compiled 13728 to 3635 computations (73.5% saved)

regimes1.9s (15.4%)

Accuracy

Total 4.2b remaining (42.1%)

Threshold costs 0b (0%)

Compiler

Compiled 6456 to 3786 computations (41.4% saved)

bsearch31.0ms (0.3%)

Steps

Iters	Range		Point
2	3.259171884535959e-89	3.7213833768997876e-89	3.6636069403543086e-89
6	-5.045126685015859e+86	-1.1486306167505172e+86	-3.451742738610391e+86

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	89	53
1	89	53

end0.0ms (0%)

sample2.6s (21.9%)

Algorithm

1×

intervals

Results

302.0ms	1191×	body	2048	valid
263.0ms	5138×	body	128	valid
139.0ms	721×	body	1024	valid
118.0ms	394×	body	4096	valid
59.0ms	365×	body	512	valid
38.0ms	762×	body	128	nan
19.0ms	191×	body	256	valid
16.0ms	247×	body	128	invalid

Compiler

Compiled 1656 to 975 computations (41.1% saved)

Details

analyze1.2s (9.8%)

sample48.0ms (0.4%)

simplify85.0ms (0.7%)

prune11.0ms (0.1%)

localize19.0ms (0.2%)

rewrite177.0ms (1.5%)

series797.0ms (6.6%)

simplify82.0ms (0.7%)

prune197.0ms (1.6%)

localize9.0ms (0.1%)

rewrite141.0ms (1.2%)

series744.0ms (6.1%)

simplify52.0ms (0.4%)

prune141.0ms (1.2%)

localize10.0ms (0.1%)

rewrite238.0ms (2%)

series791.0ms (6.5%)

simplify97.0ms (0.8%)

prune203.0ms (1.7%)

localize16.0ms (0.1%)

rewrite906.0ms (7.5%)

series776.0ms (6.4%)

simplify264.0ms (2.2%)

prune568.0ms (4.7%)

regimes1.9s (15.4%)

bsearch31.0ms (0.3%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample2.6s (21.9%)

Profiling