Details

analyze1.0s (6.6%)

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)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

8.0ms	168×	body	128	valid
7.0ms	34×	body	2048	valid
4.0ms	23×	body	1024	valid
4.0ms	13×	body	4096	valid
1.0ms	10×	body	512	valid
1.0ms	23×	body	128	nan
1.0ms	8×	body	256	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune8.0ms (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

32.4b

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)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
2.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite195.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

32.1b

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:

18.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.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 1746 to 313 computations (82.1% saved)

series901.0ms (5.9%)

Error

5.6b

Counts

4 → 68

Calls

4 calls:

280.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
200.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
195.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
190.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2117 to 1600 computations (24.4% saved)

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5234	2964

prune139.0ms (0.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	141	13	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	13	155

Error

5.4b

Counts

155 → 13

Compiler

Compiled 1940 to 525 computations (72.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
2.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite252.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

5.4b

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:

14.0ms	(/.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)
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 4001 to 971 computations (75.7% saved)

series872.0ms (5.7%)

Error

5.4b

Counts

4 → 68

Calls

4 calls:

277.0ms	(/.f64 1 (/.f64 a (-.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)
190.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
174.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2314 to 1791 computations (22.6% saved)

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5071	5955

prune195.0ms (1.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	228	4	232
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	232	13	245

Error

5.4b

Counts

245 → 13

Compiler

Compiled 3161 to 873 computations (72.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
7.7b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (/.f64 b_2 a))
21.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite201.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

5.4b

Rules

49×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
17×	`sqrt-prod_binary64`
14×	`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`
4×	`flip3--_binary64` `sqrt-div_binary64` `flip--_binary64` `div-inv_binary64` `distribute-lft-out--_binary64`
3×	`associate-/r*_binary64`
2×	`diff-log_binary64` `sub-neg_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `frac-sub_binary64` `sub-div_binary64` `distribute-rgt-out--_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64`

Counts

4 → 105

Calls

4 calls:

23.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (/.f64 b_2 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))

Compiler

Compiled 2422 to 437 computations (82% saved)

series978.0ms (6.4%)

Error

5.4b

Counts

4 → 70

Calls

4 calls:

318.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (/.f64 b_2 a))
250.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
193.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
183.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2324 to 1675 computations (27.9% saved)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4956	3289
1	4956	3289

prune159.0ms (1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	171	4	175
Fresh	3	8	11
Picked	0	1	1
Done	1	0	1
Total	175	13	188

Error

5.4b

Counts

188 → 13

Compiler

Compiled 2315 to 584 computations (74.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) (/.f64 1 a))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
12.1b	(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) (/.f64 1 a)) (/.f64 b_2 a))
21.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite209.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

5.4b

Rules

36×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`
13×	`add-exp-log_binary64` `associate-r_binary64`
10×	`sqrt-div_binary64`
9×	`add-cbrt-cube_binary64` `sqrt-prod_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
6×	`frac-sub_binary64` `unswap-sqr_binary64` `associate-l_binary64`
4×	`frac-times_binary64` `associate-*l/_binary64` `prod-exp_binary64`
3×	`un-div-inv_binary64` `associate-*r/_binary64` `div-inv_binary64`
2×	`diff-log_binary64` `sub-div_binary64` `sub-neg_binary64` `div-exp_binary64` `cbrt-unprod_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-rgt-out--_binary64` `pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64` `*-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) (/.f64 1 a))
14.0ms	(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) (/.f64 1 a)) (/.f64 b_2 a))
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 2718 to 799 computations (70.6% saved)

series993.0ms (6.5%)

Error

5.4b

Counts

4 → 70

Calls

4 calls:

316.0ms	(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) (/.f64 1 a)) (/.f64 b_2 a))
261.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) (/.f64 1 a))
193.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
186.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2472 to 1812 computations (26.7% saved)

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4952	3112
1	4952	3112

prune156.0ms (1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	176	13	189

Error

5.4b

Counts

189 → 13

Compiler

Compiled 2166 to 636 computations (70.6% saved)

regimes7.1s (46.5%)

Accuracy

Total 4.7b remaining (45.8%)

Threshold costs 0b (0%)

Compiler

Compiled 40802 to 25752 computations (36.9% saved)

bsearch89.0ms (0.6%)

Steps

Iters	Range		Point
9	9.640416885130221e-89	1.2995848864263519e-83	2.466272322022482e-84
8	-1.1543132078325348e+138	-3.994290222871883e+133	-5.676559387027347e+135

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	84	49
1	84	49

end3.0ms (0%)

Compiler: Compiled 33 to 22 computations (33.3% saved)

sample1.4s (8.9%)

Algorithm

1×

intervals

Results

237.0ms	1156×	body	2048	valid
225.0ms	5186×	body	128	valid
121.0ms	721×	body	1024	valid
100.0ms	407×	body	4096	valid
43.0ms	345×	body	512	valid
33.0ms	848×	body	128	nan
15.0ms	185×	body	256	valid
14.0ms	273×	body	128	invalid

Compiler

Compiled 307 to 202 computations (34.2% saved)

Details

analyze1.0s (6.6%)

sample40.0ms (0.3%)

simplify69.0ms (0.5%)

prune8.0ms (0.1%)

localize10.0ms (0.1%)

rewrite195.0ms (1.3%)

series901.0ms (5.9%)

simplify70.0ms (0.5%)

prune139.0ms (0.9%)

localize9.0ms (0.1%)

rewrite252.0ms (1.6%)

series872.0ms (5.7%)

simplify78.0ms (0.5%)

prune195.0ms (1.3%)

localize9.0ms (0.1%)

rewrite201.0ms (1.3%)

series978.0ms (6.4%)

simplify76.0ms (0.5%)

prune159.0ms (1%)

localize10.0ms (0.1%)

rewrite209.0ms (1.4%)

series993.0ms (6.5%)

simplify85.0ms (0.6%)

prune156.0ms (1%)

regimes7.1s (46.5%)

bsearch89.0ms (0.6%)

simplify3.0ms (0%)

end3.0ms (0%)

sample1.4s (8.9%)

Profiling