Details

analyze612.0ms (10.3%)

Algorithm

1×

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)

sample36.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	178×	body	128	valid
7.0ms	31×	body	2048	valid
3.0ms	21×	body	1024	valid
2.0ms	14×	body	512	valid
2.0ms	7×	body	4096	valid
1.0ms	25×	body	128	nan
0.0ms	5×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify194.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	309	18
1	309	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

Merged error: 32.1b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (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))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`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`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 82

Calls

4 calls:

16.0ms	(-.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)
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series495.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
127.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
64.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4975	2155
1	4975	2155

prune102.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 6.3b

Counts

95 → 9

Compiler

Compiled 2016 to 425 computations (78.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.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))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_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×	`prod-exp_binary64` `difference-of-squares_binary64`
3×	`unswap-sqr_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

16.0ms	(.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))

series480.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
112.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
62.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify102.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4895	1889
1	4895	1889

prune81.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	93	11	104

Merged error: 6.3b

Counts

104 → 11

Compiler

Compiled 2043 to 607 computations (70.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 58

Calls

4 calls:

8.0ms	(-.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	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series447.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
114.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
106.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
105.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4965	1324
1	4965	1324

prune73.0ms (1.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	70	11	81

Merged error: 6.3b

Counts

81 → 11

Compiler

Compiled 2312 to 447 computations (80.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.0b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (/.f64 b_2 a))
22.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
17×	`sqrt-prod_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` `distribute-lft-out--_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64`
1×	`pow1/2_binary64` `distribute-rgt-out--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 91

Calls

4 calls:

27.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (/.f64 b_2 a))
7.0ms	(/.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))

series526.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

215.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
152.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (/.f64 b_2 a))
107.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
51.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5051	2437

prune77.0ms (1.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	102	12	114

Merged error: 6.2b

Counts

114 → 12

Compiler

Compiled 2297 to 411 computations (82.1% saved)

regimes565.0ms (9.5%)

Compiler: Compiled 2544 to 1602 computations (37% saved)

bsearch129.0ms (2.2%)

Steps

Iters	Range		Point
8	4.575371571350041e+103	3.5137682369026495e+107	5.38924907603627e+103
6	1.057771586821974e-69	1.0893100279669435e-68	1.350743022224145e-69
7	2.122143227960374e-142	1.5096449843192667e-140	4.664337940942095e-142
11	-2.9568430544839144e+171	-2.6830436756501767e+147	-9.156580055033079e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	131	123
1	131	123

end0.0ms (0%)

sample1.6s (26.9%)

Algorithm

1×

intervals

Results

253.0ms	1178×	body	2048	valid
240.0ms	5138×	body	128	valid
122.0ms	704×	body	1024	valid
115.0ms	430×	body	4096	valid
45.0ms	365×	body	512	valid
34.0ms	796×	body	128	nan
15.0ms	185×	body	256	valid
11.0ms	236×	body	128	invalid

Compiler

Compiled 724 to 443 computations (38.8% saved)

Details

analyze612.0ms (10.3%)

sample36.0ms (0.6%)

simplify194.0ms (3.3%)

prune7.0ms (0.1%)

localize10.0ms (0.2%)

rewrite48.0ms (0.8%)

series495.0ms (8.3%)

simplify70.0ms (1.2%)

prune102.0ms (1.7%)

localize9.0ms (0.2%)

rewrite41.0ms (0.7%)

series480.0ms (8.1%)

simplify102.0ms (1.7%)

prune81.0ms (1.4%)

localize11.0ms (0.2%)

rewrite31.0ms (0.5%)

series447.0ms (7.5%)

simplify63.0ms (1.1%)

prune73.0ms (1.2%)

localize9.0ms (0.2%)

rewrite52.0ms (0.9%)

series526.0ms (8.9%)

simplify70.0ms (1.2%)

prune77.0ms (1.3%)

regimes565.0ms (9.5%)

bsearch129.0ms (2.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (26.9%)

Profiling