Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample33.0ms (1.3%)

Algorithm

1×

intervals

Results

14.0ms	69×	body	640	valid
6.0ms	31×	body	1280	valid
5.0ms	130×	body	80	valid
1.0ms	14×	body	320	valid
1.0ms	12×	body	160	valid

simplify16.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	265	11
1	265	11

prune4.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 20.2b

Counts

2 → 1

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
0.2b	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
0.3b	(/.f64 1.0 (sqrt.f64 x))
3.1b	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

rewrite52.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64`
73×	`add-sqr-sqrt_binary64`
69×	`times-frac_binary64`
50×	`sqrt-prod_binary64`
42×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`
11×	`distribute-lft-out--_binary64`
9×	`difference-of-squares_binary64`
8×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64`
5×	`pow1_binary64`
4×	`div-inv_binary64` `sqrt-div_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 132

Calls

4 calls:

30.0ms	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
6.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
5.0ms	(sqrt.f64 (+.f64 x 1.0))
4.0ms	(/.f64 1.0 (sqrt.f64 x))

series39.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
10.0ms	(/.f64 1.0 (sqrt.f64 x))
8.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
5.0ms	(sqrt.f64 (+.f64 x 1.0))

simplify35.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5076	1839

prune228.0ms (9.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	132	12	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Merged error: 19.6b

Counts

145 → 12

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1.0 x))
0.2b	(/.f64 (.f64 1.0 (-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
3.1b	(-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))

rewrite42.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
23×	`sqrt-prod_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-r/_binary64` `associate-l*_binary64` `sqrt-div_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `div-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 92

Calls

4 calls:

18.0ms	(/.f64 (.f64 1.0 (-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
3.0ms	(sqrt.f64 (+.f64 1.0 x))

series70.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(/.f64 (.f64 1.0 (-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
16.0ms	(-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
8.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
5.0ms	(sqrt.f64 (+.f64 1.0 x))

simplify44.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5212	1577

prune155.0ms (6.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	112	4	116

Merged error: 0.3b

Counts

116 → 4

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
0.2b	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
0.3b	(/.f64 (.f64 1.0 (/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))

rewrite56.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
35×	`sqrt-prod_binary64`
32×	`distribute-lft-out_binary64`
29×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
7×	`associate-/r_binary64` `associate-r*_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
5×	`flip3-+_binary64` `associate-r/_binary64` `associate-/l_binary64` `flip-+_binary64`
4×	`associate-/r/_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `associate-/l/_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`sqrt-unprod_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 125

Calls

4 calls:

21.0ms	(/.f64 (.f64 1.0 (/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
13.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
8.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))

series78.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/.f64 (.f64 1.0 (/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
13.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))

simplify63.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5516	2087

prune234.0ms (9.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	131	10	141

Merged error: 0.0b

Counts

141 → 10

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1.0 (+.f64 (+.f64 1.0 x) (*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
0.1b	(.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (+.f64 (+.f64 1.0 x) (.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
0.3b	(*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
0.3b	(/.f64 1.0 (sqrt.f64 x))

rewrite52.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
55×	`*-un-lft-identity_binary64`
53×	`add-cube-cbrt_binary64`
34×	`sqrt-prod_binary64`
29×	`associate-l_binary64`
28×	`associate-r_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-/r/_binary64`
11×	`flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`
10×	`associate-/r*_binary64` `pow1_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
8×	`distribute-lft-out_binary64` `frac-add_binary64`
6×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `div-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-*r/_binary64` `sqrt-unprod_binary64` `frac-times_binary64`

Counts

4 → 179

Calls

4 calls:

21.0ms	(.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (+.f64 (+.f64 1.0 x) (.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
9.0ms	(*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
8.0ms	(/.f64 1.0 (+.f64 (+.f64 1.0 x) (*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
6.0ms	(/.f64 1.0 (sqrt.f64 x))

series56.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (+.f64 (+.f64 1.0 x) (.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
11.0ms	(/.f64 1.0 (sqrt.f64 x))
10.0ms	(/.f64 1.0 (+.f64 (+.f64 1.0 x) (*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
9.0ms	(*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))

simplify48.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5018	3178

prune310.0ms (12.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	192	9	201

Merged error: 0.0b

Counts

201 → 9

regimes44.0ms (1.7%)

Accuracy

Total 0.3b remaining (86.5%)

Threshold costs 0.3b (86.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	14	18

end0.0ms (0%)

sample813.0ms (32.4%)

Algorithm

1×

intervals

Results

260.0ms	1833×	body	640	valid
214.0ms	1140×	body	1280	valid
153.0ms	4101×	body	80	valid
67.0ms	610×	body	320	valid
22.0ms	316×	body	160	valid

Details

analyze1.0ms (0%)

sample33.0ms (1.3%)

simplify16.0ms (0.6%)

prune4.0ms (0.2%)

localize7.0ms (0.3%)

rewrite52.0ms (2.1%)

series39.0ms (1.6%)

simplify35.0ms (1.4%)

prune228.0ms (9.1%)

localize8.0ms (0.3%)

rewrite42.0ms (1.7%)

series70.0ms (2.8%)

simplify44.0ms (1.7%)

prune155.0ms (6.2%)

localize10.0ms (0.4%)

rewrite56.0ms (2.2%)

series78.0ms (3.1%)

simplify63.0ms (2.5%)

prune234.0ms (9.3%)

localize9.0ms (0.4%)

rewrite52.0ms (2.1%)

series56.0ms (2.2%)

simplify48.0ms (1.9%)

prune310.0ms (12.3%)

regimes44.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample813.0ms (32.4%)

Profiling