Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample35.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms	49×	body	1024	valid
8.0ms	143×	body	128	valid
6.0ms	39×	body	512	valid
2.0ms	8×	body	2048	valid
2.0ms	17×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify158.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

27.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_8960`
14×	`*-un-lft-identity_binary64_8944` `add-sqr-sqrt_binary64_8966`
6×	`cancel-sign-sub-inv_binary64_8910`
5×	`add-cube-cbrt_binary64_8979`
4×	`difference-of-squares_binary64_8913` `add-log-exp_binary64_8983`
3×	`pow1_binary64_9005` `distribute-lft-out--_binary64_8896`
2×	`add-cbrt-cube_binary64_8980` `distribute-lft-out_binary64_8895` `sqrt-div_binary64_8961` `add-exp-log_binary64_8982`
1×	`flip3-+_binary64_8947` `flip3--_binary64_8948` `flip--_binary64_8919` `diff-log_binary64_9036` `pow1/2_binary64_9024` `sub-neg_binary64_8937` `rem-sqrt-square_binary64_8957` `flip-+_binary64_8918` `sqrt-pow1_binary64_8962`

Counts

2 → 40

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))

series81.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

66.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
15.0ms	(sqrt.f64 (+.f64 x 1))

simplify80.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4936	794
1	4936	794

prune47.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	3	47

Error

0.1b

Counts

47 → 3

Compiler

Compiled 690 to 454 computations (34.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite47.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_8944`
24×	`sqrt-prod_binary64_8960`
21×	`distribute-lft-out_binary64_8895`
18×	`times-frac_binary64_8950`
16×	`add-sqr-sqrt_binary64_8966`
15×	`add-cube-cbrt_binary64_8979`
7×	`add-exp-log_binary64_8982`
6×	`associate-/r*_binary64_8888`
5×	`pow1_binary64_9005` `add-cbrt-cube_binary64_8980` `add-log-exp_binary64_8983`
3×	`flip3-+_binary64_8947` `associate-/l*_binary64_8889` `flip-+_binary64_8918`
2×	`associate-/r/_binary64_8890` `div-exp_binary64_8995` `sqrt-div_binary64_8961`
1×	`inv-pow_binary64_9029` `+-commutative_binary64_8874` `clear-num_binary64_8943` `frac-2neg_binary64_8955` `rec-exp_binary64_8994` `sum-log_binary64_9035` `pow1/2_binary64_9024` `rem-sqrt-square_binary64_8957` `div-inv_binary64_8941` `cbrt-undiv_binary64_8978` `sqrt-pow1_binary64_8962` `pow-flip_binary64_9018` `1-exp_binary64_8988`

Counts

3 → 75

Calls

3 calls:

15.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
15.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))

series86.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

38.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
32.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
16.0ms	(sqrt.f64 (+.f64 x 1))

simplify75.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4917	1530
1	4917	1530

prune156.0ms (3.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Error

0.0b

Counts

87 → 8

Compiler

Compiled 1481 to 1051 computations (29% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.3b	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

rewrite150.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod_binary64_8960`
74×	`*-un-lft-identity_binary64_8944`
37×	`pow1_binary64_9005`
32×	`distribute-lft-out_binary64_8895` `add-sqr-sqrt_binary64_8966`
28×	`sqrt-div_binary64_8961`
18×	`pow1/2_binary64_9024` `sqrt-pow1_binary64_8962`
17×	`add-exp-log_binary64_8982`
16×	`add-cube-cbrt_binary64_8979`
15×	`swap-sqr_binary64_8911`
14×	`flip3-+_binary64_8947` `flip-+_binary64_8918` `pow-flip_binary64_9018`
11×	`add-cbrt-cube_binary64_8980`
10×	`pow-prod-up_binary64_9014`
9×	`associate-l_binary64_8885` `associate-r_binary64_8884`
8×	`associate-/r/_binary64_8890` `frac-times_binary64_8954`
6×	`pow-sqr_binary64_8917` `pow-prod-down_binary64_9015`
4×	`associate-r/_binary64_8886` `div-exp_binary64_8995` `prod-exp_binary64_8993` `associate-l/_binary64_8887` `rem-sqrt-square_binary64_8957` `unswap-sqr_binary64_8912` `add-log-exp_binary64_8983`
3×	`times-frac_binary64_8950` `associate-/l*_binary64_8889`
2×	`pow2_binary64_9025` `rec-exp_binary64_8994` `pow-plus_binary64_9007` `cbrt-undiv_binary64_8978` `cbrt-unprod_binary64_8977` `1-exp_binary64_8988`
1×	`inv-pow_binary64_9029` `sqrt-unprod_binary64_8964` `clear-num_binary64_8943` `associate-/r_binary64_8888` `frac-2neg_binary64_8955` `-commutative_binary64_8875` `sqr-abs_binary64_8959` `rem-square-sqrt_binary64_8956` `div-inv_binary64_8941`

Counts

4 → 155

Calls

4 calls:

41.0ms	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
40.0ms	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
16.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series232.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
60.0ms	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
55.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
53.0ms	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

simplify127.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4900	3040
1	4900	3040

prune254.0ms (6.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	167	8	175

Error

0.0b

Counts

175 → 8

Compiler

Compiled 3647 to 2565 computations (29.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.3b	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite90.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64_8944`
36×	`sqrt-prod_binary64_8960`
33×	`distribute-lft-out_binary64_8895`
12×	`pow1_binary64_9005` `add-sqr-sqrt_binary64_8966`
10×	`swap-sqr_binary64_8911`
9×	`flip3-+_binary64_8947` `add-cube-cbrt_binary64_8979` `flip-+_binary64_8918`
8×	`add-log-exp_binary64_8983`
6×	`associate-l_binary64_8885` `associate-r_binary64_8884` `add-cbrt-cube_binary64_8980` `add-exp-log_binary64_8982`
4×	`frac-times_binary64_8954`
2×	`associate-r/_binary64_8886` `+-commutative_binary64_8874` `associate-l/_binary64_8887` `sum-log_binary64_9035` `sqrt-div_binary64_8961`
1×	`pow-sqr_binary64_8917` `pow2_binary64_9025` `distribute-rgt-in_binary64_8894` `prod-exp_binary64_8993` `*-commutative_binary64_8875` `pow1/2_binary64_9024` `rem-sqrt-square_binary64_8957` `pow-plus_binary64_9007` `unswap-sqr_binary64_8912` `pow-prod-down_binary64_9015` `sqrt-pow1_binary64_8962` `cbrt-unprod_binary64_8977` `distribute-lft-in_binary64_8893` `pow-prod-up_binary64_9014`

Counts

4 → 92

Calls

4 calls:

29.0ms	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
22.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
14.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 1 x))

series161.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
42.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
38.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
24.0ms	(sqrt.f64 (+.f64 1 x))

simplify108.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4916	1965
1	4916	1965

prune218.0ms (5.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	103	9	112

Error

0.0b

Counts

112 → 9

Compiler

Compiled 2307 to 1580 computations (31.5% saved)

regimes119.0ms (2.9%)

Accuracy

Total 0.2b remaining (92.2%)

Threshold costs 0.2b (92.2%)

Compiler

Compiled 1318 to 1073 computations (18.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.9s (44.8%)

Algorithm

1×

intervals

Results

343.0ms	2049×	body	1024	valid
187.0ms	4246×	body	128	valid
122.0ms	987×	body	512	valid
52.0ms	214×	body	2048	valid
41.0ms	504×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 631 to 516 computations (18.2% saved)

Details

analyze5.0ms (0.1%)

sample35.0ms (0.8%)

simplify158.0ms (3.8%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite22.0ms (0.5%)

series81.0ms (1.9%)

simplify80.0ms (1.9%)

prune47.0ms (1.1%)

localize8.0ms (0.2%)

rewrite47.0ms (1.1%)

series86.0ms (2.1%)

simplify75.0ms (1.8%)

prune156.0ms (3.7%)

localize22.0ms (0.5%)

rewrite150.0ms (3.6%)

series232.0ms (5.6%)

simplify127.0ms (3.1%)

prune254.0ms (6.1%)

localize9.0ms (0.2%)

rewrite90.0ms (2.2%)

series161.0ms (3.9%)

simplify108.0ms (2.6%)

prune218.0ms (5.2%)

regimes119.0ms (2.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.9s (44.8%)

Profiling