Details

analyze3.0ms (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)

sample20.0ms (0.7%)

Algorithm

1×

intervals

Results

5.0ms	49×	body	1024	valid
4.0ms	143×	body	128	valid
3.0ms	39×	body	512	valid
1.0ms	8×	body	2048	valid
1.0ms	17×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify102.0ms (3.5%)

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 (0.2%)

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))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_11347`
14×	`*-un-lft-identity_binary64_11331` `add-sqr-sqrt_binary64_11353`
6×	`cancel-sign-sub-inv_binary64_11297`
5×	`add-cube-cbrt_binary64_11366`
4×	`difference-of-squares_binary64_11300` `add-log-exp_binary64_11370`
3×	`distribute-lft-out--_binary64_11283` `pow1_binary64_11392`
2×	`add-exp-log_binary64_11369` `sqrt-div_binary64_11348` `distribute-lft-out_binary64_11282` `add-cbrt-cube_binary64_11367`
1×	`sub-neg_binary64_11324` `sqrt-pow1_binary64_11349` `pow1/2_binary64_11411` `flip3--_binary64_11335` `diff-log_binary64_11423` `flip3-+_binary64_11334` `flip-+_binary64_11305` `rem-sqrt-square_binary64_11344` `flip--_binary64_11306`

Counts

2 → 40

Calls

2 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series52.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

38.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify79.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4936	794
1	4936	794

prune52.0ms (1.8%)

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)

localize7.0ms (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)))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_11331`
24×	`sqrt-prod_binary64_11347`
21×	`distribute-lft-out_binary64_11282`
18×	`times-frac_binary64_11337`
16×	`add-sqr-sqrt_binary64_11353`
15×	`add-cube-cbrt_binary64_11366`
7×	`add-exp-log_binary64_11369`
6×	`associate-/r*_binary64_11275`
5×	`pow1_binary64_11392` `add-log-exp_binary64_11370` `add-cbrt-cube_binary64_11367`
3×	`associate-/l*_binary64_11276` `flip3-+_binary64_11334` `flip-+_binary64_11305`
2×	`div-exp_binary64_11382` `associate-/r/_binary64_11277` `sqrt-div_binary64_11348`
1×	`1-exp_binary64_11375` `+-commutative_binary64_11261` `pow-flip_binary64_11405` `rec-exp_binary64_11381` `div-inv_binary64_11328` `sum-log_binary64_11422` `cbrt-undiv_binary64_11365` `frac-2neg_binary64_11342` `sqrt-pow1_binary64_11349` `pow1/2_binary64_11411` `inv-pow_binary64_11416` `rem-sqrt-square_binary64_11344` `clear-num_binary64_11330`

Counts

3 → 75

Calls

3 calls:

10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series68.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
23.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify65.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4917	1530
1	4917	1530

prune98.0ms (3.4%)

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)

localize12.0ms (0.4%)

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))))

rewrite83.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod_binary64_11347`
74×	`*-un-lft-identity_binary64_11331`
37×	`pow1_binary64_11392`
32×	`add-sqr-sqrt_binary64_11353` `distribute-lft-out_binary64_11282`
28×	`sqrt-div_binary64_11348`
18×	`sqrt-pow1_binary64_11349` `pow1/2_binary64_11411`
17×	`add-exp-log_binary64_11369`
16×	`add-cube-cbrt_binary64_11366`
15×	`swap-sqr_binary64_11298`
14×	`pow-flip_binary64_11405` `flip3-+_binary64_11334` `flip-+_binary64_11305`
11×	`add-cbrt-cube_binary64_11367`
10×	`pow-prod-up_binary64_11401`
9×	`associate-r_binary64_11271` `associate-l_binary64_11272`
8×	`associate-/r/_binary64_11277` `frac-times_binary64_11341`
6×	`pow-sqr_binary64_11304` `pow-prod-down_binary64_11402`
4×	`div-exp_binary64_11382` `add-log-exp_binary64_11370` `unswap-sqr_binary64_11299` `associate-l/_binary64_11274` `prod-exp_binary64_11380` `associate-r/_binary64_11273` `rem-sqrt-square_binary64_11344`
3×	`associate-/l*_binary64_11276` `times-frac_binary64_11337`
2×	`cbrt-unprod_binary64_11364` `1-exp_binary64_11375` `rec-exp_binary64_11381` `cbrt-undiv_binary64_11365` `pow-plus_binary64_11394` `pow2_binary64_11412`
1×	`sqrt-unprod_binary64_11351` `-commutative_binary64_11262` `sqr-abs_binary64_11346` `div-inv_binary64_11328` `frac-2neg_binary64_11342` `associate-/r_binary64_11275` `rem-square-sqrt_binary64_11343` `inv-pow_binary64_11416` `clear-num_binary64_11330`

Counts

4 → 155

Calls

4 calls:

23.0ms	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
23.0ms	(/.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)))))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series139.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
42.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
31.0ms	(/.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)))))
24.0ms	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

simplify85.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4900	3040
1	4900	3040

prune210.0ms (7.2%)

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)

localize10.0ms (0.3%)

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)))

rewrite50.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64_11331`
36×	`sqrt-prod_binary64_11347`
33×	`distribute-lft-out_binary64_11282`
12×	`pow1_binary64_11392` `add-sqr-sqrt_binary64_11353`
10×	`swap-sqr_binary64_11298`
9×	`add-cube-cbrt_binary64_11366` `flip3-+_binary64_11334` `flip-+_binary64_11305`
8×	`add-log-exp_binary64_11370`
6×	`add-exp-log_binary64_11369` `associate-r_binary64_11271` `associate-l_binary64_11272` `add-cbrt-cube_binary64_11367`
4×	`frac-times_binary64_11341`
2×	`+-commutative_binary64_11261` `sum-log_binary64_11422` `associate-l/_binary64_11274` `sqrt-div_binary64_11348` `associate-r/_binary64_11273`
1×	`*-commutative_binary64_11262` `cbrt-unprod_binary64_11364` `distribute-lft-in_binary64_11280` `pow-prod-up_binary64_11401` `unswap-sqr_binary64_11299` `sqrt-pow1_binary64_11349` `pow1/2_binary64_11411` `prod-exp_binary64_11380` `distribute-rgt-in_binary64_11281` `pow-plus_binary64_11394` `pow-sqr_binary64_11304` `pow-prod-down_binary64_11402` `pow2_binary64_11412` `rem-sqrt-square_binary64_11344`

Counts

4 → 92

Calls

4 calls:

19.0ms	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
12.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

series86.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
21.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
20.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
13.0ms	(sqrt.f64 (+.f64 1 x))

simplify79.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4916	1965
1	4916	1965

prune126.0ms (4.3%)

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 (4.1%)

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%)

sample1.3s (45%)

Algorithm

1×

intervals

Results

232.0ms	2049×	body	1024	valid
139.0ms	4246×	body	128	valid
85.0ms	987×	body	512	valid
30.0ms	214×	body	2048	valid
28.0ms	504×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 631 to 516 computations (18.2% saved)

Details

analyze3.0ms (0.1%)

sample20.0ms (0.7%)

simplify102.0ms (3.5%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite15.0ms (0.5%)

series52.0ms (1.8%)

simplify79.0ms (2.7%)

prune52.0ms (1.8%)

localize7.0ms (0.2%)

rewrite26.0ms (0.9%)

series68.0ms (2.4%)

simplify65.0ms (2.2%)

prune98.0ms (3.4%)

localize12.0ms (0.4%)

rewrite83.0ms (2.9%)

series139.0ms (4.8%)

simplify85.0ms (2.9%)

prune210.0ms (7.2%)

localize10.0ms (0.3%)

rewrite50.0ms (1.7%)

series86.0ms (2.9%)

simplify79.0ms (2.7%)

prune126.0ms (4.3%)

regimes119.0ms (4.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (45%)

Profiling