Details

analyze167.0ms (1.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11
0	1	1
1	1	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)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	68×	body	1024	valid
7.0ms	132×	body	128	valid
6.0ms	37×	body	512	valid
2.0ms	6×	body	2048	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune4.0ms (0%)

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

30.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
1.7b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite113.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

29.8b

Rules

15×	`sqrt-prod_binary64_2481`
14×	`add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465`
6×	`cancel-sign-sub-inv_binary64_2431`
5×	`add-cube-cbrt_binary64_2500`
4×	`add-log-exp_binary64_2504` `difference-of-squares_binary64_2434`
3×	`pow1_binary64_2526` `distribute-lft-out--_binary64_2417`
2×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `distribute-lft-out_binary64_2416` `sqrt-div_binary64_2482`
1×	`diff-log_binary64_2557` `flip3--_binary64_2469` `sub-neg_binary64_2458` `flip--_binary64_2440` `pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `flip3-+_binary64_2468` `flip-+_binary64_2439` `rem-sqrt-square_binary64_2478`

Counts

2 → 40

Calls

2 calls:

15.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 571 to 370 computations (35.2% saved)

series92.0ms (0.7%)

Error

29.9b

Counts

2 → 9

Calls

2 calls:

51.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
27.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 245 to 193 computations (21.2% saved)

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4932	589
1	4932	589

prune83.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	3	50

Error

0.2b

Counts

50 → 3

Compiler

Compiled 565 to 370 computations (34.5% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite200.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

52×	`*-un-lft-identity_binary64_2465`
24×	`sqrt-prod_binary64_2481`
21×	`distribute-lft-out_binary64_2416`
18×	`times-frac_binary64_2471`
16×	`add-sqr-sqrt_binary64_2487`
15×	`add-cube-cbrt_binary64_2500`
7×	`add-exp-log_binary64_2503`
6×	`associate-/r*_binary64_2409`
5×	`pow1_binary64_2526` `add-log-exp_binary64_2504` `add-cbrt-cube_binary64_2501`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-/l*_binary64_2410`
2×	`div-exp_binary64_2516` `associate-/r/_binary64_2411` `sqrt-div_binary64_2482`
1×	`inv-pow_binary64_2550` `pow-flip_binary64_2539` `1-exp_binary64_2509` `rec-exp_binary64_2515` `cbrt-undiv_binary64_2499` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462` `sum-log_binary64_2556` `+-commutative_binary64_2395` `pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478`

Counts

3 → 75

Calls

3 calls:

18.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
13.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 1268 to 926 computations (27% saved)

series91.0ms (0.7%)

Error

0.2b

Counts

3 → 12

Calls

3 calls:

29.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
26.0ms	(sqrt.f64 (+.f64 1 x))
24.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 268 to 232 computations (13.4% saved)

simplify158.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4859	1227
1	4859	1227

prune159.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	1	1
Picked	0	1	1
Done	1	0	1
Total	83	7	90

Error

0.0b

Counts

90 → 7

Compiler

Compiled 1299 to 948 computations (27% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.2b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))

rewrite297.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465`
18×	`add-cube-cbrt_binary64_2500`
13×	`cbrt-prod_binary64_2496`
10×	`add-exp-log_binary64_2503` `associate-r_binary64_2405`
9×	`times-frac_binary64_2471` `sqrt-prod_binary64_2481`
8×	`add-cbrt-cube_binary64_2501`
7×	`pow1_binary64_2526`
6×	`cbrt-div_binary64_2497`
4×	`add-log-exp_binary64_2504` `flip3-+_binary64_2468` `flip-+_binary64_2439`
3×	`distribute-lft-out_binary64_2416` `associate-/l_binary64_2410` `associate-/r_binary64_2409` `unswap-sqr_binary64_2433` `associate-l_binary64_2406`
2×	`pow1/3_binary64_2547` `div-exp_binary64_2516` `associate-/r/_binary64_2411` `sqrt-div_binary64_2482` `associate-*r/_binary64_2407`
1×	`inv-pow_binary64_2550` `pow-flip_binary64_2539` `1-exp_binary64_2509` `rec-exp_binary64_2515` `cbrt-undiv_binary64_2499` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462` `pow-prod-down_binary64_2536` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `*-commutative_binary64_2396`

Counts

4 → 90

Calls

4 calls:

19.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
17.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
5.0ms	(cbrt.f64 (+.f64 1 x))
5.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 2392 to 1869 computations (21.9% saved)

series539.0ms (4.1%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

167.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
135.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
85.0ms	(cbrt.f64 (+.f64 1 x))
82.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1892 to 1612 computations (14.8% saved)

simplify187.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	4840	2640
1	4840	2640

prune329.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	117	10	127

Error

0.0b

Counts

127 → 10

Compiler

Compiled 3070 to 2365 computations (23% saved)

localize17.0ms (0.1%)

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)))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

rewrite2.7s (20.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

742×	`*-un-lft-identity_binary64_2465`
700×	`sqrt-prod_binary64_2481`
594×	`times-frac_binary64_2471`
280×	`distribute-lft-out_binary64_2416`
254×	`add-sqr-sqrt_binary64_2487`
252×	`add-cube-cbrt_binary64_2500`
36×	`associate-/l*_binary64_2410`
28×	`sqrt-div_binary64_2482`
24×	`associate-/r/_binary64_2411`
18×	`associate-/r*_binary64_2409`
17×	`add-exp-log_binary64_2503`
15×	`pow1_binary64_2526`
14×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
12×	`div-inv_binary64_2462`
11×	`add-cbrt-cube_binary64_2501`
8×	`pow-flip_binary64_2539` `div-exp_binary64_2516`
7×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483`
6×	`pow-div_binary64_2540`
4×	`add-log-exp_binary64_2504` `cbrt-undiv_binary64_2499`
2×	`inv-pow_binary64_2550` `1-exp_binary64_2509` `rec-exp_binary64_2515` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `rem-sqrt-square_binary64_2478`
1×	`associate-/l/_binary64_2412`

Counts

4 → 459

Calls

4 calls:

59.0ms	(/.f64 (/.f64 1 (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 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
16.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
15.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 16963 to 12555 computations (26% saved)

series155.0ms (1.2%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

39.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
38.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
33.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
32.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

Compiler

Compiled 545 to 470 computations (13.8% saved)

simplify373.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

471 → 471

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	4875	14772
1	4875	14772

prune1.2s (9.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	468	3	471
Fresh	3	4	7
Picked	1	0	1
Done	1	1	2
Total	473	8	481

Error

Counts

481 → 8

Compiler

Compiled 11392 to 8378 computations (26.5% saved)

regimes603.0ms (4.5%)

Accuracy

Total 0.2b remaining (98%)

Threshold costs 0.2b (98%)

Compiler

Compiled 4736 to 3770 computations (20.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample5.6s (42.2%)

Algorithm

1×

intervals

Results

411.0ms	1988×	body	1024	valid
226.0ms	4291×	body	128	valid
145.0ms	994×	body	512	valid
54.0ms	215×	body	2048	valid
49.0ms	512×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 2341 to 1866 computations (20.3% saved)

Details

analyze167.0ms (1.3%)

sample40.0ms (0.3%)

simplify18.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite113.0ms (0.9%)

series92.0ms (0.7%)

simplify66.0ms (0.5%)

prune83.0ms (0.6%)

localize12.0ms (0.1%)

rewrite200.0ms (1.5%)

series91.0ms (0.7%)

simplify158.0ms (1.2%)

prune159.0ms (1.2%)

localize18.0ms (0.1%)

rewrite297.0ms (2.2%)

series539.0ms (4.1%)

simplify187.0ms (1.4%)

prune329.0ms (2.5%)

localize17.0ms (0.1%)

rewrite2.7s (20.3%)

series155.0ms (1.2%)

simplify373.0ms (2.8%)

prune1.2s (9.4%)

regimes603.0ms (4.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.6s (42.2%)

Profiling