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)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	62×	body	1024	valid
4.0ms	142×	body	128	valid
2.0ms	28×	body	512	valid
1.0ms	8×	body	2048	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify170.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

Merged error: 28.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_16927` `sqrt-prod_binary64_16942` `add-sqr-sqrt_binary64_16948`
4×	`difference-of-squares_binary64_16896` `add-log-exp_binary64_16963`
3×	`pow1_binary64_16985` `distribute-lft-out--_binary64_16881` `add-cube-cbrt_binary64_16959`
2×	`add-cbrt-cube_binary64_16960` `add-exp-log_binary64_16962` `sqrt-div_binary64_16943` `distribute-lft-out_binary64_16880`
1×	`flip3--_binary64_16931` `sqrt-pow1_binary64_16944` `flip3-+_binary64_16930` `sub-neg_binary64_16920` `flip--_binary64_16902` `pow1/2_binary64_17004` `flip-+_binary64_16901` `diff-log_binary64_17016` `rem-sqrt-square_binary64_16940`

Counts

2 → 34

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series97.0ms (3%)

Counts

2 → 6

Calls

2 calls:

71.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify95.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4907	747
1	4907	747

prune50.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Merged error: 0.1b

Counts

41 → 4

Compiler

Compiled 657 to 439 computations (33.2% saved)

localize6.0ms (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))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_16927`
24×	`sqrt-prod_binary64_16942`
21×	`distribute-lft-out_binary64_16880`
18×	`times-frac_binary64_16933`
16×	`add-sqr-sqrt_binary64_16948`
15×	`add-cube-cbrt_binary64_16959`
7×	`add-exp-log_binary64_16962`
6×	`associate-/r*_binary64_16873`
5×	`add-cbrt-cube_binary64_16960` `pow1_binary64_16985` `add-log-exp_binary64_16963`
3×	`flip3-+_binary64_16930` `flip-+_binary64_16901` `associate-/l*_binary64_16874`
2×	`div-exp_binary64_16975` `associate-/r/_binary64_16875` `sqrt-div_binary64_16943`
1×	`div-inv_binary64_16924` `1-exp_binary64_16968` `inv-pow_binary64_17009` `rec-exp_binary64_16974` `+-commutative_binary64_16859` `sum-log_binary64_17015` `sqrt-pow1_binary64_16944` `pow-flip_binary64_16998` `frac-2neg_binary64_16938` `pow1/2_binary64_17004` `clear-num_binary64_16926` `cbrt-undiv_binary64_16958` `rem-sqrt-square_binary64_16940`

Counts

3 → 75

Calls

3 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
11.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series125.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

59.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
40.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify69.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5545	1516

prune95.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	80	8	88

Merged error: 0.0b

Counts

88 → 8

Compiler

Compiled 1472 to 1049 computations (28.7% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

rewrite70.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`sqrt-prod_binary64_16942`
62×	`add-sqr-sqrt_binary64_16948`
46×	`*-un-lft-identity_binary64_16927`
40×	`sqrt-pow1_binary64_16944`
32×	`pow1_binary64_16985` `sqrt-div_binary64_16943`
28×	`add-cube-cbrt_binary64_16959`
20×	`pow1/2_binary64_17004`
18×	`swap-sqr_binary64_16894`
10×	`add-exp-log_binary64_16962` `associate-l_binary64_16870` `associate-r_binary64_16869`
9×	`unswap-sqr_binary64_16895` `pow-prod-up_binary64_16994` `flip3-+_binary64_16930` `flip-+_binary64_16901` `times-frac_binary64_16933`
8×	`add-cbrt-cube_binary64_16960` `distribute-lft-out_binary64_16880`
5×	`pow-prod-down_binary64_16995` `pow-sqr_binary64_16900`
4×	`frac-times_binary64_16937` `add-log-exp_binary64_16963` `rem-sqrt-square_binary64_16940`
3×	`associate-/r_binary64_16873` `associate-/l_binary64_16874`
2×	`div-exp_binary64_16975` `associate-/r/_binary64_16875` `associate-r/_binary64_16871` `associate-l/_binary64_16872`
1×	`div-inv_binary64_16924` `cbrt-unprod_binary64_16957` `1-exp_binary64_16968` `inv-pow_binary64_17009` `rec-exp_binary64_16974` `rem-square-sqrt_binary64_16939` `pow-plus_binary64_16987` `*-commutative_binary64_16860` `pow-flip_binary64_16998` `prod-exp_binary64_16973` `sqrt-unprod_binary64_16946` `frac-2neg_binary64_16938` `clear-num_binary64_16926` `pow2_binary64_17005` `cbrt-undiv_binary64_16958`

Counts

4 → 165

Calls

4 calls:

22.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
20.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

series194.0ms (6%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
46.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
44.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
32.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify88.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5041	2482

prune209.0ms (6.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	176	9	185

Merged error: 0.0b

Counts

185 → 9

Compiler

Compiled 3464 to 2597 computations (25% saved)

localize10.0ms (0.3%)

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))

rewrite39.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_16927` `add-sqr-sqrt_binary64_16948`
18×	`add-cube-cbrt_binary64_16959`
13×	`cbrt-prod_binary64_16955`
10×	`add-exp-log_binary64_16962` `associate-r_binary64_16869`
9×	`sqrt-prod_binary64_16942` `times-frac_binary64_16933`
8×	`add-cbrt-cube_binary64_16960`
7×	`pow1_binary64_16985`
6×	`cbrt-div_binary64_16956`
4×	`flip3-+_binary64_16930` `flip-+_binary64_16901` `add-log-exp_binary64_16963`
3×	`unswap-sqr_binary64_16895` `associate-l_binary64_16870` `distribute-lft-out_binary64_16880` `associate-/r_binary64_16873` `associate-/l_binary64_16874`
2×	`pow1/3_binary64_17006` `div-exp_binary64_16975` `associate-/r/_binary64_16875` `associate-*r/_binary64_16871` `sqrt-div_binary64_16943`
1×	`div-inv_binary64_16924` `cbrt-unprod_binary64_16957` `1-exp_binary64_16968` `inv-pow_binary64_17009` `rec-exp_binary64_16974` `pow-prod-down_binary64_16995` `*-commutative_binary64_16860` `pow-flip_binary64_16998` `prod-exp_binary64_16973` `frac-2neg_binary64_16938` `clear-num_binary64_16926` `cbrt-undiv_binary64_16958`

Counts

4 → 90

Calls

4 calls:

13.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
10.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
4.0ms	(cbrt.f64 (+.f64 1 x))
4.0ms	(cbrt.f64 (+.f64 1 x))

series738.0ms (22.6%)

Counts

4 → 12

Calls

4 calls:

582.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
70.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
43.0ms	(cbrt.f64 (+.f64 1 x))
42.0ms	(cbrt.f64 (+.f64 1 x))

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5344	3235

prune174.0ms (5.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	102	9	111

Merged error: 0.0b

Counts

111 → 9

Compiler

Compiled 2977 to 2294 computations (22.9% saved)

regimes29.0ms (0.9%)

Compiler: Compiled 248 to 202 computations (18.5% 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%)

sample844.0ms (25.9%)

Algorithm

1×

intervals

Results

194.0ms	1934×	body	1024	valid
122.0ms	4310×	body	128	valid
77.0ms	1007×	body	512	valid
36.0ms	246×	body	2048	valid
27.0ms	503×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 272 to 224 computations (17.6% saved)

Details

analyze3.0ms (0.1%)

sample19.0ms (0.6%)

simplify170.0ms (5.2%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite17.0ms (0.5%)

series97.0ms (3%)

simplify95.0ms (2.9%)

prune50.0ms (1.5%)

localize6.0ms (0.2%)

rewrite33.0ms (1%)

series125.0ms (3.8%)

simplify69.0ms (2.1%)

prune95.0ms (2.9%)

localize8.0ms (0.3%)

rewrite70.0ms (2.2%)

series194.0ms (6%)

simplify88.0ms (2.7%)

prune209.0ms (6.4%)

localize10.0ms (0.3%)

rewrite39.0ms (1.2%)

series738.0ms (22.6%)

simplify68.0ms (2.1%)

prune174.0ms (5.3%)

regimes29.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample844.0ms (25.9%)

Profiling