Details

analyze2.0ms (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	60×	body	1024	valid
4.0ms	144×	body	128	valid
2.0ms	31×	body	512	valid
1.0ms	7×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune6.0ms (0.2%)

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: 28.5b

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))
2.7b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 34

Calls

2 calls:

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

series95.0ms (3%)

Counts

2 → 6

Calls

2 calls:

68.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify89.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4907	747
1	4907	747

prune47.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 0.1b

Counts

41 → 3

Compiler

Compiled 630 to 419 computations (33.5% 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)))

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
7×	`add-exp-log_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

3 → 75

Calls

3 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series131.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

63.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
41.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify64.0ms (2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5545	1516

prune95.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Merged error: 0.0b

Counts

87 → 8

Compiler

Compiled 1494 to 1067 computations (28.6% 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))))

rewrite65.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`sqrt-prod_binary64`
62×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
40×	`sqrt-pow1_binary64`
32×	`pow1_binary64` `sqrt-div_binary64`
28×	`add-cube-cbrt_binary64`
20×	`pow1/2_binary64`
18×	`swap-sqr_binary64`
10×	`associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
9×	`flip3-+_binary64` `pow-prod-up_binary64` `unswap-sqr_binary64` `times-frac_binary64` `flip-+_binary64`
8×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64` `rem-sqrt-square_binary64` `frac-times_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`associate-r/_binary64` `associate-/r/_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `inv-pow_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-flip_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 165

Calls

4 calls:

20.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
18.0ms	(/.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)))

series183.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
49.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
40.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
31.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify85.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5041	2482

prune207.0ms (6.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	177	8	185

Merged error: 0.0b

Counts

185 → 8

Compiler

Compiled 3410 to 2554 computations (25.1% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.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))

rewrite36.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
13×	`cbrt-prod_binary64`
10×	`associate-r_binary64` `add-exp-log_binary64`
9×	`times-frac_binary64` `sqrt-prod_binary64`
8×	`add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`cbrt-div_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
2×	`associate-*r/_binary64` `pow1/3_binary64` `associate-/r/_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
9.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
4.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

series731.0ms (22.8%)

Counts

4 → 12

Calls

4 calls:

571.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
76.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
43.0ms	(cbrt.f64 (+.f64 1 x))
40.0ms	(cbrt.f64 (+.f64 1 x))

simplify57.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5344	3235

prune168.0ms (5.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	101	9	110

Merged error: 0.0b

Counts

110 → 9

Compiler

Compiled 2977 to 2294 computations (22.9% saved)

regimes26.0ms (0.8%)

Compiler: Compiled 216 to 177 computations (18.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	13	26

end0.0ms (0%)

sample1.0s (31.5%)

Algorithm

1×

intervals

Results

200.0ms	2001×	body	1024	valid
124.0ms	4252×	body	128	valid
76.0ms	1014×	body	512	valid
27.0ms	218×	body	2048	valid
26.0ms	515×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 247 to 205 computations (17% saved)

Details

analyze2.0ms (0.1%)

sample19.0ms (0.6%)

simplify10.0ms (0.3%)

prune6.0ms (0.2%)

localize5.0ms (0.2%)

rewrite15.0ms (0.5%)

series95.0ms (3%)

simplify89.0ms (2.8%)

prune47.0ms (1.5%)

localize6.0ms (0.2%)

rewrite30.0ms (1%)

series131.0ms (4.1%)

simplify64.0ms (2%)

prune95.0ms (3%)

localize8.0ms (0.3%)

rewrite65.0ms (2%)

series183.0ms (5.7%)

simplify85.0ms (2.6%)

prune207.0ms (6.5%)

localize12.0ms (0.4%)

rewrite36.0ms (1.1%)

series731.0ms (22.8%)

simplify57.0ms (1.8%)

prune168.0ms (5.2%)

regimes26.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (31.5%)

Profiling