Details

analyze337.0ms (12.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	11
1	12	11
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	50%	50%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample17.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	11
1	12	11

prune4.0ms (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

0.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize11.0ms (0.4%)

Local error

Found 1 expressions with local error:

0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

rewrite63.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

17×	`add-sqr-sqrt_binary64`
14×	`sqrt-prod_binary64`
10×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64`
6×	`associate-r_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64` `associate-*l/_binary64` `difference-of-squares_binary64`
1×	`prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `flip3--_binary64` `flip--_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

1 → 36

Calls

1 calls:

18.0ms

(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 505 to 324 computations (35.8% saved)

series42.0ms (1.5%)

Error

0.0b

Counts

1 → 6

Calls

1 calls:

37.0ms

(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 106 to 89 computations (16% saved)

simplify97.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4856	553
1	4856	553

prune34.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	4	43

Error

Counts

43 → 4

Compiler

Compiled 529 to 337 computations (36.3% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 x 1))
0.5b	(cbrt.f64 (-.f64 x 1))
0.5b	(cbrt.f64 (-.f64 x 1))
0.5b	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))

rewrite213.0ms (7.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

61×	`cbrt-prod_binary64`
55×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
18×	`cbrt-div_binary64`
16×	`difference-of-squares_binary64`
15×	`add-cube-cbrt_binary64`
14×	`swap-sqr_binary64`
11×	`pow1_binary64`
10×	`associate-l_binary64` `associate-r_binary64`
9×	`pow1/3_binary64` `flip3--_binary64` `flip--_binary64` `distribute-lft-out--_binary64` `difference-of-sqr-1_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `frac-times_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `associate-l/_binary64` `associate-r/_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `*-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

17.0ms	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
4.0ms	(cbrt.f64 (-.f64 x 1))
3.0ms	(cbrt.f64 (-.f64 x 1))
3.0ms	(cbrt.f64 (-.f64 x 1))

Compiler

Compiled 3117 to 2347 computations (24.7% saved)

series264.0ms (9.7%)

Error

Counts

4 → 27

Calls

4 calls:

89.0ms	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
46.0ms	(cbrt.f64 (-.f64 x 1))
44.0ms	(cbrt.f64 (-.f64 x 1))
43.0ms	(cbrt.f64 (-.f64 x 1))

Compiler

Compiled 1817 to 1546 computations (14.9% saved)

simplify57.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5022	2292

prune203.0ms (7.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	142	4	146

Error

Counts

146 → 4

Compiler

Compiled 3581 to 2649 computations (26% saved)

localize2.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

Counts

4 → 4

Compiler

Compiled 14 to 11 computations (21.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 x x) 1)
0.2b	(.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (.f64 x x) 1)))
18.1b	(/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 x 1)))
28.1b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite153.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

27×	`sqrt-prod_binary64`
26×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64` `associate-r_binary64`
8×	`sqrt-div_binary64`
7×	`times-frac_binary64` `associate-/r*_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64` `associate-l_binary64`
4×	`flip3--_binary64` `flip--_binary64` `associate-*r/_binary64` `unswap-sqr_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `difference-of-sqr-1_binary64` `pow-prod-down_binary64` `cancel-sign-sub-inv_binary64`
2×	`prod-exp_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `distribute-lft-out_binary64` `associate-/l/_binary64` `associate-/r/_binary64`
1×	`rem-sqrt-square_binary64` `sqrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-/l_binary64` `-commutative_binary64` `diff-log_binary64` `sub-neg_binary64`

Counts

4 → 104

Calls

4 calls:

13.0ms	(/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 x 1)))
11.0ms	(.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
4.0ms	(-.f64 (*.f64 x x) 1)

Compiler

Compiled 2291 to 1404 computations (38.7% saved)

series124.0ms (4.5%)

Error

Counts

4 → 21

Calls

4 calls:

34.0ms	(/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 x 1)))
31.0ms	(-.f64 (*.f64 x x) 1)
27.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
17.0ms	(.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (.f64 x x) 1)))

Compiler

Compiled 624 to 495 computations (20.7% saved)

simplify80.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4977	1881
1	4977	1881

prune116.0ms (4.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	125	4	129

Error

Counts

129 → 4

Compiler

Compiled 2207 to 1369 computations (38% saved)

regimes97.0ms (3.5%)

Accuracy

Total 0.5b remaining (100%)

Threshold costs 0.5b (100%)

Compiler

Compiled 616 to 492 computations (20.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	11
1	18	11

end0.0ms (0%)

sample783.0ms (28.6%)

Algorithm

1×

intervals

Results

231.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 315 to 253 computations (19.7% saved)

Details

analyze337.0ms (12.3%)

sample17.0ms (0.6%)

simplify8.0ms (0.3%)

prune4.0ms (0.1%)

localize11.0ms (0.4%)

rewrite63.0ms (2.3%)

series42.0ms (1.5%)

simplify97.0ms (3.5%)

prune34.0ms (1.2%)

localize10.0ms (0.4%)

rewrite213.0ms (7.8%)

series264.0ms (9.7%)

simplify57.0ms (2.1%)

prune203.0ms (7.4%)

localize2.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.2%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite153.0ms (5.6%)

series124.0ms (4.5%)

simplify80.0ms (2.9%)

prune116.0ms (4.3%)

regimes97.0ms (3.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample783.0ms (28.6%)

Profiling