Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
25%	0%	75%	1

Compiler

Compiled 13 to 7 computations (46.2% saved)

sample14.0ms (0.7%)

Algorithm

1×

intervals

Results

5.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 22 to 12 computations (45.5% saved)

simplify248.0ms (12.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (153.0ms)

Iter	Nodes	Cost
0	4762	10
1	4762	10

prune6.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 16 to 9 computations (43.8% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (.f64 x x))
0.0b	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
0.0b	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
0.1b	(.f64 x (.f64 x x))

rewrite18.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64_2526`
10×	`add-cbrt-cube_binary64_2501`
7×	`add-exp-log_binary64_2503`
5×	`pow-prod-up_binary64_2535`
4×	`add-log-exp_binary64_2504` `add-sqr-sqrt_binary64_2487`
3×	`-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `associate-l*_binary64_2406` `cbrt-unprod_binary64_2498`
1×	`flip3-+_binary64_2468` `distribute-lft1-in_binary64_2420` `-commutative_binary64_2396` `+-commutative_binary64_2395` `pow-plus_binary64_2528` `sum-log_binary64_2556` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `cube-unmult_binary64_2502` `pow2_binary64_2546` `associate-r*_binary64_2405` `distribute-lft-out_binary64_2416` `pow-sqr_binary64_2438` `rem-3cbrt-rft_binary64_2491`

Counts

2 → 38

Calls

4 calls:

8.0ms	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
6.0ms	(.f64 x (.f64 x x))
0.0ms	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
0.0ms	(.f64 x (.f64 x x))

series81.0ms (4.1%)

Counts

2 → 9

Calls

2 calls:

51.0ms	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
29.0ms	(.f64 x (.f64 x x))

Compiler

Compiled 93 to 75 computations (19.4% saved)

simplify103.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4931	316
1	4931	316

prune40.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Error

Counts

48 → 3

Compiler

Compiled 479 to 222 computations (53.7% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 x (+.f64 x (.f64 x x)))
0.0b	(.f64 x (+.f64 x (.f64 x x)))

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2487` `associate-r_binary64_2405`
4×	`*-un-lft-identity_binary64_2465`
3×	`add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526` `associate-l_binary64_2406`
2×	`associate-*r/_binary64_2407`
1×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `distribute-lft-in_binary64_2414` `*-commutative_binary64_2396` `flip-+_binary64_2439` `distribute-rgt1-in_binary64_2421` `unswap-sqr_binary64_2433` `distribute-rgt-in_binary64_2415` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `distribute-rgt-out_binary64_2418` `cbrt-unprod_binary64_2498`

Counts

1 → 24

Calls

2 calls:

6.0ms	(.f64 x (+.f64 x (.f64 x x)))
0.0ms	(.f64 x (+.f64 x (.f64 x x)))

series55.0ms (2.8%)

Counts

1 → 6

Calls

1 calls:

55.0ms

(*.f64 x (+.f64 x (*.f64 x x)))

Compiler

Compiled 51 to 45 computations (11.8% saved)

simplify91.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4925	319
1	4925	319

prune18.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	30	3	33

Error

Counts

33 → 3

Compiler

Compiled 343 to 97 computations (71.7% saved)

localize7.0ms (0.4%)

Local error

Found 8 expressions with local error:

29.7b	(sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 3)))
0.0b	(+.f64 (*.f64 x x) (pow.f64 x 3))
0.0b	(+.f64 (*.f64 x x) (pow.f64 x 3))
0.0b	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 3))))
0.0b	(+.f64 (*.f64 x x) (pow.f64 x 3))
0.0b	(+.f64 (*.f64 x x) (pow.f64 x 3))
29.7b	(sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 3)))
29.7b	(sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 3)))

rewrite30.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_2481`
8×	`add-log-exp_binary64_2504` `add-sqr-sqrt_binary64_2487` `cube-mult_binary64_2495`
6×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
4×	`flip3-+_binary64_2468` `unpow3_binary64_2531` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `distribute-rgt1-in_binary64_2421` `add-cbrt-cube_binary64_2501` `distribute-lft-out_binary64_2416` `sqrt-div_binary64_2482` `distribute-rgt-out_binary64_2418`
2×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`

Counts

4 → 64

Calls

8 calls:

7.0ms	(+.f64 (*.f64 x x) (pow.f64 x 3))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 3)))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 3)))
6.0ms	(+.f64 (*.f64 x x) (pow.f64 x 3))
0.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 3))))

series157.0ms (8%)

Counts

4 → 24

Calls

4 calls:

54.0ms	(+.f64 (*.f64 x x) (pow.f64 x 3))
51.0ms	(+.f64 (*.f64 x x) (pow.f64 x 3))
29.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 3)))
23.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 3)))

Compiler

Compiled 558 to 424 computations (24% saved)

simplify91.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4937	1100
1	4937	1100

prune85.0ms (4.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	88	3	91

Error

Counts

91 → 3

Compiler

Compiled 1778 to 988 computations (44.4% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 x) (.f64 (+.f64 x 1) (pow.f64 x 3/2)))
0.0b	(*.f64 (+.f64 x 1) (pow.f64 x 3/2))
0.0b	(*.f64 (+.f64 x 1) (pow.f64 x 3/2))
0.2b	(.f64 (sqrt.f64 x) (.f64 (+.f64 x 1) (pow.f64 x 3/2)))

rewrite25.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64_2503`
12×	`add-sqr-sqrt_binary64_2487`
10×	`prod-exp_binary64_2514` `associate-l_binary64_2406`
9×	`*-un-lft-identity_binary64_2465` `add-cbrt-cube_binary64_2501`
8×	`associate-r_binary64_2405`
7×	`add-cube-cbrt_binary64_2500`
4×	`associate-*l/_binary64_2408` `unpow-prod-down_binary64_2544` `pow1_binary64_2526` `cbrt-unprod_binary64_2498`
3×	`sqrt-prod_binary64_2481` `unswap-sqr_binary64_2433`
2×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `-commutative_binary64_2396` `flip-+_binary64_2439` `associate-r/_binary64_2407` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `sqr-pow_binary64_2437`
1×	`pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416`

Counts

2 → 52

Calls

4 calls:

11.0ms	(*.f64 (+.f64 x 1) (pow.f64 x 3/2))
10.0ms	(.f64 (sqrt.f64 x) (.f64 (+.f64 x 1) (pow.f64 x 3/2)))
0.0ms	(*.f64 (+.f64 x 1) (pow.f64 x 3/2))
0.0ms	(.f64 (sqrt.f64 x) (.f64 (+.f64 x 1) (pow.f64 x 3/2)))

series63.0ms (3.2%)

Counts

2 → 8

Calls

2 calls:

43.0ms	(.f64 (sqrt.f64 x) (.f64 (+.f64 x 1) (pow.f64 x 3/2)))
20.0ms	(*.f64 (+.f64 x 1) (pow.f64 x 3/2))

Compiler

Compiled 148 to 122 computations (17.6% saved)

simplify92.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4912	728
1	4912	728

prune42.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	60	3	63

Error

Counts

63 → 3

Compiler

Compiled 781 to 407 computations (47.9% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	180
1	105	180

regimes21.0ms (1.1%)

Compiler: Compiled 127 to 89 computations (29.9% saved)

bsearch0.0ms (0%)

regimes11.0ms (0.6%)

Compiler: Compiled 15 to 15 computations (0% saved)

bsearch0.0ms (0%)

regimes9.0ms (0.4%)

Compiler: Compiled 8 to 10 computations (-25% saved)

bsearch0.0ms (0%)

regimes7.0ms (0.4%)

Accuracy

Total 0.0b remaining (99.2%)

Threshold costs 0.0b (99.2%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 19 to 15 computations (21.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	26
1	13	26

end0.0ms (0%)

sample623.0ms (31.6%)

Algorithm

1×

intervals

Results

150.0ms	8000×	body	128	valid
111.0ms	8000×	pre	128	true

Compiler

Compiled 164 to 115 computations (29.9% saved)

Pareto

0.6434824103885094

Details

analyze1.0ms (0.1%)

sample14.0ms (0.7%)

simplify248.0ms (12.6%)

prune6.0ms (0.3%)

localize5.0ms (0.2%)

rewrite18.0ms (0.9%)

series81.0ms (4.1%)

simplify103.0ms (5.2%)

prune40.0ms (2%)

localize4.0ms (0.2%)

rewrite8.0ms (0.4%)

series55.0ms (2.8%)

simplify91.0ms (4.6%)

prune18.0ms (0.9%)

localize7.0ms (0.4%)

rewrite30.0ms (1.5%)

series157.0ms (8%)

simplify91.0ms (4.6%)

prune85.0ms (4.3%)

localize9.0ms (0.4%)

rewrite25.0ms (1.3%)

series63.0ms (3.2%)

simplify92.0ms (4.7%)

prune42.0ms (2.1%)

simplify5.0ms (0.3%)

regimes21.0ms (1.1%)

bsearch0.0ms (0%)

regimes11.0ms (0.6%)

bsearch0.0ms (0%)

regimes9.0ms (0.4%)

bsearch0.0ms (0%)

regimes7.0ms (0.4%)

bsearch2.0ms (0.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample623.0ms (31.6%)

Profiling