Details

analyze884.0ms (9.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample34.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
6.0ms	108×	body	128	invalid

Compiler

Compiled 40 to 26 computations (35% saved)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
795×	`div-sub_binary64`
536×	`times-frac_binary64`
518×	`neg-mul-1_binary64`
376×	`distribute-frac-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	27	20
2	65	20
3	126	20
4	278	20
5	602	20
6	1317	19
7	2853	19
8	4446	19
9	4743	19
10	4991	19

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

10.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	10.8b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
	27.4b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 58 computations (41.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
✓	0.7b	(-.f64 (.f64 z z) (.f64 x x))
✓	10.7b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-cube-cbrt_binary64`
14×	`add-log-exp_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`flip3--_binary64`

Counts

3 → 147

Calls

3 calls:

19.0ms	(-.f64 (.f64 z z) (.f64 x x))
17.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
15.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)

series147.0ms (1.6%)

Counts

3 → 96

Calls

3 calls:

66.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
63.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
17.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify181.0ms (2%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-neg_binary64`
684×	`fma-def_binary64`
373×	`cancel-sign-sub-inv_binary64`
234×	`distribute-rgt-neg-in_binary64`
205×	`distribute-lft-neg-in_binary64`

Counts

243 → 393

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	3769
1	494	3575
2	2057	3411
3	4220	3393
4	4974	3393
5	4880	3393

prune154.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	386	7	393
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	388	7	395

Error

2.5b

Counts

395 → 7

Alt Table

Status	Error	Program
	11.1b	(.f64 -1/2 (-.f64 (/.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) y))
	52.7b	(.f64 -1/2 (neg.f64 (/.f64 (.f64 x x) y)))
	10.8b	(.f64 -1/2 (-.f64 (.f64 (-.f64 (.f64 z z) (.f64 x x)) (/.f64 1 y)) y))
	12.8b	(*.f64 -1/2 (neg.f64 (fma.f64 (/.f64 x y) x y)))
	25.0b	(.f64 -1/2 (-.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) 3)) y))
	11.1b	(.f64 -1/2 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y)) 3) y))
▶	10.8b	(.f64 -1/2 (-.f64 (pow.f64 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x))) -1) y))

Compiler

Compiled 4862 to 1350 computations (72.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (pow.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))) -1) y)
✓	0.5b	(pow.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))) -1)
	0.7b	(-.f64 (.f64 z z) (.f64 x x))
✓	10.8b	(/.f64 y (-.f64 (.f64 z z) (.f64 x x)))

rewrite52.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-cube-cbrt_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`
11×	`pow1_binary64`

Counts

3 → 137

Calls

3 calls:

18.0ms	(/.f64 y (-.f64 (.f64 z z) (.f64 x x)))
16.0ms	(-.f64 (pow.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))) -1) y)
11.0ms	(pow.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))) -1)

series349.0ms (3.8%)

Counts

3 → 108

Calls

3 calls:

157.0ms	(pow.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))) -1)
124.0ms	(-.f64 (pow.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))) -1) y)
68.0ms	(/.f64 y (-.f64 (.f64 z z) (.f64 x x)))

simplify171.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

628×	`fma-def_binary64`
479×	`fma-neg_binary64`
312×	`distribute-rgt-in_binary64`
216×	`cancel-sign-sub-inv_binary64`
157×	`distribute-rgt-neg-in_binary64`

Counts

245 → 424

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	4425
1	484	4034
2	2003	3880
3	4572	3877
4	4918	3877

prune195.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	536	1	537
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	537	7	544

Error

2.5b

Counts

544 → 7

Alt Table

Status	Error	Program
	12.8b	(*.f64 -1/2 (neg.f64 (fma.f64 (/.f64 x y) x y)))
	11.1b	(.f64 -1/2 (-.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) 3) -1) y))
	11.1b	(.f64 -1/2 (-.f64 (/.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) y))
	52.7b	(.f64 -1/2 (neg.f64 (/.f64 (.f64 x x) y)))
▶	10.8b	(.f64 -1/2 (-.f64 (.f64 (-.f64 (.f64 z z) (.f64 x x)) (/.f64 1 y)) y))
	11.1b	(.f64 -1/2 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y)) 3) y))
✓	10.8b	(.f64 -1/2 (-.f64 (pow.f64 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x))) -1) y))

Compiler

Compiled 6902 to 2431 computations (64.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y)) y)
	0.7b	(-.f64 (.f64 z z) (.f64 x x))
✓	10.8b	(.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-cube-cbrt_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`flip3--_binary64`
9×	`pow1_binary64`
8×	`add-log-exp_binary64`

Counts

2 → 93

Calls

2 calls:

19.0ms	(-.f64 (.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y)) y)
17.0ms	(.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y))

series111.0ms (1.2%)

Counts

2 → 72

Calls

2 calls:

57.0ms	(-.f64 (.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y)) y)
54.0ms	(.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y))

simplify130.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-neg_binary64`
609×	`times-frac_binary64`
515×	`fma-def_binary64`
228×	`cancel-sign-sub-inv_binary64`
217×	`log-prod_binary64`

Counts

165 → 293

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	2903
1	383	2618
2	1428	2593
3	4329	2593
4	5138	2593

prune149.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	519	0	519
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	519	7	526

Error

2.5b

Counts

526 → 7

Alt Table

Status	Error	Program
	12.8b	(*.f64 -1/2 (neg.f64 (fma.f64 (/.f64 x y) x y)))
▶	11.1b	(.f64 -1/2 (-.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) 3) -1) y))
	11.1b	(.f64 -1/2 (-.f64 (/.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) y))
	52.7b	(.f64 -1/2 (neg.f64 (/.f64 (.f64 x x) y)))
✓	10.8b	(.f64 -1/2 (-.f64 (.f64 (-.f64 (.f64 z z) (.f64 x x)) (/.f64 1 y)) y))
	11.1b	(.f64 -1/2 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y)) 3) y))
✓	10.8b	(.f64 -1/2 (-.f64 (pow.f64 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x))) -1) y))

Compiler

Compiled 5398 to 2067 computations (61.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(pow.f64 (cbrt.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x)))) 3)
	0.7b	(-.f64 (.f64 z z) (.f64 x x))
✓	10.7b	(cbrt.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))))
	10.8b	(/.f64 y (-.f64 (.f64 z z) (.f64 x x)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cube-cbrt_binary64`
9×	`cbrt-div_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`pow1/3_binary64`
6×	`log1p-expm1-u_binary64`

Counts

2 → 84

Calls

2 calls:

12.0ms	(pow.f64 (cbrt.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x)))) 3)
9.0ms	(cbrt.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))))

series2.5s (27.3%)

Counts

2 → 72

Calls

2 calls:

1.4s	(pow.f64 (cbrt.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x)))) 3)
1.1s	(cbrt.f64 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))))

simplify226.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
461×	`unswap-sqr_binary64`
199×	`associate-r_binary64`
176×	`associate-/l*_binary64`
159×	`associate-l_binary64`

Counts

156 → 268

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	307	4798
1	829	4437
2	3071	3841
3	5328	3841

prune885.0ms (9.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	856	3	859
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	856	10	866

Error

1.2b

Counts

866 → 10

Alt Table

Status	Error	Program
	52.7b	(.f64 -1/2 (neg.f64 (/.f64 (.f64 x x) y)))
	54.9b	(.f64 -1/2 (-.f64 (pow.f64 (pow.f64 (.f64 (pow.f64 y 1/3) (pow.f64 (/.f64 1 z) 2/3)) 3) -1) y))
	12.8b	(*.f64 -1/2 (neg.f64 (fma.f64 (/.f64 x y) x y)))
✓	11.1b	(.f64 -1/2 (-.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) 3) -1) y))
	52.2b	(.f64 -1/2 (-.f64 (pow.f64 (pow.f64 (.f64 (pow.f64 y 1/3) (pow.f64 (/.f64 -1 z) 2/3)) 3) -1) y))
	11.1b	(.f64 -1/2 (-.f64 (/.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) y))
	54.9b	(.f64 -1/2 (-.f64 (pow.f64 (pow.f64 (exp.f64 (.f64 1/3 (+.f64 (*.f64 2 (log.f64 (/.f64 1 z))) (log.f64 y)))) 3) -1) y))
✓	10.8b	(.f64 -1/2 (-.f64 (.f64 (-.f64 (.f64 z z) (.f64 x x)) (/.f64 1 y)) y))
	11.1b	(.f64 -1/2 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y)) 3) y))
✓	10.8b	(.f64 -1/2 (-.f64 (pow.f64 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x))) -1) y))

Compiler

Compiled 9820 to 5646 computations (42.5% saved)

regimes1.3s (14.1%)

Accuracy

Total 1.9b remaining (49.4%)

Threshold costs 0b (0%)

Compiler

Compiled 10355 to 7057 computations (31.8% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	26	40
2	35	40
3	39	40
4	40	40
5	39	40

end1.0ms (0%)

Compiler: Compiled 31 to 15 computations (51.6% saved)

sample1.5s (16.1%)

Algorithm

1×

intervals

Results

643.0ms	8000×	body	128	valid
231.0ms	2932×	body	128	invalid

Compiler

Compiled 238 to 165 computations (30.7% saved)

Details

analyze884.0ms (9.6%)

sample34.0ms (0.4%)

simplify77.0ms (0.8%)

prune4.0ms (0%)

localize8.0ms (0.1%)

rewrite59.0ms (0.6%)

series147.0ms (1.6%)

simplify181.0ms (2%)

prune154.0ms (1.7%)

localize14.0ms (0.1%)

rewrite52.0ms (0.6%)

series349.0ms (3.8%)

simplify171.0ms (1.9%)

prune195.0ms (2.1%)

localize9.0ms (0.1%)

rewrite42.0ms (0.5%)

series111.0ms (1.2%)

simplify130.0ms (1.4%)

prune149.0ms (1.6%)

localize14.0ms (0.1%)

rewrite24.0ms (0.3%)

series2.5s (27.3%)

simplify226.0ms (2.4%)

prune885.0ms (9.6%)

regimes1.3s (14.1%)

bsearch7.0ms (0.1%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample1.5s (16.1%)

Profiling