Details

analyze363.0ms (13.1%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
43.7%	43.7%	12.6%	7
53.1%	34.3%	12.6%	8
57.8%	23.4%	18.8%	9
63.2%	18%	18.8%	10
66%	12.1%	22%	11
68.9%	9.2%	22%	12
70.3%	6.1%	23.5%	13
71.9%	4.6%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample798.0ms (28.9%)

Results

755.0ms	8256×	body	128	valid
17.0ms	196×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

13×	`fma-def_binary64`
7×	`associate-r_binary64`
7×	`associate-l_binary64`
5×	`*-commutative_binary64`
4×	`*-lft-identity_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	8
2	24	8
3	47	8
4	43	8
5	45	8
6	43	8

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

5.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.1b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.8b	(*.f64 x (fma.f64 y y 1))

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(*.f64 x (fma.f64 y y 1))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

3.0ms

(*.f64 x (fma.f64 y y 1))

simplify84.0ms (3%)

Algorithm

1×	egg-herbie

Rules

746×	`unswap-sqr_binary64`
561×	`distribute-rgt-in_binary64`
550×	`fma-def_binary64`
534×	`distribute-lft-in_binary64`
336×	`distribute-rgt-out_binary64`

Counts

46 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	447
1	81	404
2	264	404
3	597	404
4	1918	404
5	2078	404
6	2869	404
7	4919	404
8	4929	404

prune30.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	33	7	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	7	41

Error

2.5b

Counts

41 → 7

Alt Table

Status	Error	Program
	41.2b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 y y 1) x) 3))
▶	5.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	19.0b	x
	5.1b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
	5.4b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 y y 1)) (cbrt.f64 (fma.f64 y y 1)))) (cbrt.f64 (fma.f64 y y 1)))
	6.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
	31.3b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))

Compiler

Compiled 597 to 353 computations (40.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
✓	11.0b	(*.f64 (pow.f64 y 2) x)

series18.0ms (0.6%)

Counts

2 → 15

Calls

2 calls:

9.0ms	(+.f64 (*.f64 (pow.f64 y 2) x) x)
8.0ms	(*.f64 (pow.f64 y 2) x)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-l_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 45

Calls

2 calls:

4.0ms	(*.f64 (pow.f64 y 2) x)
4.0ms	(+.f64 (*.f64 (pow.f64 y 2) x) x)

simplify103.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-neg_binary64`
457×	`unswap-sqr_binary64`
452×	`associate-l_binary64`
340×	`distribute-rgt-out_binary64`
333×	`associate-r_binary64`

Counts

60 → 76

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	635
1	170	549
2	493	542
3	1822	542
4	4024	540
5	4733	540
6	4982	540
7	4937	540

prune56.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	77	6	83

Error

0.0b

Counts

83 → 6

Alt Table

Status	Error	Program
	41.2b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 y y 1) x) 3))
✓	5.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	32.9b	(+.f64 (.f64 (.f64 y (*.f64 y (sqrt.f64 x))) (sqrt.f64 x)) x)
▶	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
	5.4b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 y y 1)) (cbrt.f64 (fma.f64 y y 1)))) (cbrt.f64 (fma.f64 y y 1)))
	1.6b	(+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 2) (*.f64 (pow.f64 (cbrt.f64 y) 2) x)) x)

Compiler

Compiled 1075 to 615 computations (42.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (.f64 y x)) x)
✓	0.2b	(.f64 y (.f64 y x))

series16.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

8.0ms	(.f64 y (.f64 y x))
8.0ms	(+.f64 (.f64 y (.f64 y x)) x)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64`

Counts

2 → 34

Calls

2 calls:

7.0ms	(+.f64 (.f64 y (.f64 y x)) x)
4.0ms	(.f64 y (.f64 y x))

simplify87.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-neg_binary64`
495×	`associate-l_binary64`
399×	`cancel-sign-sub-inv_binary64`
371×	`*-commutative_binary64`
352×	`unswap-sqr_binary64`

Counts

82 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	730
1	163	709
2	497	696
3	1536	691
4	3445	689
5	4520	689
6	5015	689

prune36.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	57	5	62

Error

0.0b

Counts

62 → 5

Alt Table

Status	Error	Program
	32.1b	(+.f64 (.f64 (sqrt.f64 y) (.f64 x (pow.f64 y 3/2))) x)
	1.6b	(+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 2) (*.f64 (pow.f64 (cbrt.f64 y) 2) x)) x)
✓	5.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
✓	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
▶	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x))) x)

Compiler

Compiled 796 to 264 computations (66.8% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 y) (.f64 y x))
✓	0.3b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x)))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)

series446.0ms (16.1%)

Counts

4 → 72

Calls

4 calls:

352.0ms	(.f64 (cbrt.f64 y) (.f64 y x))
37.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
35.0ms	(cbrt.f64 y)
21.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x)))

rewrite25.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 108

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x)))
5.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
4.0ms	(.f64 (cbrt.f64 y) (.f64 y x))
1.0ms	(cbrt.f64 y)

simplify125.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

436×	`log-prod_binary64`
430×	`*-commutative_binary64`
363×	`sqr-pow_binary64`
298×	`associate-+l+_binary64`
294×	`exp-prod_binary64`

Counts

180 → 147

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	1693
1	247	1441
2	910	1400
3	1677	1330
4	3646	1230
5	4554	1230
6	4809	1230
7	4836	1230

prune144.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	2	0	2
Picked	1	0	1
Done	0	2	2
Total	183	5	188

Error

0.0b

Counts

188 → 5

Alt Table

Status	Error	Program
	5.2b	(+.f64 (.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 y x))) x)
	1.4b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 (cbrt.f64 y) y) x)) x)
	0.5b	(+.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)))) (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)))) (.f64 (cbrt.f64 y) (.f64 y x))) x)
✓	5.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
✓	0.1b	(+.f64 (.f64 y (.f64 y x)) x)

Compiler

Compiled 3397 to 909 computations (73.2% saved)

regimes292.0ms (10.6%)

Accuracy

Total 0.1b remaining (68%)

Threshold costs 0.1b (68%)

Counts

71 → 1

Compiler

Compiled 5847 to 3250 computations (44.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	9	10

end68.0ms (2.5%)

Compiler: Compiled 98 to 49 computations (50% saved)

Details

analyze363.0ms (13.1%)

sample798.0ms (28.9%)

simplify10.0ms (0.4%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify84.0ms (3%)

prune30.0ms (1.1%)

localize5.0ms (0.2%)

series18.0ms (0.6%)

rewrite9.0ms (0.3%)

simplify103.0ms (3.7%)

prune56.0ms (2%)

localize4.0ms (0.1%)

series16.0ms (0.6%)

rewrite12.0ms (0.4%)

simplify87.0ms (3.2%)

prune36.0ms (1.3%)

localize11.0ms (0.4%)

series446.0ms (16.1%)

rewrite25.0ms (0.9%)

simplify125.0ms (4.5%)

prune144.0ms (5.2%)

regimes292.0ms (10.6%)

simplify2.0ms (0.1%)

end68.0ms (2.5%)

Profiling