Details

analyze106.0ms (6.5%)

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)

sample766.0ms (46.8%)

Results

713.0ms	8256×	body	128	valid
13.0ms	165×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify7.0ms (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

4.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.1b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.8b	(*.f64 x (fma.f64 y y 1))

series11.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

11.0ms

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

rewrite3.0ms (0.2%)

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 (5.1%)

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

prune25.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	34	6	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	6	41

Error

2.0b

Counts

41 → 6

Alt Table

Status	Error	Program
	4.1b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
	34.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 y y 1)))
	5.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
	32.6b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))
▶	4.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	19.5b	x

Compiler

Compiled 557 to 323 computations (42% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
✓	8.6b	(*.f64 (pow.f64 y 2) x)

series16.0ms (1%)

Counts

2 → 15

Calls

2 calls:

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

rewrite8.0ms (0.5%)

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:

3.0ms	(*.f64 (pow.f64 y 2) x)
3.0ms	(+.f64 (*.f64 (pow.f64 y 2) x) x)

simplify106.0ms (6.5%)

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

prune60.0ms (3.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	71	5	76
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	74	8	82

Error

0.0b

Counts

82 → 8

Alt Table

Status	Error	Program
	1.8b	(+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 2) (*.f64 (pow.f64 (cbrt.f64 y) 2) x)) x)
	32.4b	(+.f64 (.f64 (.f64 y (sqrt.f64 x)) (*.f64 y (sqrt.f64 x))) x)
	4.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 y 2) x)) (cbrt.f64 (.f64 (pow.f64 y 2) x))) (cbrt.f64 (*.f64 (pow.f64 y 2) x))) x)
	34.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 y y 1)))
	5.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
✓	4.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
▶	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
	30.4b	(+.f64 (.f64 (pow.f64 (sqrt.f64 y) 2) (.f64 x y)) x)

Compiler

Compiled 1137 to 649 computations (42.9% saved)

localize4.0ms (0.2%)

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))

series19.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(+.f64 (.f64 y (.f64 y x)) x)
8.0ms	(.f64 y (.f64 y x))

rewrite9.0ms (0.5%)

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:

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

simplify82.0ms (5%)

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

prune43.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	57	7	64

Error

0.0b

Counts

64 → 7

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (*.f64 y x) x)
	32.4b	(+.f64 (.f64 (.f64 y (sqrt.f64 x)) (*.f64 y (sqrt.f64 x))) x)
	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x))) x)
	34.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 y y 1)))
	5.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
✓	4.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	30.4b	(+.f64 (.f64 (pow.f64 (sqrt.f64 y) 2) (.f64 x y)) x)

Compiler

Compiled 847 to 287 computations (66.1% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (*.f64 y x) x)

series7.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify63.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

792×	`distribute-rgt-in_binary64`
743×	`distribute-lft-in_binary64`
386×	`associate-/l*_binary64`
314×	`associate-l_binary64`
277×	`*-commutative_binary64`

Counts

34 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	310
1	36	293
2	94	293
3	299	293
4	1008	293
5	2959	293
6	3626	293
7	5141	293

prune14.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	24	7	31

Error

0.0b

Counts

31 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (*.f64 y x) x)
	32.4b	(+.f64 (.f64 (.f64 y (sqrt.f64 x)) (*.f64 y (sqrt.f64 x))) x)
	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x))) x)
	34.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 y y 1)))
	5.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
✓	4.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	30.4b	(+.f64 (.f64 (pow.f64 (sqrt.f64 y) 2) (.f64 x y)) x)

Compiler

Compiled 318 to 105 computations (67% saved)

regimes111.0ms (6.8%)

Accuracy

Total 0.1b remaining (72.9%)

Threshold costs 0.1b (72.9%)

Counts

26 → 1

Compiler

Compiled 1677 to 1034 computations (38.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	6	8
2	6	8

end76.0ms (4.6%)

Compiler: Compiled 101 to 55 computations (45.5% saved)

Details

analyze106.0ms (6.5%)

sample766.0ms (46.8%)

simplify7.0ms (0.4%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series11.0ms (0.7%)

rewrite3.0ms (0.2%)

simplify84.0ms (5.1%)

prune25.0ms (1.5%)

localize4.0ms (0.2%)

series16.0ms (1%)

rewrite8.0ms (0.5%)

simplify106.0ms (6.5%)

prune60.0ms (3.7%)

localize4.0ms (0.2%)

series19.0ms (1.2%)

rewrite9.0ms (0.5%)

simplify82.0ms (5%)

prune43.0ms (2.6%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite1.0ms (0%)

simplify63.0ms (3.8%)

prune14.0ms (0.9%)

regimes111.0ms (6.8%)

simplify2.0ms (0.1%)

end76.0ms (4.6%)

Profiling