Details

analyze116.0ms (4.6%)

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
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)

sample964.0ms (38.2%)

Results

919.0ms	8256×	body	128	valid
16.0ms	189×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify7.0ms (0.3%)

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

6.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.6b	(*.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
✓	6.1b	(*.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))

rewrite6.0ms (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:

5.0ms

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

simplify86.0ms (3.4%)

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

prune29.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Error

3.5b

Counts

41 → 4

Alt Table

Status	Error	Program
▶	6.6b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	19.4b	x
	6.6b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
	36.0b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))

Compiler

Compiled 503 to 293 computations (41.7% 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)
✓	11.4b	(*.f64 (pow.f64 y 2) x)

series19.0ms (0.8%)

Counts

2 → 15

Calls

2 calls:

11.0ms	(+.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)
3.0ms	(+.f64 (*.f64 (pow.f64 y 2) x) x)

simplify100.0ms (3.9%)

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

prune49.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	75	5	80

Error

0.0b

Counts

80 → 5

Alt Table

Status	Error	Program
	37.3b	(+.f64 (.f64 (.f64 y (*.f64 y (sqrt.f64 x))) (sqrt.f64 x)) x)
✓	6.6b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
▶	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
	6.6b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
	36.0b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))

Compiler

Compiled 1031 to 587 computations (43.1% 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)
✓	0.1b	(.f64 y (.f64 y x))

series16.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

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

rewrite12.0ms (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:

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

simplify82.0ms (3.3%)

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 (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	2	1	3
Picked	0	1	1
Done	1	0	1
Total	56	5	61

Error

Counts

61 → 5

Alt Table

Status	Error	Program
	37.3b	(+.f64 (.f64 (.f64 y (*.f64 y (sqrt.f64 x))) (sqrt.f64 x)) x)
✓	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
	37.0b	(+.f64 (.f64 (sqrt.f64 y) (.f64 x (pow.f64 y 3/2))) x)
▶	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x))) x)
	21.6b	(+.f64 (.f64 (sqrt.f64 (.f64 y (.f64 y x))) (sqrt.f64 (.f64 y (*.f64 y x)))) x)

Compiler

Compiled 811 to 264 computations (67.4% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series449.0ms (17.8%)

Counts

4 → 72

Calls

4 calls:

358.0ms	(.f64 (cbrt.f64 y) (.f64 y x))
36.0ms	(cbrt.f64 y)
35.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
20.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x)))

rewrite25.0ms (1%)

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:

8.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x)))
7.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
4.0ms	(.f64 (cbrt.f64 y) (.f64 y x))
1.0ms	(cbrt.f64 y)

simplify123.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

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

Counts

180 → 146

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

prune106.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	182	5	187

Error

Counts

187 → 5

Alt Table

Status	Error	Program
	37.3b	(+.f64 (.f64 (.f64 y (*.f64 y (sqrt.f64 x))) (sqrt.f64 x)) x)
✓	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
	37.0b	(+.f64 (.f64 (sqrt.f64 y) (.f64 x (pow.f64 y 3/2))) x)
✓	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x))) x)
	21.6b	(+.f64 (.f64 (sqrt.f64 (.f64 y (.f64 y x))) (sqrt.f64 (.f64 y (*.f64 y x)))) x)

Compiler

Compiled 3371 to 900 computations (73.3% saved)

regimes197.0ms (7.8%)

Accuracy

Total 0.0b remaining (53.8%)

Threshold costs 0.0b (53.8%)

Counts

47 → 1

Compiler

Compiled 3140 to 1915 computations (39% 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

end61.0ms (2.4%)

Compiler: Compiled 85 to 45 computations (47.1% saved)

Details

analyze116.0ms (4.6%)

sample964.0ms (38.2%)

simplify7.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite6.0ms (0.2%)

simplify86.0ms (3.4%)

prune29.0ms (1.1%)

localize4.0ms (0.2%)

series19.0ms (0.8%)

rewrite9.0ms (0.3%)

simplify100.0ms (3.9%)

prune49.0ms (2%)

localize4.0ms (0.2%)

series16.0ms (0.6%)

rewrite12.0ms (0.5%)

simplify82.0ms (3.3%)

prune36.0ms (1.4%)

localize7.0ms (0.3%)

series449.0ms (17.8%)

rewrite25.0ms (1%)

simplify123.0ms (4.9%)

prune106.0ms (4.2%)

regimes197.0ms (7.8%)

simplify2.0ms (0.1%)

end61.0ms (2.4%)

Profiling