Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample826.0ms (34.5%)

Results

573.0ms	7628×	body	128	valid
75.0ms	340×	body	1024	valid
40.0ms	212×	body	512	valid
11.0ms	76×	body	256	valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify75.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

927×	`fma-def_binary64`
405×	`fma-neg_binary64`
127×	`cancel-sign-sub-inv_binary64`
85×	`distribute-rgt-in_binary64`
63×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	92	8
4	173	8
5	259	8
6	365	8
7	561	8
8	580	8
9	675	8
10	798	8
11	821	8
12	918	8
13	922	8
14	922	8
15	803	8

prune6.0ms (0.2%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 x (fma.f64 x -9 6))
	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)

Compiler

Compiled 50 to 38 computations (24% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x -9 6)
✓	0.1b	(*.f64 x (fma.f64 x -9 6))

series9.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(*.f64 x (fma.f64 x -9 6))
3.0ms	(fma.f64 x -9 6)

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

6.0ms	(*.f64 x (fma.f64 x -9 6))
1.0ms	(fma.f64 x -9 6)

simplify74.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

773×	`distribute-rgt-in_binary64`
772×	`distribute-lft-in_binary64`
771×	`distribute-rgt-neg-out_binary64`
353×	`unsub-neg_binary64`
312×	`fma-def_binary64`

Counts

56 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	575
1	96	457
2	263	457
3	848	457
4	3098	457
5	5369	457

prune81.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	41	7	48
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Error

0.0b

Counts

50 → 7

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	14.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
	1.2b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 x -9 6)) (cbrt.f64 (fma.f64 x -9 6)))) (cbrt.f64 (fma.f64 x -9 6)))
	34.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
	1.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
	47.4b	(.f64 (sqrt.f64 (.f64 x (fma.f64 x -9 6))) (sqrt.f64 (*.f64 x (fma.f64 x -9 6))))
	3.6b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))

Compiler

Compiled 670 to 477 computations (28.8% saved)

localize12.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
✓	0.1b	(*.f64 9 (pow.f64 x 2))

series11.0ms (0.5%)

Counts

2 → 3

Calls

2 calls:

6.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
5.0ms	(*.f64 9 (pow.f64 x 2))

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 45

Calls

2 calls:

9.0ms	(*.f64 9 (pow.f64 x 2))
6.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))

simplify104.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

678×	`fma-neg_binary64`
408×	`associate-l_binary64`
344×	`cancel-sign-sub-inv_binary64`
343×	`associate-r_binary64`
266×	`distribute-rgt-neg-in_binary64`

Counts

48 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	604
1	186	503
2	497	466
3	1973	465
4	4384	465
5	4806	465

prune245.0ms (10.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Error

0.0b

Counts

83 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	14.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
	34.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
	47.4b	(.f64 (sqrt.f64 (.f64 x (fma.f64 x -9 6))) (sqrt.f64 (*.f64 x (fma.f64 x -9 6))))
	3.6b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	0.2b	(-.f64 (.f64 6 x) (.f64 (.f64 x 3) (.f64 x 3)))

Compiler

Compiled 1236 to 941 computations (23.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
✓	0.1b	(.f64 -9 (.f64 x x))

series9.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(fma.f64 6 x (.f64 -9 (.f64 x x)))
4.0ms	(.f64 -9 (.f64 x x))

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`associate-l_binary64`

Counts

2 → 31

Calls

2 calls:

8.0ms	(.f64 -9 (.f64 x x))
1.0ms	(fma.f64 6 x (.f64 -9 (.f64 x x)))

simplify101.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

920×	`fma-def_binary64`
581×	`neg-mul-1_binary64`
503×	`distribute-rgt-neg-out_binary64`
449×	`unsub-neg_binary64`
302×	`*-commutative_binary64`

Counts

55 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	583
1	99	505
2	228	496
3	795	458
4	1990	458
5	4389	458
6	5088	458

prune35.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	46	6	52

Error

0.0b

Counts

52 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	14.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
	34.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
	47.4b	(.f64 (sqrt.f64 (.f64 x (fma.f64 x -9 6))) (sqrt.f64 (*.f64 x (fma.f64 x -9 6))))
	3.6b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
▶	0.2b	(-.f64 (.f64 6 x) (.f64 (.f64 x 3) (.f64 x 3)))

Compiler

Compiled 693 to 454 computations (34.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 6 x) (.f64 (.f64 x 3) (.f64 x 3)))
✓	0.3b	(.f64 (.f64 x 3) (*.f64 x 3))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (.f64 6 x) (.f64 (.f64 x 3) (.f64 x 3)))
3.0ms	(.f64 (.f64 x 3) (*.f64 x 3))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`pow1_binary64`
17×	`pow-prod-down_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
8×	`cbrt-unprod_binary64`

Counts

2 → 52

Calls

2 calls:

5.0ms	(.f64 (.f64 x 3) (*.f64 x 3))
5.0ms	(-.f64 (.f64 6 x) (.f64 (.f64 x 3) (.f64 x 3)))

simplify106.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

919×	`fma-def_binary64`
381×	`times-frac_binary64`
343×	`fma-neg_binary64`
331×	`distribute-rgt-neg-in_binary64`
325×	`distribute-lft-neg-in_binary64`

Counts

76 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	769
1	186	642
2	635	613
3	1701	569
4	4101	569
5	4808	569

prune94.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	70	6	76

Error

0.0b

Counts

76 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	14.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
	34.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
	47.4b	(.f64 (sqrt.f64 (.f64 x (fma.f64 x -9 6))) (sqrt.f64 (*.f64 x (fma.f64 x -9 6))))
	3.6b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
✓	0.2b	(-.f64 (.f64 6 x) (.f64 (.f64 x 3) (.f64 x 3)))

Compiler

Compiled 1128 to 824 computations (27% saved)

regimes423.0ms (17.7%)

Accuracy

Total 0.1b remaining (70.4%)

Threshold costs 0.1b (70.4%)

Counts

50 → 1

Compiler

Compiled 1086 to 820 computations (24.5% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
2	8	11

end104.0ms (4.4%)

Compiler: Compiled 90 to 65 computations (27.8% saved)

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	92	8
4	173	8
5	259	8
6	365	8
7	561	8
8	580	8
9	675	8
10	798	8
11	821	8
12	918	8
13	922	8
14	922	8
15	803	8

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	92	8
4	173	8
5	259	8
6	365	8
7	561	8
8	580	8
9	675	8
10	798	8
11	821	8
12	918	8
13	922	8
14	922	8
15	803	8

Details

analyze1.0ms (0%)

sample826.0ms (34.5%)

simplify75.0ms (3.1%)

prune6.0ms (0.2%)

localize7.0ms (0.3%)

series9.0ms (0.4%)

rewrite9.0ms (0.4%)

simplify74.0ms (3.1%)

prune81.0ms (3.4%)

localize12.0ms (0.5%)

series11.0ms (0.5%)

rewrite18.0ms (0.7%)

simplify104.0ms (4.3%)

prune245.0ms (10.2%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite11.0ms (0.5%)

simplify101.0ms (4.2%)

prune35.0ms (1.5%)

localize6.0ms (0.2%)

series6.0ms (0.3%)

rewrite13.0ms (0.5%)

simplify106.0ms (4.4%)

prune94.0ms (3.9%)

regimes423.0ms (17.7%)

simplify4.0ms (0.2%)

end104.0ms (4.4%)

Profiling

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	92	8
4	173	8
5	259	8
6	365	8
7	561	8
8	580	8
9	675	8
10	798	8
11	821	8
12	918	8
13	922	8
14	922	8
15	803	8