Details

analyze4.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample67.0ms (4.7%)

Algorithm

1×

intervals

Results

7.0ms	230×	body	128	valid
2.0ms	21×	body	1024	valid
0.0ms	3×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify41.0ms (2.8%)

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

prune3.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 x (fma.f64 x -9 6))
	0.3b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)

Compiler

Compiled 50 to 38 computations (24% saved)

localize4.0ms (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))

series5.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(*.f64 x (fma.f64 x -9 6))
2.0ms	(fma.f64 x -9 6)

rewrite4.0ms (0.3%)

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:

3.0ms	(*.f64 x (fma.f64 x -9 6))
0.0ms	(fma.f64 x -9 6)

simplify50.0ms (3.5%)

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

prune44.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	39	9	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	40	10	50

Error

0.0b

Counts

50 → 10

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 x (fma.f64 x -9 6))
	29.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
	8.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
▶	0.2b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	13.3b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
	1.5b	(.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)))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
	42.5b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x -9 6))) (*.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x -9 6))))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (fma.f64 x -9 6))) (cbrt.f64 (.f64 x (fma.f64 x -9 6)))) (cbrt.f64 (*.f64 x (fma.f64 x -9 6))))
	41.3b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -9 6)) 3))

Compiler

Compiled 749 to 536 computations (28.4% saved)

localize7.0ms (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)))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series6.0ms (0.4%)

Counts

2 → 3

Calls

2 calls:

3.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
3.0ms	(*.f64 9 (pow.f64 x 2))

rewrite8.0ms (0.6%)

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:

4.0ms	(*.f64 9 (pow.f64 x 2))
3.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))

simplify65.0ms (4.5%)

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

prune59.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	79	7	86

Error

0.0b

Counts

86 → 7

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 x (fma.f64 x -9 6))
	29.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
▶	0.2b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	8.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	0.3b	(-.f64 (.f64 6 x) (.f64 (.f64 x 3) (.f64 x 3)))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
	42.5b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x -9 6))) (*.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x -9 6))))

Compiler

Compiled 1247 to 942 computations (24.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
✓	0.2b	(.f64 -9 (.f64 x x))

series5.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

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

rewrite8.0ms (0.6%)

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:

7.0ms	(.f64 -9 (.f64 x x))
0.0ms	(fma.f64 6 x (.f64 -9 (.f64 x x)))

simplify60.0ms (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

prune30.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	46	7	53

Error

0.0b

Counts

53 → 7

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 x (fma.f64 x -9 6))
	29.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
✓	0.2b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	8.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
▶	0.3b	(-.f64 (.f64 6 x) (.f64 (.f64 x 3) (.f64 x 3)))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
	42.5b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x -9 6))) (*.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x -9 6))))

Compiler

Compiled 704 to 455 computations (35.4% saved)

localize5.0ms (0.3%)

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 (0.4%)

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))

rewrite15.0ms (1.1%)

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:

10.0ms	(.f64 (.f64 x 3) (*.f64 x 3))
3.0ms	(-.f64 (.f64 6 x) (.f64 (.f64 x 3) (.f64 x 3)))

simplify62.0ms (4.3%)

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

prune46.0ms (3.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	70	7	77

Error

0.0b

Counts

77 → 7

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 x (fma.f64 x -9 6))
	29.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
✓	0.2b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	8.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
✓	0.3b	(-.f64 (.f64 6 x) (.f64 (.f64 x 3) (.f64 x 3)))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
	42.5b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x -9 6))) (*.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x -9 6))))

Compiler

Compiled 1137 to 827 computations (27.3% saved)

regimes63.0ms (4.4%)

Accuracy

Total 0.1b remaining (77.6%)

Threshold costs 0.1b (77.6%)

Counts

31 → 1

Compiler

Compiled 766 to 578 computations (24.5% saved)

simplify3.0ms (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

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample763.0ms (53.1%)

Algorithm

1×

intervals

Results

253.0ms	7227×	body	128	valid
52.0ms	484×	body	1024	valid
15.0ms	189×	body	512	valid
5.0ms	100×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 102 to 72 computations (29.4% 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

analyze4.0ms (0.3%)

sample67.0ms (4.7%)

simplify41.0ms (2.8%)

prune3.0ms (0.2%)

localize4.0ms (0.3%)

series5.0ms (0.3%)

rewrite4.0ms (0.3%)

simplify50.0ms (3.5%)

prune44.0ms (3.1%)

localize7.0ms (0.5%)

series6.0ms (0.4%)

rewrite8.0ms (0.6%)

simplify65.0ms (4.5%)

prune59.0ms (4.1%)

localize5.0ms (0.3%)

series5.0ms (0.4%)

rewrite8.0ms (0.6%)

simplify60.0ms (4.2%)

prune30.0ms (2.1%)

localize5.0ms (0.3%)

series6.0ms (0.4%)

rewrite15.0ms (1.1%)

simplify62.0ms (4.3%)

prune46.0ms (3.2%)

regimes63.0ms (4.4%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample763.0ms (53.1%)

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