Details

analyze4.0ms (0.2%)

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)

sample918.0ms (48.3%)

Results

663.0ms	7443×	body	128	valid
128.0ms	472×	body	1024	valid
44.0ms	215×	body	512	valid
19.0ms	126×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify42.0ms (2.2%)

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

Compiler

Compiled 50 to 38 computations (24% saved)

localize4.0ms (0.2%)

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))

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(*.f64 x (fma.f64 x -9 6))
1.0ms	(fma.f64 x -9 6)

rewrite4.0ms (0.2%)

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)

simplify51.0ms (2.7%)

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

prune36.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	41	7	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	42	8	50

Error

0.0b

Counts

50 → 8

Alt Table

Status	Error	Program
	9.3b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
▶	0.2b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	39.8b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -9 6)) 3))
	9.3b	(.f64 x (.f64 (sqrt.f64 (fma.f64 x -9 6)) (sqrt.f64 (fma.f64 x -9 6))))
	6.8b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
	40.9b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x -9 6))) (*.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x -9 6))))
✓	0.2b	(*.f64 x (fma.f64 x -9 6))

Compiler

Compiled 683 to 488 computations (28.6% saved)

localize6.0ms (0.3%)

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 (0.3%)

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))

rewrite9.0ms (0.4%)

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)))

simplify64.0ms (3.4%)

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

prune58.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	77	7	84

Error

0.0b

Counts

84 → 7

Alt Table

Status	Error	Program
	0.3b	(-.f64 (.f64 6 x) (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (cbrt.f64 9) (pow.f64 x 2))))
▶	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	9.3b	(.f64 x (.f64 (sqrt.f64 (fma.f64 x -9 6)) (sqrt.f64 (fma.f64 x -9 6))))
	6.8b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	9.3b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
✓	0.2b	(*.f64 x (fma.f64 x -9 6))

Compiler

Compiled 1271 to 970 computations (23.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
✓	0.2b	(.f64 -9 (.f64 x x))

series9.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(.f64 -9 (.f64 x x))
3.0ms	(fma.f64 6 x (.f64 -9 (.f64 x x)))

rewrite6.0ms (0.3%)

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:

4.0ms	(.f64 -9 (.f64 x x))
0.0ms	(fma.f64 6 x (.f64 -9 (.f64 x x)))

simplify63.0ms (3.3%)

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

prune31.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	46	7	53

Error

0.0b

Counts

53 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	9.3b	(.f64 x (.f64 (sqrt.f64 (fma.f64 x -9 6)) (sqrt.f64 (fma.f64 x -9 6))))
	6.8b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	9.3b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
▶	0.2b	(fma.f64 6 x (.f64 (.f64 (cbrt.f64 -9) (cbrt.f64 -9)) (.f64 (cbrt.f64 -9) (.f64 x x))))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
✓	0.2b	(*.f64 x (fma.f64 x -9 6))

Compiler

Compiled 726 to 479 computations (34% saved)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 6 x (.f64 (.f64 (cbrt.f64 -9) (cbrt.f64 -9)) (.f64 (cbrt.f64 -9) (.f64 x x))))
✓	0.2b	(.f64 (cbrt.f64 -9) (.f64 x x))
✓	0.2b	(.f64 (.f64 (cbrt.f64 -9) (cbrt.f64 -9)) (.f64 (cbrt.f64 -9) (.f64 x x)))

series95.0ms (5%)

Counts

3 → 36

Calls

3 calls:

41.0ms

(*.f64 (*.f64 (cbrt.f64 -9) (cbrt.f64 -9)) (*.f64 (cbrt.f64 -9) (*.f64 x x)))

32.0ms

(fma.f64 6 x (*.f64 (*.f64 (cbrt.f64 -9) (cbrt.f64 -9)) (*.f64 (cbrt.f64 -9) (*.f64 x x))))

21.0ms

(*.f64 (cbrt.f64 -9) (*.f64 x x))

rewrite20.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64`
29×	`pow1_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`
18×	`pow-prod-down_binary64`

Counts

3 → 65

Calls

3 calls:

10.0ms

(*.f64 (*.f64 (cbrt.f64 -9) (cbrt.f64 -9)) (*.f64 (cbrt.f64 -9) (*.f64 x x)))

5.0ms

(*.f64 (cbrt.f64 -9) (*.f64 x x))

0.0ms

(fma.f64 6 x (*.f64 (*.f64 (cbrt.f64 -9) (cbrt.f64 -9)) (*.f64 (cbrt.f64 -9) (*.f64 x x))))

simplify92.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-def_binary64`
537×	`neg-mul-1_binary64`
340×	`distribute-rgt-neg-out_binary64`
323×	`distribute-lft-neg-out_binary64`
306×	`unsub-neg_binary64`

Counts

101 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1172
1	163	981
2	482	932
3	958	894
4	1933	894
5	4326	894
6	4991	894
7	4903	894

prune69.0ms (3.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	97	7	104

Error

0.0b

Counts

104 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	9.3b	(.f64 x (.f64 (sqrt.f64 (fma.f64 x -9 6)) (sqrt.f64 (fma.f64 x -9 6))))
	6.8b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	9.3b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
✓	0.2b	(fma.f64 6 x (.f64 (.f64 (cbrt.f64 -9) (cbrt.f64 -9)) (.f64 (cbrt.f64 -9) (.f64 x x))))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
✓	0.2b	(*.f64 x (fma.f64 x -9 6))

Compiler

Compiled 1943 to 1436 computations (26.1% saved)

regimes65.0ms (3.4%)

Accuracy

Total 0.1b remaining (75.8%)

Threshold costs 0.1b (75.8%)

Counts

34 → 1

Compiler

Compiled 866 to 658 computations (24% 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

end223.0ms (11.7%)

Compiler: Compiled 110 to 80 computations (27.3% 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 (0.2%)

sample918.0ms (48.3%)

simplify42.0ms (2.2%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite4.0ms (0.2%)

simplify51.0ms (2.7%)

prune36.0ms (1.9%)

localize6.0ms (0.3%)

series6.0ms (0.3%)

rewrite9.0ms (0.4%)

simplify64.0ms (3.4%)

prune58.0ms (3.1%)

localize5.0ms (0.2%)

series9.0ms (0.5%)

rewrite6.0ms (0.3%)

simplify63.0ms (3.3%)

prune31.0ms (1.6%)

localize9.0ms (0.5%)

series95.0ms (5%)

rewrite20.0ms (1%)

simplify92.0ms (4.9%)

prune69.0ms (3.7%)

regimes65.0ms (3.4%)

simplify4.0ms (0.2%)

end223.0ms (11.7%)

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