Details

analyze5.0ms (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)

sample838.0ms (45.8%)

Results

604.0ms	7470×	body	128	valid
108.0ms	440×	body	1024	valid
41.0ms	227×	body	512	valid
19.0ms	119×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify39.0ms (2.1%)

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

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))
	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)

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)

simplify54.0ms (3%)

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

prune40.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	39	9	48
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	41	9	50

Error

0.0b

Counts

50 → 9

Alt Table

Status	Error	Program
	1.3b	(.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))))
	41.7b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -9 6)) 3))
	6.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
▶	0.2b	(.f64 x (-.f64 6 (.f64 9 x)))
	10.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
	35.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
	0.2b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	44.5b	(.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 718 to 511 computations (28.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series4.0ms (0.2%)

Counts

2 → 15

Calls

2 calls:

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

rewrite9.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
5×	`distribute-lft-in_binary64`

Counts

2 → 52

Calls

2 calls:

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

simplify75.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

590×	`fma-def_binary64`
333×	`associate-l_binary64`
330×	`*-commutative_binary64`
287×	`distribute-rgt-neg-out_binary64`
280×	`distribute-lft-neg-out_binary64`

Counts

67 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	944
1	179	746
2	494	581
3	1558	581
4	2707	581
5	4678	581
6	4780	581

prune77.0ms (4.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	91	9	100

Error

0.0b

Counts

100 → 9

Alt Table

Status	Error	Program
	6.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	5.5b	(/.f64 (.f64 x (-.f64 (.f64 6 6) (.f64 (.f64 9 x) (.f64 9 x)))) (+.f64 6 (.f64 9 x)))
	1.3b	(.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))))
	41.7b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -9 6)) 3))
	10.5b	(/.f64 (.f64 x (-.f64 (pow.f64 6 3) (pow.f64 (.f64 9 x) 3))) (+.f64 (.f64 6 6) (+.f64 (.f64 (.f64 9 x) (.f64 9 x)) (.f64 6 (.f64 9 x)))))
	35.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
▶	0.2b	(+.f64 (.f64 (fma.f64 1 6 (neg.f64 (.f64 x 9))) x) (.f64 (fma.f64 (neg.f64 x) 9 (.f64 x 9)) x))
	0.2b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	10.0b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (-.f64 6 (*.f64 9 x))))

Compiler

Compiled 1468 to 1108 computations (24.5% saved)

localize16.0ms (0.9%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1 6 (neg.f64 (*.f64 x 9)))
✓	0.1b	(.f64 (fma.f64 1 6 (neg.f64 (.f64 x 9))) x)
✓	52.6b	(fma.f64 (neg.f64 x) 9 (*.f64 x 9))

series7.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(.f64 (fma.f64 1 6 (neg.f64 (.f64 x 9))) x)
3.0ms	(fma.f64 (neg.f64 x) 9 (*.f64 x 9))
2.0ms	(fma.f64 1 6 (neg.f64 (*.f64 x 9)))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

2.0ms	(.f64 (fma.f64 1 6 (neg.f64 (.f64 x 9))) x)
0.0ms	(fma.f64 (neg.f64 x) 9 (*.f64 x 9))
0.0ms	(fma.f64 1 6 (neg.f64 (*.f64 x 9)))

simplify79.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

835×	`distribute-rgt-in_binary64`
790×	`distribute-lft-in_binary64`
528×	`unsub-neg_binary64`
335×	`neg-mul-1_binary64`
317×	`fma-def_binary64`

Counts

76 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	747
1	113	603
2	305	476
3	988	476
4	3368	476
5	4512	476
6	4906	476

prune85.0ms (4.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Error

Counts

89 → 9

Alt Table

Status	Error	Program
	1.3b	(.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))))
	1.4b	(+.f64 (.f64 (.f64 (fma.f64 x -9 6) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 (fma.f64 (neg.f64 x) 9 (*.f64 x 9)) x))
	10.5b	(/.f64 (.f64 x (-.f64 (pow.f64 6 3) (pow.f64 (.f64 9 x) 3))) (+.f64 (.f64 6 6) (+.f64 (.f64 (.f64 9 x) (.f64 9 x)) (.f64 6 (.f64 9 x)))))
	6.0b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)) x) (.f64 (fma.f64 (neg.f64 x) 9 (*.f64 x 9)) x))
	41.7b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -9 6)) 3))
	5.5b	(/.f64 (.f64 x (-.f64 (.f64 6 6) (.f64 (.f64 9 x) (.f64 9 x)))) (+.f64 6 (.f64 9 x)))
	35.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
▶	0.2b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	10.0b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (-.f64 6 (*.f64 9 x))))

Compiler

Compiled 2106 to 1502 computations (28.7% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(-.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:

4.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
2.0ms	(*.f64 9 (pow.f64 x 2))

rewrite8.0ms (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)))

simplify61.0ms (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

prune70.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	79	6	85

Error

Counts

85 → 6

Alt Table

Status	Error	Program
	10.5b	(/.f64 (.f64 x (-.f64 (pow.f64 6 3) (pow.f64 (.f64 9 x) 3))) (+.f64 (.f64 6 6) (+.f64 (.f64 (.f64 9 x) (.f64 9 x)) (.f64 6 (.f64 9 x)))))
	6.0b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)) x) (.f64 (fma.f64 (neg.f64 x) 9 (*.f64 x 9)) x))
	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	0.2b	(+.f64 (.f64 x (+.f64 6 (.f64 x -9))) 0)
	35.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x -9 6)))
	10.0b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (-.f64 6 (*.f64 9 x))))

Compiler

Compiled 1187 to 908 computations (23.5% saved)

regimes237.0ms (12.9%)

Accuracy

Total 0.1b remaining (83.1%)

Threshold costs 0.1b (83.1%)

Counts

121 → 1

Compiler

Compiled 3510 to 2678 computations (23.7% saved)

simplify2.0ms (0.1%)

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

end89.0ms (4.8%)

Compiler: Compiled 113 to 85 computations (24.8% 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

analyze5.0ms (0.3%)

sample838.0ms (45.8%)

simplify39.0ms (2.1%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite4.0ms (0.2%)

simplify54.0ms (3%)

prune40.0ms (2.2%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite9.0ms (0.5%)

simplify75.0ms (4.1%)

prune77.0ms (4.2%)

localize16.0ms (0.9%)

series7.0ms (0.4%)

rewrite4.0ms (0.2%)

simplify79.0ms (4.3%)

prune85.0ms (4.6%)

localize5.0ms (0.3%)

series6.0ms (0.3%)

rewrite8.0ms (0.4%)

simplify61.0ms (3.4%)

prune70.0ms (3.8%)

regimes237.0ms (12.9%)

simplify2.0ms (0.1%)

end89.0ms (4.8%)

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