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)

sample644.0ms (28.7%)

Infinites

26.2% of outputs are infinite.

Results

490.0ms	7693×	body	128	valid
43.0ms	300×	body	1024	valid
23.0ms	181×	body	512	valid
7.0ms	82×	body	256	valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify44.0ms (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 (0.1%)

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
▶	0.1b	(*.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))
2.0ms	(fma.f64 x -9 6)

rewrite5.0ms (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:

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

simplify65.0ms (2.9%)

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

prune54.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	41	9	50

Error

0.0b

Counts

50 → 9

Alt Table

Status	Error	Program
	5.4b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	27.1b	(cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
▶	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	17.8b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))
	0.7b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	1.0b	(.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))))
	1.1b	(.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)))
	1.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))
	17.7b	(.f64 x (.f64 (sqrt.f64 (fma.f64 x -9 6)) (sqrt.f64 (fma.f64 x -9 6))))

Compiler

Compiled 772 to 557 computations (27.8% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 2 (*.f64 x 3))
✓	0.1b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
✓	0.1b	(.f64 3 (-.f64 2 (.f64 x 3)))

series6.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
2.0ms	(.f64 3 (-.f64 2 (.f64 x 3)))
1.0ms	(-.f64 2 (*.f64 x 3))

rewrite17.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

6.0ms	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
4.0ms	(.f64 3 (-.f64 2 (.f64 x 3)))
3.0ms	(-.f64 2 (*.f64 x 3))

simplify88.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary64`
395×	`*-commutative_binary64`
243×	`distribute-rgt-neg-out_binary64`
241×	`unsub-neg_binary64`
203×	`neg-mul-1_binary64`

Counts

110 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1350
1	252	1068
2	679	824
3	1775	820
4	3020	820
5	4857	820
6	5042	820

prune126.0ms (5.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Error

0.0b

Counts

141 → 9

Alt Table

Status	Error	Program
	32.7b	(.f64 (.f64 (.f64 3 (-.f64 2 (.f64 x 3))) (sqrt.f64 x)) (sqrt.f64 x))
	0.6b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (-.f64 2 (.f64 x 3)))) x)
	5.4b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	27.1b	(cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	0.7b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	1.0b	(.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))))
	5.5b	(/.f64 (fma.f64 x 12 (pow.f64 (.f64 x -3) 3)) (+.f64 2 (.f64 x 3)))
▶	0.2b	(.f64 x (.f64 3 (-.f64 2 (*.f64 x 3))))
	1.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))

Compiler

Compiled 2145 to 1699 computations (20.8% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 2 (*.f64 x 3))
✓	0.1b	(.f64 x (.f64 3 (-.f64 2 (*.f64 x 3))))
	0.1b	(.f64 3 (-.f64 2 (.f64 x 3)))

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

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

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`distribute-lft-in_binary64`
20×	`distribute-rgt-in_binary64`
12×	`prod-diff_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

1 → 42

Calls

1 calls:

6.0ms

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

simplify85.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
451×	`*-commutative_binary64`
274×	`unsub-neg_binary64`
274×	`fma-neg_binary64`
241×	`distribute-rgt-neg-out_binary64`

Counts

54 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	939
1	221	699
2	614	586
3	1674	504
4	2940	504
5	4761	504
6	4996	504
7	4831	504

prune153.0ms (6.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	152	9	161

Error

0.0b

Counts

161 → 9

Alt Table

Status	Error	Program
	32.7b	(.f64 (.f64 (.f64 3 (-.f64 2 (.f64 x 3))) (sqrt.f64 x)) (sqrt.f64 x))
▶	0.6b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (-.f64 2 (.f64 x 3)))) x)
	5.4b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	27.1b	(cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	0.7b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	1.0b	(.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))))
	5.5b	(/.f64 (fma.f64 x 12 (.f64 (pow.f64 x 3) -27)) (+.f64 2 (.f64 x 3)))
✓	0.2b	(.f64 x (.f64 3 (-.f64 2 (*.f64 x 3))))
	1.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))

Compiler

Compiled 2551 to 2016 computations (21% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 2 (*.f64 x 3))
✓	0.1b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (-.f64 2 (.f64 x 3)))) x)
✓	0.2b	(.f64 (sqrt.f64 3) (-.f64 2 (.f64 x 3)))
✓	0.7b	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (-.f64 2 (*.f64 x 3))))

series24.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

11.0ms	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (-.f64 2 (.f64 x 3)))) x)
7.0ms	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (-.f64 2 (*.f64 x 3))))
6.0ms	(.f64 (sqrt.f64 3) (-.f64 2 (.f64 x 3)))

rewrite219.0ms (9.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`

Counts

3 → 106

Calls

3 calls:

199.0ms	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (-.f64 2 (.f64 x 3)))) x)
8.0ms	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (-.f64 2 (*.f64 x 3))))
6.0ms	(.f64 (sqrt.f64 3) (-.f64 2 (.f64 x 3)))

simplify117.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-def_binary64`
434×	`*-commutative_binary64`
324×	`distribute-rgt-in_binary64`
314×	`distribute-lft-in_binary64`
306×	`associate-l_binary64`

Counts

142 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2168
1	351	1679
2	1085	1314
3	2798	1304
4	4899	1304

prune203.0ms (9.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	203	9	212

Error

0.0b

Counts

212 → 9

Alt Table

Status	Error	Program
✓	0.6b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (-.f64 2 (.f64 x 3)))) x)
	5.4b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	27.1b	(cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
	0.7b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	1.0b	(.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))))
	32.8b	(.f64 (.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (-.f64 2 (*.f64 x 3)))) (sqrt.f64 x)) (sqrt.f64 x))
	0.6b	(.f64 (sqrt.f64 3) (.f64 (.f64 (sqrt.f64 3) (-.f64 2 (.f64 x 3))) x))
✓	0.2b	(.f64 x (.f64 3 (-.f64 2 (*.f64 x 3))))
	1.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 x -9 6)))

Compiler

Compiled 3989 to 3383 computations (15.2% saved)

regimes218.0ms (9.7%)

Accuracy

Total 0.1b remaining (81.2%)

Threshold costs 0.1b (81.2%)

Counts

116 → 1

Compiler

Compiled 2796 to 2224 computations (20.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end130.0ms (5.8%)

Compiler: Compiled 158 to 120 computations (24.1% 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%)

sample644.0ms (28.7%)

simplify44.0ms (2%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite5.0ms (0.2%)

simplify65.0ms (2.9%)

prune54.0ms (2.4%)

localize6.0ms (0.3%)

series6.0ms (0.3%)

rewrite17.0ms (0.7%)

simplify88.0ms (3.9%)

prune126.0ms (5.6%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite9.0ms (0.4%)

simplify85.0ms (3.8%)

prune153.0ms (6.8%)

localize8.0ms (0.3%)

series24.0ms (1.1%)

rewrite219.0ms (9.8%)

simplify117.0ms (5.2%)

prune203.0ms (9.1%)

regimes218.0ms (9.7%)

simplify3.0ms (0.1%)

end130.0ms (5.8%)

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