Details

analyze80.0ms (2.9%)

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)

sample26.0ms (0.9%)

Algorithm

1×

intervals

Results

12.0ms	230×	body	128	valid
3.0ms	15×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify64.0ms (2.3%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(.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)

localize7.0ms (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))

series10.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

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

rewrite8.0ms (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:

5.0ms	(*.f64 x (fma.f64 x -9 6))
1.0ms	(fma.f64 x -9 6)

simplify68.0ms (2.4%)

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

prune68.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	43	7	50

Error

0.0b

Counts

50 → 7

Alt Table

Status	Error	Program
	7.0b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))
▶	0.2b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	33.1b	(.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)))
	38.1b	(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 x (fma.f64 x -9 6))
	9.8b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -9 6))) (sqrt.f64 (fma.f64 x -9 6)))

Compiler

Compiled 665 to 470 computations (29.3% saved)

localize10.0ms (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))

series10.0ms (0.4%)

Counts

2 → 3

Calls

2 calls:

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

rewrite17.0ms (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:

9.0ms	(*.f64 9 (pow.f64 x 2))
5.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))

simplify83.0ms (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

prune105.0ms (3.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	77	6	83

Error

0.0b

Counts

83 → 6

Alt Table

Status	Error	Program
	33.1b	(.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)))
▶	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
	0.5b	(-.f64 (.f64 6 x) (.f64 (.f64 9 (.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))
✓	0.2b	(*.f64 x (fma.f64 x -9 6))
	7.0b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))

Compiler

Compiled 1235 to 932 computations (24.5% saved)

localize9.0ms (0.3%)

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))

series10.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

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

rewrite11.0ms (0.4%)

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)))

simplify103.0ms (3.7%)

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

prune64.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	46	6	52

Error

0.0b

Counts

52 → 6

Alt Table

Status	Error	Program
	33.1b	(.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)))
✓	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
▶	0.5b	(-.f64 (.f64 6 x) (.f64 (.f64 9 (.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))
✓	0.2b	(*.f64 x (fma.f64 x -9 6))
	7.0b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))

Compiler

Compiled 692 to 445 computations (35.7% saved)

localize19.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 9 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))
✓	0.3b	(.f64 9 (.f64 x (cbrt.f64 x)))
✓	0.5b	(pow.f64 (cbrt.f64 x) 2)
✓	0.6b	(cbrt.f64 x)

series240.0ms (8.6%)

Counts

4 → 48

Calls

4 calls:

77.0ms	(pow.f64 (cbrt.f64 x) 2)
74.0ms	(.f64 9 (.f64 x (cbrt.f64 x)))
64.0ms	(cbrt.f64 x)
24.0ms	(.f64 (.f64 9 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))

rewrite37.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
21×	`prod-exp_binary64`
16×	`add-cbrt-cube_binary64`
12×	`associate-r_binary64`
12×	`unpow-prod-down_binary64`

Counts

4 → 91

Calls

4 calls:

14.0ms	(.f64 (.f64 9 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))
8.0ms	(.f64 9 (.f64 x (cbrt.f64 x)))
4.0ms	(pow.f64 (cbrt.f64 x) 2)
1.0ms	(cbrt.f64 x)

simplify180.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

515×	`*-commutative_binary64`
444×	`log-prod_binary64`
349×	`sqr-pow_binary64`
318×	`exp-prod_binary64`
310×	`associate-/l/_binary64`

Counts

139 → 135

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	128	1352
1	271	1152
2	914	1067
3	1644	1067
4	3457	1013
5	4455	1003
6	4758	994
7	4760	994

prune209.0ms (7.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	153	6	159

Error

0.0b

Counts

159 → 6

Alt Table

Status	Error	Program
	33.1b	(.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)))
✓	0.1b	(fma.f64 6 x (.f64 -9 (.f64 x x)))
✓	0.5b	(-.f64 (.f64 6 x) (.f64 (.f64 9 (.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))
✓	0.2b	(*.f64 x (fma.f64 x -9 6))
	7.0b	(.f64 x (cbrt.f64 (.f64 (*.f64 (fma.f64 x -9 6) (fma.f64 x -9 6)) (fma.f64 x -9 6))))

Compiler

Compiled 3007 to 1788 computations (40.5% saved)

regimes127.0ms (4.6%)

Accuracy

Total 0.1b remaining (70.1%)

Threshold costs 0.1b (70.1%)

Counts

31 → 1

Compiler

Compiled 796 to 592 computations (25.6% saved)

simplify4.0ms (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

end1.0ms (0%)

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

sample1.2s (43.6%)

Algorithm

1×

intervals

Results

428.0ms	7207×	body	128	valid
280.0ms	449×	body	1024	valid
32.0ms	211×	body	512	valid
16.0ms	133×	body	256	valid

Compiler

Compiled 96 to 67 computations (30.2% 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

analyze80.0ms (2.9%)

sample26.0ms (0.9%)

simplify64.0ms (2.3%)

prune6.0ms (0.2%)

localize7.0ms (0.2%)

series10.0ms (0.4%)

rewrite8.0ms (0.3%)

simplify68.0ms (2.4%)

prune68.0ms (2.4%)

localize10.0ms (0.3%)

series10.0ms (0.4%)

rewrite17.0ms (0.6%)

simplify83.0ms (3%)

prune105.0ms (3.8%)

localize9.0ms (0.3%)

series10.0ms (0.4%)

rewrite11.0ms (0.4%)

simplify103.0ms (3.7%)

prune64.0ms (2.3%)

localize19.0ms (0.7%)

series240.0ms (8.6%)

rewrite37.0ms (1.3%)

simplify180.0ms (6.4%)

prune209.0ms (7.5%)

regimes127.0ms (4.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.2s (43.6%)

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