Details

analyze5.0ms (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
62.5%	6.2%	31.3%	6
65.6%	3.1%	31.3%	7
65.6%	1.6%	32.8%	8
66.4%	0.8%	32.8%	9
66.4%	0.4%	33.2%	10
66.6%	0.2%	33.2%	11
66.6%	0.1%	33.3%	12
66.6%	0%	33.3%	13
66.6%	0%	33.3%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.0s (47.2%)

Results

834.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify145.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

1355×	`fma-neg_binary64`
877×	`fma-def_binary64`
720×	`distribute-rgt-neg-in_binary64`
564×	`cancel-sign-sub-inv_binary64`
530×	`sqr-pow_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	21	11
2	49	11
3	107	11
4	170	11
5	291	11
6	516	11
7	1002	11
8	1492	11
9	2128	11
10	2734	11
11	3154	11
12	3358	11
13	3535	11
14	4106	11
15	3099	11
16	3528	11
17	4668	11
18	4732	11

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
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))

Status

Error

Program

▶

0.2b

(-.f64 (*.f64 238732414637843/250000000000000 x) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))

0.2b

(*.f64 x (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))

Compiler

Compiled 62 to 40 computations (35.5% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
✓	0.1b	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
✓	0.1b	(.f64 (.f64 x x) x)
✓	0.1b	(*.f64 238732414637843/250000000000000 x)

series11.0ms (0.5%)

Counts

4 → 36

Calls

4 calls:

3.0ms	(.f64 (.f64 x x) x)
3.0ms	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
3.0ms	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
2.0ms	(*.f64 238732414637843/250000000000000 x)

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64`
23×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64`

Counts

4 → 90

Calls

4 calls:

7.0ms	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
4.0ms	(.f64 (.f64 x x) x)
3.0ms	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
3.0ms	(*.f64 238732414637843/250000000000000 x)

simplify81.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

926×	`fma-def_binary64`
402×	`fma-neg_binary64`
340×	`distribute-rgt-neg-in_binary64`
321×	`distribute-lft-neg-in_binary64`
303×	`cancel-sign-sub-inv_binary64`

Counts

126 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1075
1	244	966
2	796	954
3	1898	929
4	4654	929
5	4817	929

prune100.0ms (4.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Error

0.0b

Counts

126 → 7

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
	1.1b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
	31.8b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)))
	16.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (sqrt.f64 (.f64 (.f64 x x) x)) (sqrt.f64 (.f64 (*.f64 x x) x)))))

Compiler

Compiled 2097 to 1235 computations (41.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
✓	0.1b	(*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000)

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
3.0ms	(*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

4.0ms	(*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000)
0.0ms	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))

simplify72.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

996×	`fma-def_binary64`
421×	`exp-prod_binary64`
402×	`log-prod_binary64`
287×	`cube-prod_binary64`
285×	`*-commutative_binary64`

Counts

67 → 67

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	698
1	130	663
2	484	663
3	1057	639
4	2821	633
5	4771	633
6	4929	633

prune87.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Error

0.0b

Counts

74 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
	1.1b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
▶	0.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	31.8b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)))

Compiler

Compiled 1017 to 777 computations (23.6% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))
✓	0.1b	(*.f64 x -6450306886639899/50000000000000000)
✓	0.1b	(.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000))

series11.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

6.0ms

(fma.f64 238732414637843/250000000000000 x (*.f64 (*.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))

3.0ms

(*.f64 (*.f64 x x) (*.f64 x -6450306886639899/50000000000000000))

1.0ms

(*.f64 x -6450306886639899/50000000000000000)

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 54

Calls

3 calls:

5.0ms

(*.f64 (*.f64 x x) (*.f64 x -6450306886639899/50000000000000000))

3.0ms

(*.f64 x -6450306886639899/50000000000000000)

0.0ms

(fma.f64 238732414637843/250000000000000 x (*.f64 (*.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))

simplify72.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1001×	`fma-def_binary64`
337×	`distribute-rgt-neg-out_binary64`
318×	`distribute-lft-neg-out_binary64`
296×	`unswap-sqr_binary64`
282×	`distribute-rgt-neg-in_binary64`

Counts

90 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	834
1	152	724
2	523	724
3	931	724
4	1972	709
5	4434	709
6	4873	709

prune63.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	83	5	88

Error

0.0b

Counts

88 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
	1.1b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))
▶	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	31.8b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)))

Compiler

Compiled 1329 to 810 computations (39.1% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 238732414637843/250000000000000) x)
	0.1b	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
	0.1b	(.f64 (.f64 x x) x)
✓	0.3b	(.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x))

series13.0ms (0.6%)

Counts

2 → 12

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x))
4.0ms	(*.f64 (sqrt.f64 238732414637843/250000000000000) x)

rewrite12.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

6.0ms	(.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x))
4.0ms	(*.f64 (sqrt.f64 238732414637843/250000000000000) x)

simplify79.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-def_binary64`
342×	`associate-l_binary64`
332×	`unswap-sqr_binary64`
263×	`associate-*r/_binary64`
234×	`associate-*l/_binary64`

Counts

59 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	459
1	121	420
2	338	420
3	627	412
4	823	412
5	1265	412
6	3215	412
7	4673	412
8	4934	412

prune97.0ms (4.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	120	6	126

Error

0.0b

Counts

126 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
	1.1b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.3b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 238732414637843/250000000000000)) (.f64 x (pow.f64 (sqrt.f64 238732414637843/250000000000000) 3/2))) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))
✓	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	31.8b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)))

Compiler

Compiled 2407 to 1615 computations (32.9% saved)

regimes92.0ms (4.2%)

Accuracy

Total 0.2b remaining (81.1%)

Threshold costs 0.2b (81.1%)

Counts

43 → 1

Compiler

Compiled 1244 to 900 computations (27.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11
2	9	11

end148.0ms (6.7%)

Compiler: Compiled 112 to 81 computations (27.7% saved)

Details

analyze5.0ms (0.2%)

sample1.0s (47.2%)

simplify145.0ms (6.6%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

series11.0ms (0.5%)

rewrite21.0ms (0.9%)

simplify81.0ms (3.7%)

prune100.0ms (4.5%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite7.0ms (0.3%)

simplify72.0ms (3.3%)

prune87.0ms (3.9%)

localize6.0ms (0.3%)

series11.0ms (0.5%)

rewrite11.0ms (0.5%)

simplify72.0ms (3.3%)

prune63.0ms (2.8%)

localize10.0ms (0.5%)

series13.0ms (0.6%)

rewrite12.0ms (0.5%)

simplify79.0ms (3.6%)

prune97.0ms (4.4%)

regimes92.0ms (4.2%)

simplify2.0ms (0.1%)

end148.0ms (6.7%)

Profiling