Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample816.0ms (44.2%)

Infinites

33.9% of outputs are infinite.

Results

608.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify149.0ms (8.1%)

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 (0.2%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
▶	0.1b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))

Status

Error

Program

0.1b

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

▶

0.1b

(*.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 2 expressions with local error:

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

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

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

simplify47.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

907×	`distribute-rgt-in_binary64`
906×	`distribute-lft-in_binary64`
386×	`fma-def_binary64`
240×	`associate-l_binary64`
199×	`associate-r_binary64`

Counts

56 → 64

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	716
1	106	613
2	301	613
3	1063	613
4	5380	613

prune65.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	60	6	66

Error

0.0b

Counts

66 → 6

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	9.5b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	32.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))
	35.0b	(.f64 (sqrt.f64 (.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))) (sqrt.f64 (.f64 x (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
✓	0.1b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
	1.0b	(.f64 (.f64 (cbrt.f64 (.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))) (cbrt.f64 (.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))) (cbrt.f64 (.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))

Compiler

Compiled 1007 to 601 computations (40.3% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series6.0ms (0.3%)

Counts

2 → 0

Calls

2 calls:

4.0ms	(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))
2.0ms	(*.f64 238732414637843/250000000000000 x)

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
9×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 53

Calls

2 calls:

5.0ms	(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))
3.0ms	(*.f64 238732414637843/250000000000000 x)

simplify94.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

629×	`associate-l_binary64`
574×	`associate-r_binary64`
469×	`fma-def_binary64`
366×	`log-prod_binary64`
326×	`cube-prod_binary64`

Counts

53 → 69

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	496
1	156	444
2	392	444
3	2006	444
4	3156	412
5	4363	412
6	4947	412
7	4907	412

prune98.0ms (5.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	3	1	4
Picked	0	1	1
Done	1	0	1
Total	69	6	75

Error

0.0b

Counts

75 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	9.5b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
▶	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 (.f64 x x)) x))
	32.6b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3/2)) (pow.f64 (sqrt.f64 x) 3)))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3))))
	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 x) (.f64 x x)))

Compiler

Compiled 1105 to 860 computations (22.2% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 (.f64 6450306886639899/50000000000000000 (*.f64 x x)) x)
3.0ms	(.f64 6450306886639899/50000000000000000 (.f64 x x))

rewrite13.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

6.0ms	(.f64 (.f64 6450306886639899/50000000000000000 (*.f64 x x)) x)
5.0ms	(.f64 6450306886639899/50000000000000000 (.f64 x x))

simplify80.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
714×	`unswap-sqr_binary64`
295×	`associate-/l/_binary64`
287×	`*-commutative_binary64`
284×	`associate-/l*_binary64`

Counts

68 → 55

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	65	652
1	139	565
2	477	556
3	741	551
4	1155	539
5	2405	539
6	4666	539
7	5018	539

prune70.0ms (3.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	78	6	84

Error

Counts

84 → 6

Alt Table

Status	Error	Program
	32.6b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 5/2)) (sqrt.f64 x)))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3))))
	9.5b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
✓	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 (.f64 x x)) x))
	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 x) (.f64 x x)))
▶	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 6450306886639899/50000000000000000 x) x) x))

Compiler

Compiled 1360 to 849 computations (37.6% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series9.0ms (0.5%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(.f64 (.f64 6450306886639899/50000000000000000 x) x)
3.0ms	(.f64 (.f64 (*.f64 6450306886639899/50000000000000000 x) x) x)
2.0ms	(*.f64 6450306886639899/50000000000000000 x)

rewrite16.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
19×	`pow1_binary64`
10×	`cbrt-unprod_binary64`
10×	`prod-exp_binary64`

Counts

3 → 63

Calls

3 calls:

5.0ms	(.f64 (.f64 (*.f64 6450306886639899/50000000000000000 x) x) x)
4.0ms	(.f64 (.f64 6450306886639899/50000000000000000 x) x)
4.0ms	(*.f64 6450306886639899/50000000000000000 x)

simplify86.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
411×	`unswap-sqr_binary64`
408×	`associate-*r/_binary64`
356×	`associate-*l/_binary64`
281×	`*-commutative_binary64`

Counts

87 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	853
1	174	685
2	557	676
3	748	669
4	1095	669
5	2045	669
6	4874	669
7	5232	669

prune92.0ms (5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	107	6	113

Error

Counts

113 → 6

Alt Table

Status	Error	Program
	32.6b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 5/2)) (sqrt.f64 x)))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3))))
	9.5b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
✓	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 (.f64 x x)) x))
	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 x) (.f64 x x)))
✓	0.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 6450306886639899/50000000000000000 x) x) x))

Compiler

Compiled 1749 to 1152 computations (34.1% saved)

regimes61.0ms (3.3%)

Accuracy

Total 0.1b remaining (88.9%)

Threshold costs 0.1b (88.9%)

Counts

31 → 1

Compiler

Compiled 872 to 610 computations (30% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`distribute-rgt-neg-in_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	17	16
2	34	16
3	44	16
4	50	16
5	52	16
6	51	16

end82.0ms (4.4%)

Compiler: Compiled 98 to 70 computations (28.6% saved)

Details

analyze1.0ms (0%)

sample816.0ms (44.2%)

simplify149.0ms (8.1%)

prune3.0ms (0.2%)

localize6.0ms (0.3%)

series6.0ms (0.3%)

rewrite4.0ms (0.2%)

simplify47.0ms (2.6%)

prune65.0ms (3.5%)

localize5.0ms (0.3%)

series6.0ms (0.3%)

rewrite10.0ms (0.5%)

simplify94.0ms (5.1%)

prune98.0ms (5.3%)

localize7.0ms (0.4%)

series6.0ms (0.3%)

rewrite13.0ms (0.7%)

simplify80.0ms (4.3%)

prune70.0ms (3.8%)

localize6.0ms (0.3%)

series9.0ms (0.5%)

rewrite16.0ms (0.9%)

simplify86.0ms (4.7%)

prune92.0ms (5%)

regimes61.0ms (3.3%)

simplify4.0ms (0.2%)

end82.0ms (4.4%)

Profiling