Details

analyze4.0ms (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)

sample985.0ms (48.6%)

Results

820.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify144.0ms (7.1%)

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

0.2b

Counts

3 → 2

Alt Table

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

Status

Error

Program

▶

0.2b

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

0.2b

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

Compiler

Compiled 62 to 40 computations (35.5% saved)

localize5.0ms (0.2%)

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)

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:

3.0ms	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
0.0ms	(fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)

simplify49.0ms (2.4%)

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

prune44.0ms (2.2%)

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
	1.5b	(.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))))
	43.9b	(cbrt.f64 (pow.f64 (.f64 x (fma.f64 -6450306886639899/50000000000000000 (.f64 x x) 238732414637843/250000000000000)) 3))
✓	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	16.2b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	35.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))

Compiler

Compiled 991 to 593 computations (40.2% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
✓	0.1b	(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))
✓	0.1b	(*.f64 238732414637843/250000000000000 x)

series8.0ms (0.4%)

Counts

3 → 3

Calls

3 calls:

3.0ms

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

3.0ms

(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))

2.0ms

(*.f64 238732414637843/250000000000000 x)

rewrite17.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

7.0ms

(*.f64 238732414637843/250000000000000 x)

4.0ms

(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))

3.0ms

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

simplify85.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

648×	`fma-def_binary64`
428×	`unswap-sqr_binary64`
420×	`fma-neg_binary64`
276×	`exp-prod_binary64`
268×	`times-frac_binary64`

Counts

72 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	113	782
1	223	713
2	650	705
3	1572	703
4	4052	669
5	4564	669
6	4781	669

prune77.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	97	7	104

Error

Counts

104 → 7

Alt Table

Status	Error	Program
	43.9b	(cbrt.f64 (pow.f64 (.f64 x (fma.f64 -6450306886639899/50000000000000000 (.f64 x x) 238732414637843/250000000000000)) 3))
✓	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
	31.9b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)))
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	16.2b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	16.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (*.f64 6450306886639899/50000000000000000 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (pow.f64 x 3))))
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 x) (.f64 x x)))

Compiler

Compiled 1581 to 1237 computations (21.8% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 x) (.f64 x x)))
✓	0.1b	(*.f64 6450306886639899/50000000000000000 x)
	0.1b	(*.f64 238732414637843/250000000000000 x)
✓	0.2b	(.f64 (.f64 6450306886639899/50000000000000000 x) (*.f64 x x))

series8.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

3.0ms

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

3.0ms

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

1.0ms

(*.f64 6450306886639899/50000000000000000 x)

rewrite16.0ms (0.8%)

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 → 60

Calls

3 calls:

8.0ms

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

3.0ms

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

3.0ms

(*.f64 6450306886639899/50000000000000000 x)

simplify92.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-neg_binary64`
427×	`distribute-rgt-neg-in_binary64`
411×	`distribute-lft-neg-in_binary64`
384×	`cancel-sign-sub-inv_binary64`
317×	`fma-def_binary64`

Counts

84 → 86

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	900
1	229	797
2	764	783
3	2004	783
4	4304	766
5	4999	766
6	4832	766

prune82.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	3	4
Picked	1	0	1
Done	1	1	2
Total	110	5	115

Error

Counts

115 → 5

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 6450306886639899/50000000000000000 x) x) x))
	43.9b	(cbrt.f64 (pow.f64 (.f64 x (fma.f64 -6450306886639899/50000000000000000 (.f64 x x) 238732414637843/250000000000000)) 3))
	16.2b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	16.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (*.f64 6450306886639899/50000000000000000 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (pow.f64 x 3))))

Compiler

Compiled 1828 to 1164 computations (36.3% saved)

localize7.0ms (0.4%)

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 238732414637843/250000000000000 x)
✓	0.2b	(.f64 (.f64 6450306886639899/50000000000000000 x) x)

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite71.0ms (3.5%)

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 → 43

Calls

2 calls:

65.0ms	(.f64 (.f64 (*.f64 6450306886639899/50000000000000000 x) x) x)
4.0ms	(.f64 (.f64 6450306886639899/50000000000000000 x) x)

simplify78.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
411×	`unswap-sqr_binary64`
398×	`associate-*r/_binary64`
346×	`associate-*l/_binary64`
285×	`*-commutative_binary64`

Counts

67 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	711
1	152	555
2	539	546
3	730	539
4	1075	539
5	2027	539
6	4816	539
7	5174	539

prune73.0ms (3.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	105	5	110

Error

Counts

110 → 5

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 6450306886639899/50000000000000000 x) x) x))
	43.9b	(cbrt.f64 (pow.f64 (.f64 x (fma.f64 -6450306886639899/50000000000000000 (.f64 x x) 238732414637843/250000000000000)) 3))
	16.2b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	16.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (*.f64 6450306886639899/50000000000000000 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (pow.f64 x 3))))

Compiler

Compiled 1706 to 1125 computations (34.1% saved)

regimes70.0ms (3.5%)

Accuracy

Total 0.2b remaining (86.6%)

Threshold costs 0.2b (86.6%)

Counts

35 → 1

Compiler

Compiled 984 to 696 computations (29.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`distribute-rgt-neg-in_binary64`
5×	`+-commutative_binary64`
5×	`distribute-lft-neg-in_binary64`
5×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	18	16
2	33	16
3	47	16
4	53	16
5	55	16
6	54	16

end76.0ms (3.8%)

Compiler: Compiled 85 to 62 computations (27.1% saved)

Details

analyze4.0ms (0.2%)

sample985.0ms (48.6%)

simplify144.0ms (7.1%)

prune3.0ms (0.2%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify49.0ms (2.4%)

prune44.0ms (2.2%)

localize5.0ms (0.3%)

series8.0ms (0.4%)

rewrite17.0ms (0.8%)

simplify85.0ms (4.2%)

prune77.0ms (3.8%)

localize6.0ms (0.3%)

series8.0ms (0.4%)

rewrite16.0ms (0.8%)

simplify92.0ms (4.6%)

prune82.0ms (4%)

localize7.0ms (0.4%)

series6.0ms (0.3%)

rewrite71.0ms (3.5%)

simplify78.0ms (3.8%)

prune73.0ms (3.6%)

regimes70.0ms (3.5%)

simplify3.0ms (0.1%)

end76.0ms (3.8%)

Profiling