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)

sample992.0ms (49.5%)

Results

824.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify146.0ms (7.3%)

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)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series5.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

simplify65.0ms (3.3%)

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

prune58.0ms (2.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	57	7	64
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	58	8	66

Error

0.0b

Counts

66 → 8

Alt Table

Status	Error	Program
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	44.8b	(*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3))
	31.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))
	17.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	29.6b	(.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))))
	1.4b	(.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))))
	0.2b	(.f64 x (.f64 1 (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))

Compiler

Compiled 1056 to 637 computations (39.7% saved)

localize6.0ms (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 238732414637843/250000000000000 x)
✓	0.2b	(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))

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))

1.0ms

(*.f64 238732414637843/250000000000000 x)

rewrite14.0ms (0.7%)

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:

4.0ms

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

3.0ms

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

3.0ms

(*.f64 238732414637843/250000000000000 x)

simplify84.0ms (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 → 99

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

prune99.0ms (4.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	101	6	107

Error

Counts

107 → 6

Alt Table

Status	Error	Program
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 x) (.f64 x x)))
	31.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))
	17.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	29.6b	(.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))))
▶	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3)))
	20.6b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (*.f64 6450306886639899/50000000000000000 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (pow.f64 x 3))))

Compiler

Compiled 1603 to 1245 computations (22.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3)))
✓	0.2b	(*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3))

series7.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(fma.f64 238732414637843/250000000000000 x (*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3)))
3.0ms	(*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`associate-r_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 -6450306886639899/50000000000000000 (pow.f64 x 3))
0.0ms	(fma.f64 238732414637843/250000000000000 x (*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3)))

simplify76.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

990×	`fma-def_binary64`
592×	`associate-l_binary64`
575×	`associate-r_binary64`
251×	`exp-prod_binary64`
230×	`swap-sqr_binary64`

Counts

55 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	631
1	131	568
2	358	556
3	2172	556
4	4697	556
5	5213	556

prune54.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	67	6	73

Error

Counts

73 → 6

Alt Table

Status	Error	Program
	20.6b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 -6450306886639899/50000000000000000 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (pow.f64 x 3))))
	17.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	31.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))
▶	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 -6450306886639899/50000000000000000 x) (*.f64 x x)))
	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3)))

Compiler

Compiled 1021 to 766 computations (25% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

3.0ms

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

1.0ms

(*.f64 -6450306886639899/50000000000000000 x)

rewrite12.0ms (0.6%)

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:

6.0ms

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

3.0ms

(*.f64 -6450306886639899/50000000000000000 x)

0.0ms

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

simplify73.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

592×	`fma-def_binary64`
457×	`neg-mul-1_binary64`
307×	`distribute-rgt-neg-out_binary64`
294×	`distribute-lft-neg-out_binary64`
268×	`distribute-rgt-in_binary64`

Counts

78 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	786
1	150	676
2	473	676
3	824	676
4	1744	661
5	4295	661
6	4892	661

prune51.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	75	5	80

Error

Counts

80 → 5

Alt Table

Status	Error	Program
	17.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 -6450306886639899/50000000000000000 x) (*.f64 x x)))
	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (cbrt.f64 (pow.f64 (.f64 -6450306886639899/50000000000000000 x) 3)) (*.f64 x x)))
	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 -6450306886639899/50000000000000000 (pow.f64 x 3)))

Compiler

Compiled 1136 to 696 computations (38.7% saved)

regimes110.0ms (5.5%)

Accuracy

Total 0.2b remaining (93.2%)

Threshold costs 0.2b (93.2%)

Counts

53 → 1

Compiler

Compiled 1532 to 1060 computations (30.8% 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

end99.0ms (4.9%)

Compiler: Compiled 72 to 52 computations (27.8% saved)

Details

analyze4.0ms (0.2%)

sample992.0ms (49.5%)

simplify146.0ms (7.3%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series5.0ms (0.3%)

rewrite4.0ms (0.2%)

simplify65.0ms (3.3%)

prune58.0ms (2.9%)

localize6.0ms (0.3%)

series8.0ms (0.4%)

rewrite14.0ms (0.7%)

simplify84.0ms (4.2%)

prune99.0ms (4.9%)

localize5.0ms (0.2%)

series7.0ms (0.4%)

rewrite6.0ms (0.3%)

simplify76.0ms (3.8%)

prune54.0ms (2.7%)

localize7.0ms (0.3%)

series8.0ms (0.4%)

rewrite12.0ms (0.6%)

simplify73.0ms (3.7%)

prune51.0ms (2.6%)

regimes110.0ms (5.5%)

simplify2.0ms (0.1%)

end99.0ms (4.9%)

Profiling