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)

sample944.0ms (43.9%)

Results

771.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify153.0ms (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 (0.1%)

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 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)
✓	0.2b	(.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))
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)

simplify88.0ms (4.1%)

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

prune43.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	4	66

Error

0.0b

Counts

66 → 4

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)))
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	15.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))

Compiler

Compiled 905 to 537 computations (40.7% saved)

localize5.0ms (0.2%)

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)
✓	0.1b	(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))

series20.0ms (0.9%)

Counts

3 → 3

Calls

3 calls:

15.0ms

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

3.0ms

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

2.0ms

(*.f64 238732414637843/250000000000000 x)

rewrite14.0ms (0.6%)

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:

5.0ms

(*.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)

simplify87.0ms (4%)

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

prune114.0ms (5.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	98	5	103

Error

0.0b

Counts

103 → 5

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 (.f64 6450306886639899/50000000000000000 x) (.f64 x x)))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3))))
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	15.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))

Compiler

Compiled 1534 to 1201 computations (21.7% saved)

localize10.0ms (0.5%)

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)

rewrite18.0ms (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:

7.0ms

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

6.0ms

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

3.0ms

(*.f64 6450306886639899/50000000000000000 x)

simplify92.0ms (4.3%)

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

prune80.0ms (3.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	108	6	114

Error

Counts

114 → 6

Alt Table

Status	Error	Program
	0.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 6450306886639899/50000000000000000 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 x x)))
✓	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 x) (.f64 x x)))
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3))))
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	15.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))

Compiler

Compiled 1854 to 1175 computations (36.6% saved)

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3))))
	0.1b	(*.f64 238732414637843/250000000000000 x)
✓	0.2b	(*.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3))
✓	0.2b	(.f64 (sqrt.f64 6450306886639899/50000000000000000) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3)))

series27.0ms (1.3%)

Counts

3 → 24

Calls

3 calls:

11.0ms

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

9.0ms

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

7.0ms

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

rewrite22.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
13×	`associate-r_binary64`
12×	`associate-l_binary64`
10×	`sqrt-prod_binary64`

Counts

3 → 80

Calls

3 calls:

8.0ms

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

6.0ms

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

4.0ms

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

simplify96.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-def_binary64`
420×	`distribute-rgt-neg-in_binary64`
387×	`distribute-lft-neg-in_binary64`
373×	`exp-prod_binary64`
347×	`*-commutative_binary64`

Counts

104 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	1294
1	266	1217
2	941	1183
3	2251	1175
4	4459	1162
5	4629	1162

prune116.0ms (5.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	134	6	140

Error

Counts

140 → 6

Alt Table

Status	Error	Program
	0.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 6450306886639899/50000000000000000 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 x x)))
✓	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 x) (.f64 x x)))
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (sqrt.f64 6450306886639899/50000000000000000) (pow.f64 x 3))))
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	15.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))

Compiler

Compiled 2516 to 2078 computations (17.4% saved)

regimes56.0ms (2.6%)

Accuracy

Total 0.2b remaining (93%)

Threshold costs 0.2b (93%)

Counts

25 → 1

Compiler

Compiled 702 to 470 computations (33% 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

end119.0ms (5.6%)

Compiler: Compiled 93 to 67 computations (28% saved)

Details

analyze5.0ms (0.2%)

sample944.0ms (43.9%)

simplify153.0ms (7.1%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite4.0ms (0.2%)

simplify88.0ms (4.1%)

prune43.0ms (2%)

localize5.0ms (0.2%)

series20.0ms (0.9%)

rewrite14.0ms (0.6%)

simplify87.0ms (4%)

prune114.0ms (5.3%)

localize10.0ms (0.5%)

series8.0ms (0.4%)

rewrite18.0ms (0.8%)

simplify92.0ms (4.3%)

prune80.0ms (3.7%)

localize13.0ms (0.6%)

series27.0ms (1.3%)

rewrite22.0ms (1%)

simplify96.0ms (4.5%)

prune116.0ms (5.4%)

regimes56.0ms (2.6%)

simplify2.0ms (0.1%)

end119.0ms (5.6%)

Profiling