Details

analyze182.0ms (7.7%)

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)

sample16.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify151.0ms (6.4%)

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

0.2b

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 (0.2%)

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)

simplify50.0ms (2.1%)

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

prune51.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	59	7	66

Error

Counts

66 → 7

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	16.3b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	32.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))
✓	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)))
	41.4b	(cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000) (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)) (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))))

Compiler

Compiled 1047 to 623 computations (40.5% 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 6450306886639899/50000000000000000 (pow.f64 x 3))
✓	0.2b	(*.f64 238732414637843/250000000000000 x)

series10.0ms (0.4%)

Counts

3 → 3

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)))

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)

simplify86.0ms (3.6%)

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

prune81.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	100	5	105

Error

Counts

105 → 5

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	16.3b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
✓	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)))
	0.3b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 x x) 6450306886639899/50000000000000000) (cbrt.f64 (pow.f64 x 3))))

Compiler

Compiled 1515 to 1185 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)
	0.2b	(*.f64 238732414637843/250000000000000 x)
✓	0.2b	(.f64 (.f64 6450306886639899/50000000000000000 x) (*.f64 x x))

series9.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

4.0ms

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

3.0ms

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

1.0ms

(*.f64 6450306886639899/50000000000000000 x)

rewrite15.0ms (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 → 60

Calls

3 calls:

6.0ms

(*.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)

simplify98.0ms (4.1%)

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

prune79.0ms (3.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	108	5	113

Error

Counts

113 → 5

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	16.3b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
✓	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)))
▶	0.3b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 x x) 6450306886639899/50000000000000000) (cbrt.f64 (pow.f64 x 3))))

Compiler

Compiled 1799 to 1140 computations (36.6% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (*.f64 x x) 6450306886639899/50000000000000000) (cbrt.f64 (pow.f64 x 3)))
	0.2b	(*.f64 238732414637843/250000000000000 x)
✓	0.2b	(.f64 (.f64 x x) 6450306886639899/50000000000000000)
✓	30.7b	(cbrt.f64 (pow.f64 x 3))

series19.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

10.0ms	(.f64 (.f64 (*.f64 x x) 6450306886639899/50000000000000000) (cbrt.f64 (pow.f64 x 3)))
6.0ms	(cbrt.f64 (pow.f64 x 3))
3.0ms	(.f64 (.f64 x x) 6450306886639899/50000000000000000)

rewrite38.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
18×	`associate-r_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
14×	`add-cbrt-cube_binary64`

Counts

3 → 78

Calls

3 calls:

24.0ms	(.f64 (.f64 x x) 6450306886639899/50000000000000000)
9.0ms	(.f64 (.f64 (*.f64 x x) 6450306886639899/50000000000000000) (cbrt.f64 (pow.f64 x 3)))
2.0ms	(cbrt.f64 (pow.f64 x 3))

simplify114.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
502×	`*-commutative_binary64`
398×	`sqr-pow_binary64`
373×	`exp-prod_binary64`
355×	`log-prod_binary64`

Counts

114 → 110

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	108	1007
1	206	872
2	981	845
3	1888	820
4	3030	815
5	4572	803
6	4810	803
7	4978	803

prune101.0ms (4.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	132	5	137

Error

Counts

137 → 5

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	16.3b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
✓	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)))
✓	0.3b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 x x) 6450306886639899/50000000000000000) (cbrt.f64 (pow.f64 x 3))))

Compiler

Compiled 2448 to 1643 computations (32.9% saved)

regimes138.0ms (5.8%)

Accuracy

Total 0.2b remaining (92.8%)

Threshold costs 0.2b (92.8%)

Counts

40 → 1

Compiler

Compiled 1250 to 914 computations (26.9% saved)

simplify5.0ms (0.2%)

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

end1.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample1.1s (45.2%)

Algorithm

1×

intervals

Results

620.0ms

8000×

body

128

valid

Compiler

Compiled 80 to 58 computations (27.5% saved)

Details

analyze182.0ms (7.7%)

sample16.0ms (0.7%)

simplify151.0ms (6.4%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite4.0ms (0.2%)

simplify50.0ms (2.1%)

prune51.0ms (2.2%)

localize5.0ms (0.2%)

series10.0ms (0.4%)

rewrite14.0ms (0.6%)

simplify86.0ms (3.6%)

prune81.0ms (3.4%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite15.0ms (0.6%)

simplify98.0ms (4.1%)

prune79.0ms (3.3%)

localize10.0ms (0.4%)

series19.0ms (0.8%)

rewrite38.0ms (1.6%)

simplify114.0ms (4.8%)

prune101.0ms (4.3%)

regimes138.0ms (5.8%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample1.1s (45.2%)

Profiling