Details

analyze5.0ms (0.3%)

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)

sample172.0ms (9.9%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify147.0ms (8.4%)

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 (0.2%)

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

Status

Error

Program

0.2b

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

▶

0.2b

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

Compiler

Compiled 62 to 40 computations (35.5% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

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

simplify40.0ms (2.3%)

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

prune50.0ms (2.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	60	6	66

Error

0.0b

Counts

66 → 6

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	8.3b	(.f64 x (cbrt.f64 (.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))))
	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	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))))
	34.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))
	15.8b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))

Compiler

Compiled 1026 to 615 computations (40.1% 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)

series9.0ms (0.5%)

Counts

3 → 3

Calls

3 calls:

4.0ms

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

4.0ms

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

2.0ms

(*.f64 238732414637843/250000000000000 x)

rewrite14.0ms (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:

5.0ms

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

4.0ms

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

3.0ms

(*.f64 238732414637843/250000000000000 x)

simplify83.0ms (4.8%)

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

prune93.0ms (5.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Error

Counts

104 → 7

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 6450306886639899/50000000000000000 x) (.f64 x x)))
	15.8b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	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))))
	34.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.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)))
	0.3b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 x x) 6450306886639899/50000000000000000) (cbrt.f64 (pow.f64 x 3))))

Compiler

Compiled 1612 to 1249 computations (22.5% saved)

localize7.0ms (0.4%)

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 238732414637843/250000000000000 x)
✓	0.1b	(*.f64 6450306886639899/50000000000000000 x)
✓	0.2b	(.f64 (.f64 6450306886639899/50000000000000000 x) (*.f64 x x))

series8.0ms (0.5%)

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))

2.0ms

(*.f64 6450306886639899/50000000000000000 x)

rewrite16.0ms (0.9%)

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 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)

simplify90.0ms (5.2%)

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

prune87.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	109	6	115

Error

Counts

115 → 6

Alt Table

Status	Error	Program
▶	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 x (sqrt.f64 238732414637843/250000000000000))) (.f64 (.f64 6450306886639899/50000000000000000 x) (*.f64 x x)))
	34.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.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)))
	15.8b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	0.3b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 x x) 6450306886639899/50000000000000000) (cbrt.f64 (pow.f64 x 3))))

Compiler

Compiled 1856 to 1182 computations (36.3% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 2)))
✓	0.2b	(*.f64 6450306886639899/50000000000000000 (pow.f64 x 2))
✓	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))

series11.0ms (0.6%)

Counts

3 → 15

Calls

3 calls:

5.0ms

(-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 2)))

3.0ms

(*.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))

2.0ms

(*.f64 6450306886639899/50000000000000000 (pow.f64 x 2))

rewrite16.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`associate-r_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 81

Calls

3 calls:

4.0ms

(*.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))

4.0ms

(*.f64 6450306886639899/50000000000000000 (pow.f64 x 2))

4.0ms

(-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 2)))

simplify66.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

795×	`distribute-rgt-in_binary64`
737×	`distribute-lft-in_binary64`
584×	`fma-def_binary64`
209×	`*-commutative_binary64`
173×	`unswap-sqr_binary64`

Counts

96 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1460
1	251	1152
2	731	1029
3	1675	1002
4	5249	1002

prune106.0ms (6.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	136	6	142

Error

Counts

142 → 6

Alt Table

Status	Error	Program
✓	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 x (sqrt.f64 238732414637843/250000000000000))) (.f64 (.f64 6450306886639899/50000000000000000 x) (*.f64 x x)))
	34.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.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)))
	15.8b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	0.3b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (.f64 x x) 6450306886639899/50000000000000000) (cbrt.f64 (pow.f64 x 3))))

Compiler

Compiled 2168 to 1629 computations (24.9% saved)

regimes141.0ms (8.1%)

Accuracy

Total 0.2b remaining (94.4%)

Threshold costs 0.2b (94.4%)

Counts

70 → 1

Compiler

Compiled 2022 to 1490 computations (26.3% saved)

simplify3.0ms (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)

sample555.0ms (31.7%)

Algorithm

1×

intervals

Results

294.0ms

8000×

body

128

valid

Compiler

Compiled 98 to 72 computations (26.5% saved)

Details

analyze5.0ms (0.3%)

sample172.0ms (9.9%)

simplify147.0ms (8.4%)

prune3.0ms (0.2%)

localize4.0ms (0.3%)

series7.0ms (0.4%)

rewrite4.0ms (0.2%)

simplify40.0ms (2.3%)

prune50.0ms (2.8%)

localize5.0ms (0.3%)

series9.0ms (0.5%)

rewrite14.0ms (0.8%)

simplify83.0ms (4.8%)

prune93.0ms (5.3%)

localize7.0ms (0.4%)

series8.0ms (0.5%)

rewrite16.0ms (0.9%)

simplify90.0ms (5.2%)

prune87.0ms (5%)

localize5.0ms (0.3%)

series11.0ms (0.6%)

rewrite16.0ms (0.9%)

simplify66.0ms (3.8%)

prune106.0ms (6.1%)

regimes141.0ms (8.1%)

simplify3.0ms (0.2%)

end1.0ms (0%)

sample555.0ms (31.7%)

Profiling