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)

sample962.0ms (44.6%)

Results

787.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify152.0ms (7%)

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)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series11.0ms (0.5%)

Counts

4 → 36

Calls

4 calls:

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

rewrite22.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64`
23×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64`

Counts

4 → 90

Calls

4 calls:

7.0ms	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
5.0ms	(.f64 (.f64 x x) x)
3.0ms	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
3.0ms	(*.f64 238732414637843/250000000000000 x)

simplify79.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

926×	`fma-def_binary64`
402×	`fma-neg_binary64`
340×	`distribute-rgt-neg-in_binary64`
321×	`distribute-lft-neg-in_binary64`
303×	`cancel-sign-sub-inv_binary64`

Counts

126 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1075
1	244	966
2	796	954
3	1898	929
4	4654	929
5	4817	929

prune128.0ms (5.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	112	12	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Error

0.0b

Counts

126 → 12

Alt Table

Status	Error	Program
	1.3b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 238732414637843/250000000000000 x)) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
	28.4b	(/.f64 (-.f64 (.f64 (.f64 238732414637843/250000000000000 x) (.f64 238732414637843/250000000000000 x)) (.f64 (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))) (+.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x))))
	30.2b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (sqrt.f64 x)) (sqrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	15.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (sqrt.f64 (.f64 (.f64 x x) x)) (sqrt.f64 (.f64 (*.f64 x x) x)))))
	30.9b	(-.f64 (cbrt.f64 (pow.f64 (.f64 x 238732414637843/250000000000000) 3)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	28.5b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 6450306886639899/50000000000000000 (pow.f64 x 3) (*.f64 x 238732414637843/250000000000000)))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (pow.f64 x 3) (sqrt.f64 6450306886639899/50000000000000000))))
▶	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
	15.1b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x))) (sqrt.f64 (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))))
	30.9b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 238732414637843/250000000000000 238732414637843/250000000000000) 238732414637843/250000000000000) (.f64 (.f64 x x) x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))

Compiler

Compiled 2345 to 1396 computations (40.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

5.0ms	(*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000)
0.0ms	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))

simplify76.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

996×	`fma-def_binary64`
421×	`exp-prod_binary64`
402×	`log-prod_binary64`
287×	`cube-prod_binary64`
285×	`*-commutative_binary64`

Counts

67 → 67

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	698
1	130	663
2	484	663
3	1057	639
4	2821	633
5	4771	633
6	4929	633

prune87.0ms (4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	67	12	79

Error

0.0b

Counts

79 → 12

Alt Table

Status	Error	Program
	1.3b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 238732414637843/250000000000000 x)) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
	30.9b	(-.f64 (cbrt.f64 (pow.f64 (.f64 x 238732414637843/250000000000000) 3)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
▶	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))
	28.4b	(/.f64 (-.f64 (.f64 (.f64 238732414637843/250000000000000 x) (.f64 238732414637843/250000000000000 x)) (.f64 (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))) (+.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x))))
	30.2b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (sqrt.f64 x)) (sqrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	28.5b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 6450306886639899/50000000000000000 (pow.f64 x 3) (*.f64 x 238732414637843/250000000000000)))
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (pow.f64 x 3) (sqrt.f64 6450306886639899/50000000000000000))))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
	15.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (sqrt.f64 (pow.f64 x 3)) (.f64 (sqrt.f64 (pow.f64 x 3)) -6450306886639899/50000000000000000)))
	30.9b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 238732414637843/250000000000000 238732414637843/250000000000000) 238732414637843/250000000000000) (.f64 (.f64 x x) x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))

Compiler

Compiled 1277 to 957 computations (25.1% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series9.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

4.0ms

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

3.0ms

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

1.0ms

(*.f64 x -6450306886639899/50000000000000000)

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

4.0ms

(*.f64 x -6450306886639899/50000000000000000)

0.0ms

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

simplify78.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1001×	`fma-def_binary64`
337×	`distribute-rgt-neg-out_binary64`
318×	`distribute-lft-neg-out_binary64`
296×	`unswap-sqr_binary64`
282×	`distribute-rgt-neg-in_binary64`

Counts

90 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	834
1	152	724
2	523	724
3	931	724
4	1972	709
5	4434	709
6	4873	709

prune93.0ms (4.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	82	13	95

Error

0.0b

Counts

95 → 13

Alt Table

Status	Error	Program
	1.3b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 238732414637843/250000000000000 x)) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
▶	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
	30.9b	(-.f64 (cbrt.f64 (pow.f64 (.f64 x 238732414637843/250000000000000) 3)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))
	28.4b	(/.f64 (-.f64 (.f64 (.f64 238732414637843/250000000000000 x) (.f64 238732414637843/250000000000000 x)) (.f64 (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))) (+.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x))))
	30.2b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (sqrt.f64 x)) (sqrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	28.5b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 6450306886639899/50000000000000000 (pow.f64 x 3) (*.f64 x 238732414637843/250000000000000)))
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (pow.f64 x 3) (sqrt.f64 6450306886639899/50000000000000000))))
	34.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (.f64 (sqrt.f64 (.f64 x -6450306886639899/50000000000000000)) (sqrt.f64 (*.f64 x -6450306886639899/50000000000000000)))))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
	15.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (sqrt.f64 (pow.f64 x 3)) (.f64 (sqrt.f64 (pow.f64 x 3)) -6450306886639899/50000000000000000)))
	30.9b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 238732414637843/250000000000000 238732414637843/250000000000000) 238732414637843/250000000000000) (.f64 (.f64 x x) x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))

Compiler

Compiled 1623 to 1014 computations (37.5% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite5.0ms (0.3%)

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:

4.0ms	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
0.0ms	(fma.f64 x (*.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000)

simplify43.0ms (2%)

Algorithm

1×	egg-herbie

Rules

907×	`distribute-rgt-in_binary64`
906×	`distribute-lft-in_binary64`
415×	`fma-def_binary64`
240×	`associate-l_binary64`
204×	`associate-r_binary64`

Counts

56 → 64

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	716
1	107	613
2	301	613
3	1072	613
4	5400	613

prune81.0ms (3.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	6	4	10
Picked	0	1	1
Done	0	2	2
Total	99	8	107

Error

Counts

107 → 8

Alt Table

Status	Error	Program
	15.5b	(.f64 x (log.f64 (exp.f64 (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))
✓	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
	30.2b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (sqrt.f64 x)) (sqrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (sqrt.f64 6450306886639899/50000000000000000) (*.f64 (pow.f64 x 3) (sqrt.f64 6450306886639899/50000000000000000))))
	34.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (.f64 (sqrt.f64 (.f64 x -6450306886639899/50000000000000000)) (sqrt.f64 (*.f64 x -6450306886639899/50000000000000000)))))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
	15.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (sqrt.f64 (pow.f64 x 3)) (.f64 (sqrt.f64 (pow.f64 x 3)) -6450306886639899/50000000000000000)))

Compiler

Compiled 1297 to 847 computations (34.7% saved)

regimes164.0ms (7.6%)

Accuracy

Total 0.3b remaining (96%)

Threshold costs 0.3b (96%)

Counts

80 → 1

Compiler

Compiled 2380 to 1682 computations (29.3% 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

end106.0ms (4.9%)

Compiler: Compiled 120 to 88 computations (26.7% saved)

Details

analyze5.0ms (0.2%)

sample962.0ms (44.6%)

simplify152.0ms (7%)

prune3.0ms (0.2%)

localize6.0ms (0.3%)

series11.0ms (0.5%)

rewrite22.0ms (1%)

simplify79.0ms (3.6%)

prune128.0ms (5.9%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite7.0ms (0.3%)

simplify76.0ms (3.5%)

prune87.0ms (4%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite12.0ms (0.6%)

simplify78.0ms (3.6%)

prune93.0ms (4.3%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite5.0ms (0.3%)

simplify43.0ms (2%)

prune81.0ms (3.7%)

regimes164.0ms (7.6%)

simplify2.0ms (0.1%)

end106.0ms (4.9%)

Profiling