Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 71 to 33 computations (53.5% saved)

sample1.5s (41.4%)

Results

1.5s	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify20.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

642×	`distribute-lft-out_binary64`
588×	`associate-/l*_binary64`
406×	`associate-/r*_binary64`
400×	`*-commutative_binary64`
244×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	75
1	74	59
2	251	41
3	1208	37
4	2394	37

Stop Event

1×	node limit

Counts

1 → 2

prune8.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))

Status

Error

Program

▶

0.2b

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

0.5b

(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))

Compiler

Compiled 278 to 149 computations (46.4% saved)

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
✓	0.1b	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
✓	0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	1.0b	(sqrt.f64 (PI.f64))

series75.0ms (2%)

Counts

4 → 36

Calls

4 calls:

58.0ms	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
10.0ms	(.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
8.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 (PI.f64))

rewrite37.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

274×	`add-cbrt-cube_binary64`
274×	`log1p-expm1-u_binary64`
274×	`expm1-log1p-u_binary64`
265×	`add-cube-cbrt_binary64`
265×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	86
1	619	63

Stop Event

1×	node limit

Counts

4 → 61

Calls

4 calls:

35.0ms	(.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
35.0ms	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
35.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
35.0ms	(sqrt.f64 (PI.f64))

simplify82.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

2001×	`fma-def_binary64`
662×	`associate-l_binary64`
478×	`associate-r_binary64`
213×	`sqr-pow_binary64`
198×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	684
1	63	684
2	161	684
3	504	660
4	1327	660
5	3626	660
6	4007	660
7	4106	660
8	4236	660
9	4434	660
10	4725	660

Stop Event

1×	node limit

Counts

97 → 64

prune121.0ms (3.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	75	4	79

Error

Counts

79 → 4

Alt Table

Status	Error	Program
	0.2b	(fabs.f64 (fma.f64 (pow.f64 (PI.f64) -1/2) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (.f64 (pow.f64 (PI.f64) -1/2) (.f64 1/21 (.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6))))))
▶	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fabs.f64 x) 5)) 2) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (/.f64 (fma.f64 1/21 (.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64))))

Compiler

Compiled 4642 to 2067 computations (55.5% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
✓	0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
✓	0.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
✓	0.1b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

series96.0ms (2.6%)

Counts

4 → 0

Calls

4 calls:

57.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
14.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
14.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
10.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

rewrite37.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`log1p-expm1-u_binary64`
259×	`expm1-log1p-u_binary64`
255×	`add-cbrt-cube_binary64`
248×	`add-log-exp_binary64`
247×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	69
1	562	67

Stop Event

1×	node limit

Counts

4 → 54

Calls

4 calls:

35.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
35.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
35.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
35.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

54 → 54

prune87.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	54	4	58

Error

Counts

58 → 4

Alt Table

Status	Error	Program
▶	0.2b	(fabs.f64 (fma.f64 (pow.f64 (PI.f64) -1/2) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (.f64 (pow.f64 (PI.f64) -1/2) (.f64 1/21 (.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6))))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fabs.f64 x) 5)) 2) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (/.f64 (fma.f64 1/21 (.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64))))

Compiler

Compiled 2055 to 1472 computations (28.4% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6))
	0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
✓	0.1b	(fma.f64 (pow.f64 (PI.f64) -1/2) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (.f64 (pow.f64 (PI.f64) -1/2) (.f64 1/21 (.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)))))
✓	0.1b	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

series253.0ms (6.9%)

Counts

3 → 36

Calls

3 calls:

221.0ms

(fma.f64 (pow.f64 (PI.f64) -1/2) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (*.f64 (pow.f64 (PI.f64) -1/2) (*.f64 1/21 (*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)))))

20.0ms

(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

12.0ms

(*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6))

rewrite36.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

227×	`add-sqr-sqrt_binary64`
220×	`log1p-expm1-u_binary64`
220×	`expm1-log1p-u_binary64`
214×	`add-cbrt-cube_binary64`
214×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	81
1	490	52

Stop Event

1×	node limit

Counts

3 → 59

Calls

3 calls:

34.0ms

(*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6))

34.0ms

(fma.f64 (pow.f64 (PI.f64) -1/2) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (*.f64 (pow.f64 (PI.f64) -1/2) (*.f64 1/21 (*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)))))

34.0ms

(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

simplify85.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1117×	`fma-def_binary64`
690×	`unswap-sqr_binary64`
345×	`*-commutative_binary64`
277×	`associate-l_binary64`
264×	`sqr-pow_binary64`

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	34	1116
1	91	1116
2	239	948
3	641	816
4	1688	816
5	1964	816
6	2165	816
7	2607	816
8	3486	816
9	3629	768
10	4459	768
11	4845	768

Stop Event

1×	node limit

Counts

95 → 65

prune133.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	77	4	81

Error

Counts

81 → 4

Alt Table

Status	Error	Program
✓	0.2b	(fabs.f64 (fma.f64 (pow.f64 (PI.f64) -1/2) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (.f64 (pow.f64 (PI.f64) -1/2) (.f64 1/21 (.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6))))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
▶	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fabs.f64 x) 5)) 2) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (/.f64 (fma.f64 1/21 (.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64))))

Compiler

Compiled 3057 to 2238 computations (26.8% saved)

localize27.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fabs.f64 x) 5)) 2) (fabs.f64 x)) (fabs.f64 x)))))
	0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
	1.0b	(sqrt.f64 (PI.f64))
✓	11.8b	(sqrt.f64 (pow.f64 (fabs.f64 x) 5))

series74.0ms (2%)

Counts

2 → 12

Calls

2 calls:

61.0ms

(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fabs.f64 x) 5)) 2) (fabs.f64 x)) (fabs.f64 x)))))

13.0ms

(sqrt.f64 (pow.f64 (fabs.f64 x) 5))

rewrite30.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

297×	`log1p-expm1-u_binary64`
297×	`expm1-log1p-u_binary64`
292×	`add-cbrt-cube_binary64`
284×	`add-log-exp_binary64`
282×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	61
1	684	45

Stop Event

1×	node limit

Counts

2 → 41

Calls

2 calls:

29.0ms

(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fabs.f64 x) 5)) 2) (fabs.f64 x)) (fabs.f64 x)))))

29.0ms

(sqrt.f64 (pow.f64 (fabs.f64 x) 5))

simplify73.0ms (2%)

Algorithm

1×	egg-herbie

Rules

2001×	`fma-def_binary64`
660×	`associate-l_binary64`
478×	`associate-r_binary64`
213×	`sqr-pow_binary64`
198×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	504
1	63	504
2	161	504
3	505	480
4	1327	480
5	3645	480
6	4026	480
7	4123	480
8	4254	480
9	4452	480
10	4743	480

Stop Event

1×	node limit

Counts

53 → 43

prune126.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	75	4	79

Error

Counts

79 → 4

Alt Table

Status	Error	Program
✓	0.2b	(fabs.f64 (fma.f64 (pow.f64 (PI.f64) -1/2) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (.f64 (pow.f64 (PI.f64) -1/2) (.f64 1/21 (.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6))))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
✓	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fabs.f64 x) 5)) 2) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (/.f64 (fma.f64 1/21 (.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64))))

Compiler

Compiled 4167 to 2198 computations (47.3% saved)

regimes569.0ms (15.4%)

Accuracy

Total 0.1b remaining (77.4%)

Threshold costs 0.1b (77.4%)

Counts

79 → 1

Compiler

Compiled 16626 to 11202 computations (32.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	49
1	26	49

Stop Event

1×

saturated

end127.0ms (3.4%)

Compiler: Compiled 222 to 155 computations (30.2% saved)

Details

analyze5.0ms (0.1%)

sample1.5s (41.4%)

simplify20.0ms (0.5%)

prune8.0ms (0.2%)

localize22.0ms (0.6%)

series75.0ms (2%)

rewrite37.0ms (1%)

simplify82.0ms (2.2%)

prune121.0ms (3.3%)

localize17.0ms (0.4%)

series96.0ms (2.6%)

rewrite37.0ms (1%)

simplify6.0ms (0.2%)

prune87.0ms (2.3%)

localize19.0ms (0.5%)

series253.0ms (6.9%)

rewrite36.0ms (1%)

simplify85.0ms (2.3%)

prune133.0ms (3.6%)

localize27.0ms (0.7%)

series74.0ms (2%)

rewrite30.0ms (0.8%)

simplify73.0ms (2%)

prune126.0ms (3.4%)

regimes569.0ms (15.4%)

simplify2.0ms (0.1%)

end127.0ms (3.4%)

Profiling