Details

analyze107.0ms (1.8%)

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)

sample44.0ms (0.7%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify96.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1509×	`associate-/l*_binary64`
1334×	`associate-/r*_binary64`
744×	`distribute-lft-out_binary64`
549×	`unswap-sqr_binary64`
452×	`associate-*r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	32	77
1	73	62
2	218	45
3	773	41
4	1394	41
5	3040	41
6	3379	41
7	3543	39
8	2136	39
9	2622	39
10	2670	39
11	4941	39

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.1b	(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))))))
	0.6b	(fabs.f64 (/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 x) (.f64 2/3 (pow.f64 x 3))) (.f64 1/5 (pow.f64 x 5))) (.f64 1/21 (pow.f64 x 7))) (sqrt.f64 PI.f64)))

Status

Error

Program

▶

0.1b

(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))))))

0.6b

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

Compiler

Compiled 214 to 128 computations (40.2% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (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)

rewrite265.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

45×	`add-sqr-sqrt_binary64`
39×	`add-exp-log_binary64`
38×	`add-cbrt-cube_binary64`
36×	`associate-l_binary64`
35×	`pow1_binary64`

Counts

4 → 147

Calls

4 calls:

25.0ms	(.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)))))
11.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 11748 to 4026 computations (65.7% saved)

series129.0ms (2.2%)

Error

0.0b

Counts

4 → 9

Calls

4 calls:

97.0ms	(.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)))))
11.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
9.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1135 to 632 computations (44.3% saved)

simplify240.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

519×	`associate-r_binary64`
418×	`associate-l_binary64`
389×	`cancel-sign-sub-inv_binary64`
263×	`distribute-rgt-neg-in_binary64`
213×	`*-commutative_binary64`

Counts

156 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	279	6843
1	842	5231
2	3321	4701
3	4872	4653
4	4956	4653

prune133.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	122	5	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	5	129

Error

Counts

129 → 5

Alt Table

Status	Error	Program
	28.8b	(fabs.f64 (/.f64 (+.f64 (.f64 21 (-.f64 (.f64 (.f64 x x) (.f64 (+.f64 (.f64 2/3 (.f64 x x)) 2) (+.f64 (.f64 2/3 (.f64 x x)) 2))) (.f64 1/25 (pow.f64 (.f64 x x) 5)))) (.f64 (pow.f64 (fabs.f64 x) 7) (-.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (.f64 (sqrt.f64 PI.f64) (.f64 21 (-.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
	40.0b	(fabs.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64)) 3)))
▶	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))))))
	0.4b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))))
	0.5b	(fabs.f64 (/.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64)))

Compiler

Compiled 5904 to 2905 computations (50.8% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.1b	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
0.1b	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)))))
0.2b	(.f64 2/3 (.f64 x x))

rewrite187.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

52×	`add-sqr-sqrt_binary64`
26×	`associate-r_binary64`
25×	`associate-l_binary64`
23×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 122

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)))))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
5.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
5.0ms	(.f64 2/3 (.f64 x x))

Compiler

Compiled 4632 to 3141 computations (32.2% saved)

series166.0ms (2.8%)

Error

Counts

4 → 15

Calls

4 calls:

89.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
48.0ms	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)))))
11.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
7.0ms	(.f64 2/3 (.f64 x x))

Compiler

Compiled 1164 to 900 computations (22.7% saved)

simplify198.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

354×	`cancel-sign-sub-inv_binary64`
311×	`exp-prod_binary64`
257×	`associate-l_binary64`
249×	`associate-r_binary64`
207×	`distribute-rgt-neg-in_binary64`

Counts

137 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	254	4152
1	598	3616
2	1820	3097
3	2927	3097
4	4550	3097
5	4865	3097
6	4993	3097
7	4894	3097

prune116.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	117	5	122

Error

Counts

122 → 5

Alt Table

Status	Error	Program
	28.8b	(fabs.f64 (/.f64 (+.f64 (.f64 21 (-.f64 (.f64 (.f64 x x) (.f64 (+.f64 (.f64 2/3 (.f64 x x)) 2) (+.f64 (.f64 2/3 (.f64 x x)) 2))) (.f64 1/25 (pow.f64 (.f64 x x) 5)))) (.f64 (pow.f64 (fabs.f64 x) 7) (-.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (.f64 (sqrt.f64 PI.f64) (.f64 21 (-.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
	40.0b	(fabs.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64)) 3)))
	0.5b	(fabs.f64 (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (*.f64 x x)))))) (sqrt.f64 PI.f64)))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))))))
▶	0.4b	(fabs.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (.f64 (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (*.f64 x x)))))) (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))))))

Compiler

Compiled 3434 to 2462 computations (28.3% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/21 (pow.f64 x 7))
0.2b	(.f64 2/3 (.f64 x x))
0.2b	(.f64 (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x)))))) (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (.f64 (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (*.f64 x x)))))) (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64)))))

rewrite234.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

65×	`sqrt-prod_binary64`
44×	`add-sqr-sqrt_binary64`
30×	`sqrt-div_binary64`
28×	`associate-r_binary64`
28×	`associate-l_binary64`

Counts

4 → 132

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (.f64 (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (*.f64 x x)))))) (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64)))))
17.0ms	(.f64 (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x)))))) (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))))
6.0ms	(.f64 2/3 (.f64 x x))
4.0ms	(*.f64 1/21 (pow.f64 x 7))

Compiler

Compiled 5855 to 4459 computations (23.8% saved)

series107.0ms (1.8%)

Error

Counts

4 → 30

Calls

4 calls:

41.0ms	(.f64 (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x)))))) (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))))
28.0ms	(.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (.f64 (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (*.f64 x x)))))) (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64)))))
9.0ms	(*.f64 1/21 (pow.f64 x 7))
9.0ms	(.f64 2/3 (.f64 x x))

Compiler

Compiled 1645 to 1388 computations (15.6% saved)

simplify322.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

318×	`cancel-sign-sub-inv_binary64`
285×	`associate-r_binary64`
258×	`associate-l_binary64`
253×	`unswap-sqr_binary64`
184×	`distribute-rgt-neg-in_binary64`

Counts

162 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	241	6896
1	541	6280
2	1927	5869
3	3111	5674
4	4571	5674
5	4936	5674
6	4995	5674
7	4913	5674

prune121.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	122	4	126

Error

Counts

126 → 4

Alt Table

Status	Error	Program
	28.8b	(fabs.f64 (/.f64 (+.f64 (.f64 21 (-.f64 (.f64 (.f64 x x) (.f64 (+.f64 (.f64 2/3 (.f64 x x)) 2) (+.f64 (.f64 2/3 (.f64 x x)) 2))) (.f64 1/25 (pow.f64 (.f64 x x) 5)))) (.f64 (pow.f64 (fabs.f64 x) 7) (-.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (.f64 (sqrt.f64 PI.f64) (.f64 21 (-.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
	0.5b	(fabs.f64 (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (*.f64 x x)))))) (sqrt.f64 PI.f64)))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))))))
▶	0.3b	(fabs.f64 (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x))))))) (sqrt.f64 (sqrt.f64 PI.f64))))

Compiler

Compiled 3992 to 3010 computations (24.6% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 2/3 (.f64 x x))
0.2b	(.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x)))))))
0.3b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x))))))) (sqrt.f64 (sqrt.f64 PI.f64)))
1.0b	(sqrt.f64 PI.f64)

rewrite190.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

57×	`sqrt-prod_binary64`
35×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
22×	`associate-l_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 115

Calls

4 calls:

19.0ms	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x))))))) (sqrt.f64 (sqrt.f64 PI.f64)))
17.0ms	(.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x)))))))
5.0ms	(.f64 2/3 (.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 4763 to 3327 computations (30.1% saved)

series93.0ms (1.6%)

Error

Counts

4 → 27

Calls

4 calls:

38.0ms	(.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x)))))))
28.0ms	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x))))))) (sqrt.f64 (sqrt.f64 PI.f64)))
9.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1349 to 1121 computations (16.9% saved)

simplify223.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

567×	`associate-/l*_binary64`
497×	`times-frac_binary64`
297×	`associate-*l/_binary64`
227×	`associate-r_binary64`
223×	`associate-l_binary64`

Counts

142 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	6114
1	571	5609
2	2140	5370
3	4592	5370
4	4916	5370

prune79.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	86	4	90

Error

Counts

90 → 4

Alt Table

Status	Error	Program
	28.8b	(fabs.f64 (/.f64 (+.f64 (.f64 21 (-.f64 (.f64 (.f64 x x) (.f64 (+.f64 (.f64 2/3 (.f64 x x)) 2) (+.f64 (.f64 2/3 (.f64 x x)) 2))) (.f64 1/25 (pow.f64 (.f64 x x) 5)))) (.f64 (pow.f64 (fabs.f64 x) 7) (-.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (.f64 (sqrt.f64 PI.f64) (.f64 21 (-.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
	0.5b	(fabs.f64 (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (*.f64 x x)))))) (sqrt.f64 PI.f64)))
	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))))))
	0.3b	(fabs.f64 (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 (.f64 1/21 (pow.f64 x 7)) (+.f64 (.f64 1/5 (pow.f64 x 5)) (.f64 x (+.f64 2 (.f64 2/3 (.f64 x x))))))) (sqrt.f64 (sqrt.f64 PI.f64))))

Compiler

Compiled 2404 to 1710 computations (28.9% saved)

regimes1.1s (19.3%)

Accuracy

Total 0.1b remaining (84.4%)

Threshold costs 0.1b (84.4%)

Compiler

Compiled 32033 to 19729 computations (38.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`fabs-mul_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	50
1	39	50
2	40	50
3	39	50

end1.0ms (0%)

Compiler: Compiled 32 to 25 computations (21.9% saved)

sample1.6s (27.4%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
102.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 271 to 182 computations (32.8% saved)

Details

analyze107.0ms (1.8%)

sample44.0ms (0.7%)

simplify96.0ms (1.6%)

prune5.0ms (0.1%)

localize29.0ms (0.5%)

rewrite265.0ms (4.5%)

series129.0ms (2.2%)

simplify240.0ms (4.1%)

prune133.0ms (2.2%)

localize19.0ms (0.3%)

rewrite187.0ms (3.2%)

series166.0ms (2.8%)

simplify198.0ms (3.3%)

prune116.0ms (2%)

localize20.0ms (0.3%)

rewrite234.0ms (4%)

series107.0ms (1.8%)

simplify322.0ms (5.4%)

prune121.0ms (2.1%)

localize25.0ms (0.4%)

rewrite190.0ms (3.2%)

series93.0ms (1.6%)

simplify223.0ms (3.8%)

prune79.0ms (1.3%)

regimes1.1s (19.3%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.6s (27.4%)

Profiling