Details

analyze120.0ms (3%)

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)

sample41.0ms (1%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify103.0ms (2.5%)

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

prune7.0ms (0.2%)

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))))))
	0.5b	(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))))))

0.5b

(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)

localize31.0ms (0.8%)

Local error

Found 4 expressions with local error:

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 1 5) (.f64 (.f64 (.f64 (*.f64 (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)

rewrite393.0ms (9.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

119×	`add-exp-log_binary64`
76×	`prod-exp_binary64`
75×	`add-cbrt-cube_binary64`
48×	`associate-l_binary64`
46×	`add-sqr-sqrt_binary64`

Counts

4 → 169

Calls

4 calls:

33.0ms	(.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)))))
32.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
14.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 13713 to 4683 computations (65.8% saved)

series86.0ms (2.1%)

Error

Counts

4 → 9

Calls

4 calls:

51.0ms	(.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)))))
15.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
13.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1048 to 596 computations (43.1% saved)

simplify189.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

563×	`associate-r_binary64`
470×	`associate-l_binary64`
409×	`cancel-sign-sub-inv_binary64`
379×	`unswap-sqr_binary64`
223×	`*-commutative_binary64`

Counts

178 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	7482
1	891	5888
2	3483	5163
3	5097	5163

prune140.0ms (3.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	154	2	156

Error

Counts

156 → 2

Alt Table

Status	Error	Program
▶	0.1b	(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 (/.f64 1 PI.f64))))
	0.5b	(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 (*.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 PI.f64))))

0.5b

(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 5984 to 2932 computations (51% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite213.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

52×	`add-sqr-sqrt_binary64`
39×	`associate-r_binary64`
23×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`

Counts

4 → 120

Calls

4 calls:

17.0ms	(.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 PI.f64)))
7.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
7.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
6.0ms	(.f64 2/3 (.f64 x x))

Compiler

Compiled 4562 to 3093 computations (32.2% saved)

series111.0ms (2.7%)

Error

Counts

4 → 15

Calls

4 calls:

60.0ms	(.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 PI.f64)))
16.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
14.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
11.0ms	(.f64 2/3 (.f64 x x))

Compiler

Compiled 1102 to 855 computations (22.4% saved)

simplify198.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

336×	`cancel-sign-sub-inv_binary64`
255×	`exp-prod_binary64`
242×	`associate--l+_binary64`
220×	`associate--r+_binary64`
199×	`associate-l_binary64`

Counts

135 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	3859
1	529	3643
2	1584	2976
3	2548	2976
4	4637	2976
5	4868	2976
6	4927	2976

prune119.0ms (2.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

Counts

117 → 2

Alt Table

Status	Error	Program
✓	0.1b	(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 (/.f64 1 PI.f64))))
▶	0.5b	(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 (*.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 PI.f64))))

▶

0.5b

(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 3058 to 2179 computations (28.7% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 x 5))
0.1b	(*.f64 2/3 (pow.f64 x 3))
0.3b	(/.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))
1.0b	(sqrt.f64 PI.f64)

rewrite173.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

40×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`
18×	`times-frac_binary64`

Counts

4 → 110

Calls

4 calls:

13.0ms	(/.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))
7.0ms	(*.f64 2/3 (pow.f64 x 3))
5.0ms	(*.f64 1/5 (pow.f64 x 5))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3611 to 2757 computations (23.6% saved)

series66.0ms (1.6%)

Error

Counts

4 → 18

Calls

4 calls:

32.0ms	(/.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))
12.0ms	(*.f64 1/5 (pow.f64 x 5))
10.0ms	(*.f64 2/3 (pow.f64 x 3))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 836 to 704 computations (15.8% saved)

simplify205.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

508×	`unswap-sqr_binary64`
507×	`distribute-rgt-in_binary64`
490×	`distribute-lft-in_binary64`
398×	`*-commutative_binary64`
202×	`log-prod_binary64`

Counts

128 → 90

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	197	3778
1	419	3465
2	1225	3363
3	3581	3363
4	4619	3355
5	4914	3355
6	4833	3355

prune87.0ms (2.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	90	2	92

Error

Counts

92 → 2

Alt Table

Status	Error	Program
	0.1b	(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 (/.f64 1 PI.f64))))
	0.5b	(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 (*.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 PI.f64))))

0.5b

(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 2239 to 1705 computations (23.8% saved)

regimes501.0ms (12.4%)

Accuracy

Total 0.1b remaining (78.6%)

Threshold costs 0.1b (78.6%)

Compiler

Compiled 12695 to 7335 computations (42.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`fabs-mul_binary64`
1×	`fabs-div_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	42
1	38	42
2	42	42
3	40	42

end1.0ms (0%)

Compiler: Compiled 28 to 24 computations (14.3% saved)

sample1.2s (30.4%)

Algorithm

1×

intervals

Results

754.0ms	8000×	body	128	valid
92.0ms	8000×	pre	128	true

Compiler

Compiled 157 to 104 computations (33.8% saved)

Details

analyze120.0ms (3%)

sample41.0ms (1%)

simplify103.0ms (2.5%)

prune7.0ms (0.2%)

localize31.0ms (0.8%)

rewrite393.0ms (9.7%)

series86.0ms (2.1%)

simplify189.0ms (4.7%)

prune140.0ms (3.5%)

localize18.0ms (0.5%)

rewrite213.0ms (5.3%)

series111.0ms (2.7%)

simplify198.0ms (4.9%)

prune119.0ms (2.9%)

localize17.0ms (0.4%)

rewrite173.0ms (4.3%)

series66.0ms (1.6%)

simplify205.0ms (5.1%)

prune87.0ms (2.1%)

regimes501.0ms (12.4%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.2s (30.4%)

Profiling