Details

analyze181.0ms (3.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

785×	`distribute-rgt-neg-in_binary64`
770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
289×	`sub-neg_binary64`
232×	`associate-+l+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	29	25
2	50	25
3	138	25
4	374	25
5	1117	25
6	2839	25
7	5140	25

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite103.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64`
11×	`*-un-lft-identity_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`

Counts

4 → 68

Calls

4 calls:

8.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
7.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
4.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1731 to 796 computations (54% saved)

series188.0ms (3.3%)

Error

0.0b

Counts

4 → 57

Calls

4 calls:

63.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
60.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
40.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
5.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1883 to 1494 computations (20.7% saved)

simplify149.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

476×	`associate-l_binary64`
400×	`associate-r_binary64`
330×	`cancel-sign-sub-inv_binary64`
329×	`exp-prod_binary64`
271×	`distribute-rgt-in_binary64`

Counts

125 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	2623
1	291	2414
2	821	2375
3	3093	2375
4	4458	2375
5	4838	2375
6	4980	2375

prune50.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Error

Counts

88 → 3

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))) 1)
▶	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)
	18.4b	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3) -1) (+.f64 1 (.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) (+.f64 1 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))

Compiler

Compiled 1269 to 630 computations (50.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)
0.0b	(+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
2.2b	(.f64 (.f64 a a) (*.f64 b b))

rewrite182.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

37×	`pow1_binary64`
27×	`add-log-exp_binary64`
21×	`add-cbrt-cube_binary64`
21×	`add-exp-log_binary64`
17×	`pow-prod-down_binary64`

Counts

4 → 84

Calls

4 calls:

12.0ms	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)
12.0ms	(+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b)))
7.0ms	(.f64 (.f64 a a) (*.f64 b b))
4.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 2671 to 1441 computations (46.1% saved)

series160.0ms (2.8%)

Error

Counts

4 → 45

Calls

4 calls:

68.0ms	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)
60.0ms	(+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b)))
16.0ms	(.f64 (.f64 a a) (*.f64 b b))
8.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1659 to 1324 computations (20.2% saved)

simplify102.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

574×	`unswap-sqr_binary64`
452×	`cancel-sign-sub-inv_binary64`
432×	`associate-+l+_binary64`
377×	`*-commutative_binary64`
328×	`associate-+r+_binary64`

Counts

129 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	3095
1	332	2628
2	1213	2522
3	3061	2507
4	5023	2507

prune63.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	94	3	97

Error

Counts

97 → 3

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)
	18.4b	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3) -1) (+.f64 1 (.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) (+.f64 1 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))

Compiler

Compiled 1592 to 956 computations (39.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))
0.3b	(.f64 (.f64 b b) (cbrt.f64 4))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

rewrite147.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

38×	`pow1_binary64`
33×	`add-exp-log_binary64`
26×	`add-sqr-sqrt_binary64`
20×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 109

Calls

4 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))
7.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
6.0ms	(.f64 (.f64 b b) (cbrt.f64 4))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 2925 to 1816 computations (37.9% saved)

series71.0ms (1.2%)

Error

Counts

4 → 24

Calls

4 calls:

40.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
11.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))
10.0ms	(.f64 (.f64 b b) (cbrt.f64 4))
0.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

Compiler

Compiled 1166 to 946 computations (18.9% saved)

simplify170.0ms (3%)

Algorithm

1×	egg-herbie

Rules

366×	`*-commutative_binary64`
358×	`sqr-pow_binary64`
354×	`associate-/l*_binary64`
316×	`exp-prod_binary64`
235×	`log-prod_binary64`

Counts

133 → 101

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	133	1987
1	265	1482
2	794	1444
3	1539	1427
4	2847	1335
5	4413	1335
6	4843	1335
7	4968	1335

prune52.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	101	3	104

Error

Counts

104 → 3

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)
▶	18.4b	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3) -1) (+.f64 1 (.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) (+.f64 1 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))

Compiler

Compiled 1280 to 774 computations (39.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
17.1b	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3) -1) (+.f64 1 (.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) (+.f64 1 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))

rewrite220.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

35×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
16×	`difference-of-sqr--1_binary64`

Counts

4 → 105

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3) -1) (+.f64 1 (.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) (+.f64 1 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 7578 to 3542 computations (53.3% saved)

series1.7s (30.3%)

Error

Counts

4 → 42

Calls

4 calls:

1.5s	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3) -1) (+.f64 1 (.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) (+.f64 1 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))
71.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
18.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
17.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 17813 to 14080 computations (21% saved)

simplify196.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

439×	`associate-/l*_binary64`
404×	`times-frac_binary64`
290×	`associate-/r*_binary64`
227×	`associate-*l/_binary64`
226×	`associate-*r/_binary64`

Counts

147 → 113

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	534	14352
1	1606	13401
2	4974	13401

prune257.0ms (4.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	113	3	116

Error

Counts

116 → 3

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))) 1)
	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)
	18.4b	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3) -1) (+.f64 1 (.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) (+.f64 1 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))

Compiler

Compiled 9973 to 5743 computations (42.4% saved)

regimes757.0ms (13.3%)

Accuracy

Total 0.0b remaining (36.6%)

Threshold costs 0.0b (36.6%)

Compiler

Compiled 18360 to 12195 computations (33.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	22	31
2	22	31

end1.0ms (0%)

Compiler: Compiled 23 to 17 computations (26.1% saved)

sample781.0ms (13.8%)

Algorithm

1×

intervals

Results

480.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 155 to 99 computations (36.1% saved)

Details

analyze181.0ms (3.2%)

sample22.0ms (0.4%)

simplify43.0ms (0.8%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite103.0ms (1.8%)

series188.0ms (3.3%)

simplify149.0ms (2.6%)

prune50.0ms (0.9%)

localize14.0ms (0.3%)

rewrite182.0ms (3.2%)

series160.0ms (2.8%)

simplify102.0ms (1.8%)

prune63.0ms (1.1%)

localize13.0ms (0.2%)

rewrite147.0ms (2.6%)

series71.0ms (1.2%)

simplify170.0ms (3%)

prune52.0ms (0.9%)

localize18.0ms (0.3%)

rewrite220.0ms (3.9%)

series1.7s (30.3%)

simplify196.0ms (3.5%)

prune257.0ms (4.5%)

regimes757.0ms (13.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample781.0ms (13.8%)

Profiling