Details

analyze212.0ms (4.1%)

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%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

705×	`unsub-neg_binary64`
556×	`cancel-sign-sub-inv_binary64`
344×	`+-commutative_binary64`
342×	`distribute-rgt-in_binary64`
317×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	43
1	55	43
2	150	43
3	389	43
4	1083	43
5	2233	43
6	4336	43
7	4724	43
8	4930	43

prune3.0ms (0.1%)

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 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)

Compiler

Compiled 93 to 57 computations (38.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.2b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite179.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`pow1_binary64` `add-exp-log_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
14×	`add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64` `associate-r_binary64`
6×	`pow-prod-down_binary64` `prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `cancel-sign-sub-inv_binary64`
4×	`associate-*r/_binary64`

Counts

4 → 87

Calls

4 calls:

11.0ms	(.f64 (.f64 b b) (+.f64 3 a))
9.0ms	(.f64 (.f64 a a) (-.f64 1 a))
8.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 3141 to 1575 computations (49.9% saved)

series227.0ms (4.4%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

87.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
53.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
23.0ms	(.f64 (.f64 b b) (+.f64 3 a))
17.0ms	(.f64 (.f64 a a) (-.f64 1 a))

Compiler

Compiled 3039 to 2229 computations (26.7% saved)

simplify146.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-+l+_binary64`
345×	`associate-+r+_binary64`
267×	`associate-l_binary64`
226×	`exp-prod_binary64`
217×	`associate-r_binary64` `+-commutative_binary64`

Counts

141 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	215	2929
1	585	2614
2	1868	2518
3	4258	2514
4	4953	2514
5	4946	2514

prune114.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	3	117

Error

0.0b

Counts

117 → 3

Alt Table

Status	Error	Program
	11.0b	(-.f64 (+.f64 (.f64 (pow.f64 a 3) (+.f64 a -4)) (.f64 (.f64 a a) (+.f64 (.f64 2 (*.f64 b b)) 4))) 1)
	14.6b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	0.0b	(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a))))) (+.f64 (pow.f64 a 4) (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3)))))) 1)

Compiler

Compiled 2434 to 1304 computations (46.4% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 a a) (pow.f64 a 3))
0.0b	(.f64 a (+.f64 4 (.f64 2 a)))
0.0b	(+.f64 (pow.f64 a 4) (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))))
2.5b	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))

rewrite253.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

36×	`cancel-sign-sub-inv_binary64`
26×	`associate-+r+_binary64`
22×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
15×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`

Counts

4 → 111

Calls

4 calls:

8.0ms	(+.f64 (pow.f64 a 4) (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))))
7.0ms	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))
7.0ms	(-.f64 (*.f64 a a) (pow.f64 a 3))
5.0ms	(.f64 a (+.f64 4 (.f64 2 a)))

Compiler

Compiled 4092 to 2777 computations (32.1% saved)

series137.0ms (2.6%)

Error

0.0b

Counts

4 → 31

Calls

4 calls:

43.0ms	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))
28.0ms	(+.f64 (pow.f64 a 4) (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))))
17.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
17.0ms	(-.f64 (*.f64 a a) (pow.f64 a 3))

Compiler

Compiled 2126 to 1620 computations (23.8% saved)

simplify119.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

656×	`exp-prod_binary64`
457×	`cancel-sign-sub-inv_binary64`
372×	`associate-l_binary64`
331×	`associate-r_binary64`
285×	`distribute-rgt-out_binary64`

Counts

142 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	2348
1	540	2120
2	2420	2105
3	4565	2089
4	5072	2089

prune160.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	120	4	124

Error

0.0b

Counts

124 → 4

Alt Table

Status	Error	Program
	11.0b	(-.f64 (+.f64 (.f64 (pow.f64 a 3) (+.f64 a -4)) (.f64 (.f64 a a) (+.f64 (.f64 2 (*.f64 b b)) 4))) 1)
	14.6b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
✓	0.0b	(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a))))) (+.f64 (pow.f64 a 4) (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3)))))) 1)
▶	0.1b	(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a))))) (.f64 (sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))) (sqrt.f64 (+.f64 (.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3))) (pow.f64 a 4)))))) 1)

Compiler

Compiled 3215 to 2206 computations (31.4% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))) (sqrt.f64 (+.f64 (.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))))
2.5b	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))
26.9b	(sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4)))
26.9b	(sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4)))

rewrite339.0ms (6.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

34×	`add-sqr-sqrt_binary64`
26×	`pow1_binary64`
24×	`sqrt-prod_binary64`
16×	`sqrt-div_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 112

Calls

4 calls:

28.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))) (sqrt.f64 (+.f64 (.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))))
11.0ms	(sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4)))
11.0ms	(sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4)))
10.0ms	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))

Compiler

Compiled 6246 to 4271 computations (31.6% saved)

series154.0ms (3%)

Error

0.0b

Counts

4 → 29

Calls

4 calls:

49.0ms	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))
29.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))) (sqrt.f64 (+.f64 (.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))))
22.0ms	(sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4)))
20.0ms	(sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4)))

Compiler

Compiled 2564 to 1912 computations (25.4% saved)

simplify109.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

970×	`distribute-rgt-in_binary64`
961×	`distribute-lft-in_binary64`
201×	`associate-l_binary64`
180×	`associate-r_binary64`
110×	`cancel-sign-sub-inv_binary64`

Counts

141 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	4147
1	382	3626
2	1339	3452
3	5465	3452

prune187.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	120	4	124

Error

0.0b

Counts

124 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a))))) (.f64 (sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))) (.f64 a (+.f64 a -2))))) 1)
	14.6b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
	1.2b	(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a))))) (*.f64 (pow.f64 a 3) (-.f64 a 4)))) 1)
✓	0.0b	(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a))))) (+.f64 (pow.f64 a 4) (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3)))))) 1)

Compiler

Compiled 4228 to 2893 computations (31.6% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))
0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))) (.f64 a (+.f64 a -2)))
2.5b	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))
26.9b	(sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4)))

rewrite314.0ms (6.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

26×	`associate-+l+_binary64`
24×	`cancel-sign-sub-inv_binary64`
18×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64`

Counts

4 → 108

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))) (.f64 a (+.f64 a -2)))
14.0ms	(+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))
11.0ms	(sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4)))
7.0ms	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))

Compiler

Compiled 5253 to 3591 computations (31.6% saved)

series158.0ms (3%)

Error

0.0b

Counts

4 → 32

Calls

4 calls:

46.0ms	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))
31.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))) (.f64 a (+.f64 a -2)))
29.0ms	(+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))
17.0ms	(sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4)))

Compiler

Compiled 2437 to 1843 computations (24.4% saved)

simplify178.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

821×	`exp-prod_binary64`
414×	`associate-r_binary64`
411×	`associate-l_binary64`
361×	`cancel-sign-sub-inv_binary64`
329×	`unswap-sqr_binary64`

Counts

140 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3727
1	619	3373
2	2608	3346
3	4418	3346
4	4950	3346
5	5079	3346

prune177.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	117	5	122

Error

0.0b

Counts

122 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a))))) (.f64 (sqrt.f64 (+.f64 (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3))) (pow.f64 a 4))) (.f64 a (+.f64 a -2))))) 1)
	0.1b	(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a))))) (.f64 (.f64 a (+.f64 a -2)) (*.f64 a (+.f64 a -2))))) 1)
	14.6b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
	1.2b	(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a))))) (*.f64 (pow.f64 a 3) (-.f64 a 4)))) 1)
	0.0b	(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a))))) (+.f64 (pow.f64 a 4) (.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3)))))) 1)

Compiler

Compiled 3569 to 2477 computations (30.6% saved)

regimes947.0ms (18.3%)

Accuracy

Total 0.0b remaining (60.2%)

Threshold costs 0.0b (60.2%)

Compiler

Compiled 21583 to 14696 computations (31.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
5×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	49
1	40	49
2	44	49
3	46	49
4	47	49
5	45	49

end1.0ms (0%)

Compiler: Compiled 35 to 26 computations (25.7% saved)

sample874.0ms (16.9%)

Algorithm

1×

intervals

Results

471.0ms	8000×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 240 to 171 computations (28.8% saved)

Details

analyze212.0ms (4.1%)

sample24.0ms (0.5%)

simplify80.0ms (1.5%)

prune3.0ms (0.1%)

localize15.0ms (0.3%)

rewrite179.0ms (3.5%)

series227.0ms (4.4%)

simplify146.0ms (2.8%)

prune114.0ms (2.2%)

localize19.0ms (0.4%)

rewrite253.0ms (4.9%)

series137.0ms (2.6%)

simplify119.0ms (2.3%)

prune160.0ms (3.1%)

localize23.0ms (0.4%)

rewrite339.0ms (6.6%)

series154.0ms (3%)

simplify109.0ms (2.1%)

prune187.0ms (3.6%)

localize28.0ms (0.5%)

rewrite314.0ms (6.1%)

series158.0ms (3%)

simplify178.0ms (3.4%)

prune177.0ms (3.4%)

regimes947.0ms (18.3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample874.0ms (16.9%)

Profiling