Details

analyze424.0ms (5.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample48.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	123×	body	256	valid
8.0ms	285×	pre	128	true
7.0ms	94×	body	128	valid
5.0ms	39×	body	512	valid
1.0ms	29×	body	128	nan

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify317.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

904×	`div-sub_binary64`
743×	`associate-/l*_binary64`
567×	`times-frac_binary64`
521×	`associate-/l/_binary64`
427×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	29	24
2	62	24
3	125	24
4	175	24
5	284	24
6	456	24
7	759	24
8	1186	24
9	1635	24
10	1913	24
11	1868	24
12	1916	24
13	1985	24
14	2029	24
15	1597	24
16	1589	24
17	1581	24
18	1585	24
19	1587	24
20	1587	24
21	1801	24
22	1901	24
23	1835	24
24	1843	24
25	1865	24
26	1877	24
27	1883	24
28	1883	24
29	1927	24
30	1983	24
31	1935	24
32	1935	24
33	1746	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

53.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	53.0b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))

Compiler

Compiled 57 to 39 computations (31.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.3b	(.f64 (.f64 3 a) c)
27.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)

rewrite357.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Error

50.1b

Rules

20×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

4 → 77

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

Compiler

Compiled 1868 to 1088 computations (41.8% saved)

series190.0ms (2.6%)

Error

0.2b

Counts

4 → 60

Calls

4 calls:

62.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
54.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
38.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
13.0ms	(.f64 (.f64 3 a) c)

Compiler

Compiled 2276 to 1674 computations (26.4% saved)

simplify94.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

701×	`associate-/l*_binary64`
244×	`distribute-rgt-in_binary64`
224×	`distribute-rgt-neg-in_binary64`
214×	`distribute-lft-in_binary64`
205×	`distribute-lft-neg-in_binary64`

Counts

137 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	220	3206
1	575	2948
2	2075	2923
3	5261	2923

prune75.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	98	9	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	9	108

Error

0.1b

Counts

108 → 9

Alt Table

Status	Error	Program
	52.9b	(/.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 b b)) (.f64 (.f64 3 a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))))
	53.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a))))
	53.3b	(.f64 (/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (sqrt.f64 b)) 3) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))) (sqrt.f64 b)) a))
	53.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)) 3))
	53.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b))) 3) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b)) a))
	1.7b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.f64 405/128 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))))) (*.f64 3 a))
	52.6b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))))) (.f64 3 a))
▶	1.2b	(-.f64 (-.f64 (.f64 -1/2 (/.f64 c b)) (+.f64 (.f64 3/8 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))))) (.f64 135/128 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))))
	53.0b	(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) 3) (pow.f64 b 3)) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) b)) (.f64 a (.f64 c -3)))) (.f64 3 a))

Compiler

Compiled 2220 to 1278 computations (42.4% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
0.3b	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
0.4b	(.f64 (.f64 a a) (pow.f64 c 3))
0.4b	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))

rewrite436.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

109×	`add-exp-log_binary64`
54×	`prod-exp_binary64`
42×	`add-sqr-sqrt_binary64`
30×	`div-exp_binary64`
29×	`unpow-prod-down_binary64`

Counts

4 → 178

Calls

4 calls:

11.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
10.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
8.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
8.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))

Compiler

Compiled 7318 to 4605 computations (37.1% saved)

series178.0ms (2.4%)

Error

0.1b

Counts

4 → 30

Calls

4 calls:

61.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
53.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
31.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
27.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

Compiler

Compiled 3018 to 2244 computations (25.6% saved)

simplify147.0ms (2%)

Algorithm

1×	egg-herbie

Rules

615×	`log-prod_binary64`
398×	`associate-l_binary64`
325×	`associate-r_binary64`
324×	`times-frac_binary64`
316×	`associate-/l*_binary64`

Counts

208 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	3437
1	572	3061
2	3383	2982
3	4657	2982
4	5443	2982

prune115.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	156	9	165

Error

0.1b

Counts

165 → 9

Alt Table

Status	Error	Program
	52.9b	(/.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 b b)) (.f64 (.f64 3 a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))))
	53.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a))))
	53.3b	(.f64 (/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (sqrt.f64 b)) 3) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))) (sqrt.f64 b)) a))
	53.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)) 3))
	53.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b))) 3) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b)) a))
▶	1.7b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.f64 405/128 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))))) (*.f64 3 a))
	52.6b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))))) (.f64 3 a))
✓	1.2b	(-.f64 (-.f64 (.f64 -1/2 (/.f64 c b)) (+.f64 (.f64 3/8 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))))) (.f64 135/128 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))))
	53.0b	(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) 3) (pow.f64 b 3)) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) b)) (.f64 a (.f64 c -3)))) (.f64 3 a))

Compiler

Compiled 3060 to 1894 computations (38.1% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.f64 405/128 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))))) (*.f64 3 a))
0.4b	(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
0.5b	(.f64 (.f64 a c) (*.f64 a c))
0.7b	(pow.f64 (*.f64 a c) 3)

rewrite397.0ms (5.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

59×	`times-frac_binary64`
46×	`pow1_binary64`
44×	`add-exp-log_binary64`
36×	`unpow-prod-down_binary64`
33×	`*-un-lft-identity_binary64`

Counts

4 → 179

Calls

4 calls:

28.0ms	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.f64 405/128 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))))) (*.f64 3 a))
7.0ms	(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
7.0ms	(.f64 (.f64 a c) (*.f64 a c))
4.0ms	(pow.f64 (*.f64 a c) 3)

Compiler

Compiled 10408 to 6149 computations (40.9% saved)

series225.0ms (3.1%)

Error

0.1b

Counts

4 → 42

Calls

4 calls:

89.0ms	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.f64 405/128 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))))) (*.f64 3 a))
67.0ms	(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
30.0ms	(pow.f64 (*.f64 a c) 3)
29.0ms	(.f64 (.f64 a c) (*.f64 a c))

Compiler

Compiled 3236 to 2344 computations (27.6% saved)

simplify207.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

348×	`associate-/l*_binary64`
295×	`associate-r_binary64`
280×	`times-frac_binary64`
262×	`associate-l_binary64`
207×	`log-prod_binary64`

Counts

221 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	6505
1	756	5641
2	3977	5495
3	4826	5495
4	5022	5495

prune206.0ms (2.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	171	5	176
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	172	13	185

Error

0.1b

Counts

185 → 13

Alt Table

Status	Error	Program
	52.9b	(/.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 b b)) (.f64 (.f64 3 a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))))
	53.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a))))
	53.3b	(.f64 (/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (sqrt.f64 b)) 3) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))) (sqrt.f64 b)) a))
	53.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)) 3))
	53.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b))) 3) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b)) a))
	2.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7))))) (*.f64 a 3)) 3))
	2.6b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.f64 405/128 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)))))) (cbrt.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.f64 405/128 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))))))) (/.f64 3 (/.f64 (cbrt.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (*.f64 a c) 4) (pow.f64 b 7)))))) a)))
	52.6b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))))) (.f64 3 a))
✓	1.2b	(-.f64 (-.f64 (.f64 -1/2 (/.f64 c b)) (+.f64 (.f64 3/8 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))))) (.f64 135/128 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))))
	1.7b	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7))))) a)))
	53.0b	(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) 3) (pow.f64 b 3)) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) b)) (.f64 a (.f64 c -3)))) (.f64 3 a))
▶	1.5b	(-.f64 (.f64 -1/2 (/.f64 (/.f64 (.f64 a c) b) a)) (/.f64 (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7)))) (*.f64 a 3)))
	2.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7))))) (.f64 a 3))) (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7))))) (.f64 a 3)))) (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7))))) (*.f64 a 3))))

Compiler

Compiled 6390 to 3932 computations (38.5% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7)))) (*.f64 a 3))
0.5b	(pow.f64 (*.f64 a c) 2)
0.7b	(pow.f64 (*.f64 a c) 3)
0.9b	(pow.f64 (*.f64 a c) 4)

rewrite260.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

18×	`add-exp-log_binary64`
13×	`pow1_binary64`
12×	`add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

4 → 83

Calls

4 calls:

23.0ms	(/.f64 (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7)))) (*.f64 a 3))
4.0ms	(pow.f64 (*.f64 a c) 4)
4.0ms	(pow.f64 (*.f64 a c) 2)
4.0ms	(pow.f64 (*.f64 a c) 3)

Compiler

Compiled 4926 to 3042 computations (38.2% saved)

series250.0ms (3.4%)

Error

0.1b

Counts

4 → 35

Calls

4 calls:

150.0ms	(/.f64 (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7)))) (*.f64 a 3))
29.0ms	(pow.f64 (*.f64 a c) 4)
28.0ms	(pow.f64 (*.f64 a c) 3)
27.0ms	(pow.f64 (*.f64 a c) 2)

Compiler

Compiled 3222 to 2286 computations (29.1% saved)

simplify94.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
423×	`distribute-rgt-in_binary64`
195×	`unswap-sqr_binary64`
164×	`associate-l_binary64`
158×	`associate-r_binary64`

Counts

118 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	3292
1	450	2896
2	1874	2861
3	5162	2861

prune106.0ms (1.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	87	13	100

Error

0.1b

Counts

100 → 13

Alt Table

Status	Error	Program
	52.9b	(/.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 b b)) (.f64 (.f64 3 a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))))
	53.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a))))
	53.3b	(.f64 (/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (sqrt.f64 b)) 3) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))) (sqrt.f64 b)) a))
	53.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)) 3))
	53.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b))) 3) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b)) a))
	2.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7))))) (*.f64 a 3)) 3))
	2.6b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.f64 405/128 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)))))) (cbrt.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.f64 405/128 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))))))) (/.f64 3 (/.f64 (cbrt.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (*.f64 a c) 4) (pow.f64 b 7)))))) a)))
	52.6b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))))) (.f64 3 a))
	1.2b	(-.f64 (-.f64 (.f64 -1/2 (/.f64 c b)) (+.f64 (.f64 3/8 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))))) (.f64 135/128 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))))
	1.7b	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7))))) a)))
	53.0b	(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) 3) (pow.f64 b 3)) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) b)) (.f64 a (.f64 c -3)))) (.f64 3 a))
	1.5b	(-.f64 (.f64 -1/2 (/.f64 (/.f64 (.f64 a c) b) a)) (/.f64 (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7)))) (*.f64 a 3)))
	2.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7))))) (.f64 a 3))) (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7))))) (.f64 a 3)))) (cbrt.f64 (/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (+.f64 (+.f64 (.f64 9/8 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 27/16)) (.f64 405/128 (/.f64 (pow.f64 (.f64 a c) 4) (pow.f64 b 7))))) (*.f64 a 3))))

Compiler

Compiled 2792 to 1731 computations (38% saved)

regimes1.2s (15.8%)

Accuracy

Total 1.2b remaining (87.1%)

Threshold costs 0b (0%)

Compiler

Compiled 26696 to 17647 computations (33.9% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
20×	`+-commutative_binary64`
19×	`sub-neg_binary64`
17×	`neg-sub0_binary64`
17×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	67
1	50	67
2	65	67
3	93	67
4	117	67
5	146	67
6	170	67
7	184	67
8	190	67
9	191	67
10	188	67

end1.0ms (0%)

Compiler: Compiled 48 to 35 computations (27.1% saved)

sample2.0s (26.6%)

Algorithm

1×

intervals

Results

364.0ms	3823×	body	256	valid
249.0ms	8780×	pre	128	true
210.0ms	1469×	body	512	valid
129.0ms	2708×	body	128	valid
48.0ms	780×	body	128	nan

Compiler

Compiled 873 to 569 computations (34.8% saved)

Iter	Nodes	Cost
0	34	67
1	50	67
2	65	67
3	93	67
4	117	67
5	146	67
6	170	67
7	184	67
8	190	67
9	191	67
10	188	67

Iter	Nodes	Cost
0	34	67
1	50	67
2	65	67
3	93	67
4	117	67
5	146	67
6	170	67
7	184	67
8	190	67
9	191	67
10	188	67

Details

analyze424.0ms (5.8%)

sample48.0ms (0.7%)

simplify317.0ms (4.3%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite357.0ms (4.8%)

series190.0ms (2.6%)

simplify94.0ms (1.3%)

prune75.0ms (1%)

localize30.0ms (0.4%)

rewrite436.0ms (5.9%)

series178.0ms (2.4%)

simplify147.0ms (2%)

prune115.0ms (1.6%)

localize32.0ms (0.4%)

rewrite397.0ms (5.4%)

series225.0ms (3.1%)

simplify207.0ms (2.8%)

prune206.0ms (2.8%)

localize32.0ms (0.4%)

rewrite260.0ms (3.5%)

series250.0ms (3.4%)

simplify94.0ms (1.3%)

prune106.0ms (1.4%)

regimes1.2s (15.8%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample2.0s (26.6%)

Profiling

Iter	Nodes	Cost
0	34	67
1	50	67
2	65	67
3	93	67
4	117	67
5	146	67
6	170	67
7	184	67
8	190	67
9	191	67
10	188	67