Details

analyze439.0ms (5.7%)

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)

sample41.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	100×	body	256	valid
8.0ms	278×	pre	128	true
8.0ms	156×	body	128	valid
1.0ms	22×	body	128	nan

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify328.0ms (4.2%)

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

44.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	44.9b	(/.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)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.3b	(.f64 (.f64 3 a) c)
0.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
42.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)

rewrite139.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

42.0b

Rules

20×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `*-un-lft-identity_binary64`
9×	`pow1_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `times-frac_binary64` `associate-/l*_binary64`

Counts

4 → 77

Calls

4 calls:

11.0ms	(/.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)

series194.0ms (2.5%)

Error

0.4b

Counts

4 → 60

Calls

4 calls:

65.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
50.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
42.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
15.0ms	(.f64 (.f64 3 a) c)

Compiler

Compiled 2276 to 1674 computations (26.4% saved)

simplify93.0ms (1.2%)

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

prune78.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	97	10	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	10	108

Error

0.3b

Counts

108 → 10

Alt Table

Status	Error	Program
	44.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)) 3))
	45.0b	(/.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))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b))) (.f64 3 a))
	45.0b	(/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b))) (/.f64 3 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b)) a)))
	45.2b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) (.f64 3 a)) (/.f64 b (*.f64 3 a)))
	44.9b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3) (pow.f64 b 3)) (.f64 (.f64 3 a) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) b)) (.f64 a (*.f64 c -3)))))
	44.4b	(/.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))
	44.9b	(/.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))
▶	3.2b	(-.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))))
	5.4b	(-.f64 (.f64 -1/2 (/.f64 c b)) (.f64 3/8 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))))
	3.6b	(/.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))

Compiler

Compiled 2220 to 1294 computations (41.7% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
0.3b	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
0.4b	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
0.4b	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))

rewrite446.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

155×	`add-exp-log_binary64`
72×	`prod-exp_binary64`
60×	`div-exp_binary64`
50×	`pow-to-exp_binary64` `pow-exp_binary64`
40×	`add-sqr-sqrt_binary64`

Counts

4 → 202

Calls

4 calls:

11.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
10.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
9.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
8.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))

Compiler

Compiled 7856 to 4975 computations (36.7% saved)

series237.0ms (3.1%)

Error

0.3b

Counts

4 → 33

Calls

4 calls:

75.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
68.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
57.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
31.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))

Compiler

Compiled 3306 to 2442 computations (26.1% saved)

simplify164.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

434×	`associate-/l*_binary64`
413×	`times-frac_binary64`
354×	`log-div_binary64`
349×	`associate-l_binary64`
296×	`associate-r_binary64`

Counts

235 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	4233
1	636	3876
2	3930	3758
3	4714	3758
4	5016	3758

prune117.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	169	10	179

Error

0.3b

Counts

179 → 10

Alt Table

Status	Error	Program
	44.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)) 3))
	45.0b	(/.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))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b))) (.f64 3 a))
	45.0b	(/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b))) (/.f64 3 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b)) a)))
	45.2b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) (.f64 3 a)) (/.f64 b (*.f64 3 a)))
	44.9b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3) (pow.f64 b 3)) (.f64 (.f64 3 a) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) b)) (.f64 a (*.f64 c -3)))))
	44.4b	(/.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))
	44.9b	(/.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))
✓	3.2b	(-.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))))
	5.4b	(-.f64 (.f64 -1/2 (/.f64 c b)) (.f64 3/8 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))))
▶	3.6b	(/.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))

Compiler

Compiled 2968 to 1859 computations (37.4% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
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))
0.5b	(.f64 (.f64 a c) (*.f64 a c))
0.7b	(pow.f64 (*.f64 a c) 3)

rewrite454.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

59×	`times-frac_binary64`
46×	`pow1_binary64`
44×	`add-exp-log_binary64`
36×	`unpow-prod-down_binary64`
33×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-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))
8.0ms	(/.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)

series236.0ms (3%)

Error

0.3b

Counts

4 → 42

Calls

4 calls:

91.0ms	(/.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))
76.0ms	(/.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)

simplify203.0ms (2.6%)

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

prune236.0ms (3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	169	7	176
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	171	15	186

Error

0.2b

Counts

186 → 15

Alt Table

Status	Error	Program
	3.5b	(/.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))))) 3) a)
	44.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)) 3))
	45.0b	(/.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))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b))) (.f64 3 a))
	3.6b	(/.f64 (-.f64 (.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (.f64 -3/2 (/.f64 (.f64 a c) b))) (.f64 (+.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 (+.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 (.f64 a 3) (+.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)))))))
▶	3.4b	(-.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)))
	45.0b	(/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b))) (/.f64 3 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b)) a)))
	45.2b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) (.f64 3 a)) (/.f64 b (*.f64 3 a)))
	3.9b	(/.f64 (-.f64 (.f64 (.f64 -3/2 (.f64 a c)) (.f64 (+.f64 (.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (-.f64 (.f64 (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.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)))))) (pow.f64 b 7))) (.f64 b (+.f64 (.f64 (+.f64 (pow.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) 3) (pow.f64 (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5))) 3)) (pow.f64 b 7)) (.f64 (+.f64 (.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (-.f64 (.f64 (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.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 (pow.f64 a 4) (pow.f64 c 4))))))) (.f64 (.f64 a 3) (.f64 (+.f64 (.f64 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3)) (.f64 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3)) 81/64)) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) (-.f64 (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 729/256) (.f64 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3)) 243/128)))) (pow.f64 b 8))))
	3.6b	(.f64 1/3 (/.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))
	44.9b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3) (pow.f64 b 3)) (.f64 (.f64 3 a) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) b)) (.f64 a (*.f64 c -3)))))
	44.4b	(/.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))
	3.7b	(/.f64 (-.f64 (.f64 (.f64 -3/2 (.f64 a c)) (.f64 (.f64 (pow.f64 b 3) (pow.f64 b 5)) (pow.f64 b 7))) (.f64 b (+.f64 (.f64 (+.f64 (.f64 (.f64 9/8 (.f64 (.f64 a c) (.f64 a c))) (pow.f64 b 5)) (.f64 (pow.f64 b 3) (.f64 27/16 (pow.f64 (.f64 a c) 3)))) (pow.f64 b 7)) (.f64 (.f64 (pow.f64 b 3) (pow.f64 b 5)) (.f64 405/128 (.f64 (pow.f64 a 4) (pow.f64 c 4))))))) (.f64 (.f64 a 3) (.f64 (*.f64 (pow.f64 b 3) (pow.f64 b 5)) (pow.f64 b 8))))
	4.4b	(.f64 (/.f64 (.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)))))) (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))))))) 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))
	44.9b	(/.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))
✓	3.2b	(-.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))))

Compiler

Compiled 7046 to 4344 computations (38.3% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
0.5b	(pow.f64 (*.f64 a c) 2)
0.7b	(pow.f64 (*.f64 a c) 3)
0.9b	(pow.f64 (*.f64 a c) 4)

rewrite502.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

56×	`times-frac_binary64`
38×	`unpow-prod-down_binary64`
33×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `add-exp-log_binary64`
20×	`sqr-pow_binary64`
16×	`pow-exp_binary64`

Counts

4 → 151

Calls

4 calls:

7.0ms	(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
4.0ms	(pow.f64 (*.f64 a c) 3)
4.0ms	(pow.f64 (*.f64 a c) 4)
4.0ms	(pow.f64 (*.f64 a c) 2)

Compiler

Compiled 7392 to 4422 computations (40.2% saved)

series178.0ms (2.3%)

Error

0.2b

Counts

4 → 27

Calls

4 calls:

77.0ms	(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
32.0ms	(pow.f64 (*.f64 a c) 4)
29.0ms	(pow.f64 (*.f64 a c) 3)
28.0ms	(pow.f64 (*.f64 a c) 2)

Compiler

Compiled 3072 to 2154 computations (29.9% saved)

simplify119.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

688×	`associate-/r/_binary64`
438×	`log-prod_binary64`
400×	`cube-prod_binary64`
302×	`exp-prod_binary64`
296×	`*-commutative_binary64`

Counts

178 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	2821
1	330	2728
2	1649	2586
3	3698	2586
4	5223	2586

prune172.0ms (2.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	131	15	146

Error

0.2b

Counts

146 → 15

Alt Table

Status	Error	Program
	3.5b	(/.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))))) 3) a)
	44.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b) (.f64 3 a)) 3))
	45.0b	(/.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))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b))) (.f64 3 a))
	3.6b	(/.f64 (-.f64 (.f64 (.f64 -3/2 (/.f64 (.f64 a c) b)) (.f64 -3/2 (/.f64 (.f64 a c) b))) (.f64 (+.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 (+.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 (.f64 a 3) (+.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)))))))
	3.4b	(-.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)))
	45.0b	(/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b))) (/.f64 3 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) b)) a)))
	45.2b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) (.f64 3 a)) (/.f64 b (*.f64 3 a)))
	3.9b	(/.f64 (-.f64 (.f64 (.f64 -3/2 (.f64 a c)) (.f64 (+.f64 (.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (-.f64 (.f64 (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.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)))))) (pow.f64 b 7))) (.f64 b (+.f64 (.f64 (+.f64 (pow.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) 3) (pow.f64 (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5))) 3)) (pow.f64 b 7)) (.f64 (+.f64 (.f64 (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3))) (.f64 9/8 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (-.f64 (.f64 (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5))) (.f64 27/16 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)))) (.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 (pow.f64 a 4) (pow.f64 c 4))))))) (.f64 (.f64 a 3) (.f64 (+.f64 (.f64 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3)) (.f64 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3)) 81/64)) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) (-.f64 (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) 729/256) (.f64 (/.f64 (pow.f64 (.f64 a c) 2) (pow.f64 b 3)) 243/128)))) (pow.f64 b 8))))
	3.6b	(.f64 1/3 (/.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))
	44.9b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3) (pow.f64 b 3)) (.f64 (.f64 3 a) (+.f64 (.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) b)) (.f64 a (*.f64 c -3)))))
	44.4b	(/.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))
	3.7b	(/.f64 (-.f64 (.f64 (.f64 -3/2 (.f64 a c)) (.f64 (.f64 (pow.f64 b 3) (pow.f64 b 5)) (pow.f64 b 7))) (.f64 b (+.f64 (.f64 (+.f64 (.f64 (.f64 9/8 (.f64 (.f64 a c) (.f64 a c))) (pow.f64 b 5)) (.f64 (pow.f64 b 3) (.f64 27/16 (pow.f64 (.f64 a c) 3)))) (pow.f64 b 7)) (.f64 (.f64 (pow.f64 b 3) (pow.f64 b 5)) (.f64 405/128 (.f64 (pow.f64 a 4) (pow.f64 c 4))))))) (.f64 (.f64 a 3) (.f64 (*.f64 (pow.f64 b 3) (pow.f64 b 5)) (pow.f64 b 8))))
	4.4b	(.f64 (/.f64 (.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)))))) (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))))))) 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))
	44.9b	(/.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))
	3.2b	(-.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))))

Compiler

Compiled 3388 to 2054 computations (39.4% saved)

regimes1.2s (15.3%)

Accuracy

Total 2.6b remaining (88.3%)

Threshold costs 0b (0%)

Compiler

Compiled 26980 to 17818 computations (34% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
20×	`+-commutative_binary64`
19×	`sub-neg_binary64`
17×	`neg-mul-1_binary64` `neg-sub0_binary64`
14×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_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

end2.0ms (0%)

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

sample2.1s (26.6%)

Algorithm

1×

intervals

Results

318.0ms	3006×	body	256	valid
279.0ms	8884×	pre	128	true
252.0ms	4994×	body	128	valid
49.0ms	884×	body	128	nan

Compiler

Compiled 1201 to 775 computations (35.5% 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

analyze439.0ms (5.7%)

sample41.0ms (0.5%)

simplify328.0ms (4.2%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

rewrite139.0ms (1.8%)

series194.0ms (2.5%)

simplify93.0ms (1.2%)

prune78.0ms (1%)

localize28.0ms (0.4%)

rewrite446.0ms (5.8%)

series237.0ms (3.1%)

simplify164.0ms (2.1%)

prune117.0ms (1.5%)

localize34.0ms (0.4%)

rewrite454.0ms (5.9%)

series236.0ms (3%)

simplify203.0ms (2.6%)

prune236.0ms (3%)

localize35.0ms (0.4%)

rewrite502.0ms (6.5%)

series178.0ms (2.3%)

simplify119.0ms (1.5%)

prune172.0ms (2.2%)

regimes1.2s (15.3%)

simplify8.0ms (0.1%)

end2.0ms (0%)

sample2.1s (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