Details

analyze548.0ms (6%)

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
0%	99.9%	0.1%	5
12.5%	68.6%	18.9%	6
18.7%	62.4%	18.9%	7
18.7%	59.3%	22%	8
28.1%	39%	32.9%	9
32.8%	34.3%	32.9%	10
32.8%	32%	35.3%	11
38.2%	20.7%	41.1%	12
41%	17.9%	41.1%	13
41%	16.6%	42.5%	14

Compiler

Compiled 41 to 24 computations (41.5% saved)

sample56.0ms (0.6%)

Algorithm

1×

intervals

Results

41.0ms	241×	body	256	valid
2.0ms	28×	body	128	nan
1.0ms	15×	body	128	valid

Compiler

Compiled 84 to 50 computations (40.5% saved)

simplify224.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

637×	`associate-/l*_binary64`
634×	`div-sub_binary64`
582×	`unsub-neg_binary64`
519×	`sub-neg_binary64`
502×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	53	50
2	139	50
3	381	48
4	735	48
5	1189	48
6	1409	48
7	1893	48
8	1853	48
9	2235	48
10	2889	48
11	3457	48
12	3639	48
13	3749	48
14	3797	48
15	3821	48
16	3871	48
17	4858	48
18	4799	48
19	4980	48
20	4834	48

prune6.0ms (0.1%)

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

37.2b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	37.3b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	37.3b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))

Status

Error

Program

▶

37.3b

(+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))))

37.3b

(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))

Compiler

Compiled 182 to 100 computations (45.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.4b	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
10.1b	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
32.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
32.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite197.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

34.4b

Rules

10×	`cbrt-div_binary64`
8×	`sqrt-prod_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

4 → 60

Calls

4 calls:

16.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
12.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2905 to 1013 computations (65.1% saved)

series261.0ms (2.8%)

Error

34.2b

Counts

4 → 31

Calls

4 calls:

83.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
81.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
22.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
18.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 3750 to 2665 computations (28.9% saved)

simplify98.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

463×	`div-sub_binary64`
270×	`distribute-rgt-in_binary64`
261×	`distribute-lft-in_binary64`
258×	`*-commutative_binary64`
253×	`exp-sum_binary64`

Counts

91 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	2067
1	524	1999
2	1430	1907
3	4233	1823
4	5473	1823

prune165.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	49	14	63
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	51	14	65

Error

33.9b

Counts

65 → 14

Alt Table

Status	Error	Program
	37.4b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))))
	44.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))))))
	54.7b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	53.2b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (/.f64 (sqrt.f64 (-.f64 (pow.f64 g 6) (pow.f64 h 6))) (sqrt.f64 (+.f64 (pow.f64 g 4) (+.f64 (pow.f64 h 4) (.f64 (.f64 h h) (*.f64 g g))))))))))
	35.7b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	49.7b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (.f64 (/.f64 -1 g) (.f64 1/2 (/.f64 (.f64 h h) a))))))
	45.7b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (/.f64 (cbrt.f64 (-.f64 (pow.f64 (neg.f64 g) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) (cbrt.f64 (.f64 (.f64 2 a) (+.f64 (.f64 g g) (-.f64 (.f64 g (-.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (*.f64 h h)))))))
	36.1b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (*.f64 2 a))))
▶	35.6b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	48.0b	(+.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 (/.f64 2 a) (/.f64 -1 g)))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	49.5b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	43.9b	(+.f64 (/.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3) (pow.f64 g 3)))) (cbrt.f64 (+.f64 (.f64 g g) (-.f64 (.f64 g (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (.f64 h h))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	43.6b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3) (pow.f64 g 3))) (cbrt.f64 (.f64 (.f64 2 a) (+.f64 (.f64 g g) (-.f64 (.f64 g (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	37.3b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 -1/2) (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a))))

Compiler

Compiled 3705 to 1713 computations (53.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 (.f64 g g) (.f64 h h))
6.4b	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
32.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
32.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite244.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

33.9b

Rules

8×	`sqrt-prod_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`

Counts

4 → 59

Calls

4 calls:

13.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2613 to 901 computations (65.5% saved)

series235.0ms (2.6%)

Error

33.2b

Counts

4 → 31

Calls

4 calls:

84.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
26.0ms	(-.f64 (.f64 g g) (.f64 h h))
23.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
18.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 3074 to 2152 computations (30% saved)

simplify113.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-l_binary64`
427×	`associate-r_binary64`
237×	`distribute-rgt-in_binary64`
232×	`distribute-lft-in_binary64`
224×	`exp-sum_binary64`

Counts

90 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	1647
1	380	1540
2	1076	1498
3	4149	1453
4	4903	1453
5	4919	1453

prune210.0ms (2.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	49	9	58
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	57	15	72

Error

33.2b

Counts

72 → 15

Alt Table

Status	Error	Program
▶	34.7b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (.f64 2 a))))
	53.2b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (/.f64 (sqrt.f64 (-.f64 (pow.f64 g 6) (pow.f64 h 6))) (sqrt.f64 (+.f64 (pow.f64 g 4) (+.f64 (pow.f64 h 4) (.f64 (.f64 h h) (*.f64 g g))))))))))
	43.7b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h))) 3))))))
	35.6b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a)) (cbrt.f64 -1/2)))
	35.7b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	49.7b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (.f64 (/.f64 -1 g) (.f64 1/2 (/.f64 (.f64 h h) a))))))
	54.8b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	48.0b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (.f64 (/.f64 -1 g) (.f64 1/2 (/.f64 (*.f64 h h) a))))))
	44.2b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (/.f64 (cbrt.f64 (-.f64 (pow.f64 (neg.f64 g) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) (cbrt.f64 (.f64 (.f64 2 a) (+.f64 (.f64 g g) (-.f64 (.f64 g (-.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (.f64 h h)))))))
	48.0b	(+.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 (/.f64 2 a) (/.f64 -1 g)))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	40.3b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	45.4b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (neg.f64 g) g))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	35.8b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))))
	49.5b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	43.9b	(+.f64 (/.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3) (pow.f64 g 3)))) (cbrt.f64 (+.f64 (.f64 g g) (-.f64 (.f64 g (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (.f64 h h))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))

Compiler

Compiled 3215 to 1534 computations (52.3% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 (.f64 g g) (.f64 h h))
2.6b	(-.f64 (.f64 g g) (.f64 h h))
32.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
32.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite269.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

33.2b

Rules

8×	`sqrt-prod_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

4 → 58

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2381 to 757 computations (68.2% saved)

series168.0ms (1.8%)

Error

33.2b

Counts

4 → 34

Calls

4 calls:

32.0ms	(-.f64 (.f64 g g) (.f64 h h))
24.0ms	(-.f64 (.f64 g g) (.f64 h h))
22.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
18.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2647 to 1809 computations (31.7% saved)

simplify123.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

769×	`unswap-sqr_binary64`
325×	`*-commutative_binary64`
235×	`times-frac_binary64`
228×	`exp-prod_binary64`
203×	`unsub-neg_binary64`

Counts

92 → 56

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	66	1253
1	140	1097
2	339	1097
3	1161	1097
4	2286	1097
5	4793	1097
6	4958	1097
7	4970	1097

prune192.0ms (2.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	56	15	71

Error

33.2b

Counts

71 → 15

Alt Table

Status	Error	Program
✓	34.7b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (.f64 2 a))))
	53.2b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (/.f64 (sqrt.f64 (-.f64 (pow.f64 g 6) (pow.f64 h 6))) (sqrt.f64 (+.f64 (pow.f64 g 4) (+.f64 (pow.f64 h 4) (.f64 (.f64 h h) (*.f64 g g))))))))))
▶	35.6b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a)) (cbrt.f64 -1/2)))
	35.7b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	49.7b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (.f64 (/.f64 -1 g) (.f64 1/2 (/.f64 (.f64 h h) a))))))
	43.5b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3)))) (cbrt.f64 (.f64 2 a))))
	48.0b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (.f64 (/.f64 -1 g) (.f64 1/2 (/.f64 (*.f64 h h) a))))))
	44.2b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (/.f64 (cbrt.f64 (-.f64 (pow.f64 (neg.f64 g) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) (cbrt.f64 (.f64 (.f64 2 a) (+.f64 (.f64 g g) (-.f64 (.f64 g (-.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (.f64 h h)))))))
	48.0b	(+.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 (/.f64 2 a) (/.f64 -1 g)))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	39.5b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (*.f64 2 a))))
	45.4b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (neg.f64 g) g))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	35.8b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))))
	49.5b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	53.9b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (*.f64 2 a))))
	43.9b	(+.f64 (/.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3) (pow.f64 g 3)))) (cbrt.f64 (+.f64 (.f64 g g) (-.f64 (.f64 g (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (.f64 h h))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))

Compiler

Compiled 2711 to 1329 computations (51% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 (.f64 g g) (.f64 h h))
6.5b	(cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a))
32.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
32.2b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite236.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

33.1b

Rules

20×	`*-un-lft-identity_binary64`
16×	`cbrt-prod_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`

Counts

4 → 70

Calls

4 calls:

8.0ms	(cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))

Compiler

Compiled 2825 to 832 computations (70.5% saved)

series221.0ms (2.4%)

Error

33.2b

Counts

4 → 31

Calls

4 calls:

71.0ms	(cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a))
25.0ms	(-.f64 (.f64 g g) (.f64 h h))
22.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
18.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2957 to 2034 computations (31.2% saved)

simplify108.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

257×	`exp-diff_binary64`
194×	`exp-prod_binary64`
191×	`unswap-sqr_binary64`
186×	`exp-sum_binary64`
170×	`associate-+r+_binary64`

Counts

101 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	172	2015
1	330	1898
2	700	1883
3	2007	1819
4	4603	1814
5	5063	1814

prune171.0ms (1.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	56	16	72

Error

33.2b

Counts

72 → 16

Alt Table

Status	Error	Program
	34.7b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (.f64 2 a))))
	35.7b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	43.7b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (cbrt.f64 (/.f64 (+.f64 g (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) a)) (cbrt.f64 -1/2)))
	49.7b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (.f64 (/.f64 -1 g) (.f64 1/2 (/.f64 (.f64 h h) a))))))
	48.0b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (.f64 (/.f64 -1 g) (.f64 1/2 (/.f64 (*.f64 h h) a))))))
	44.2b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (/.f64 (cbrt.f64 (-.f64 (pow.f64 (neg.f64 g) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) (cbrt.f64 (.f64 (.f64 2 a) (+.f64 (.f64 g g) (-.f64 (.f64 g (-.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (.f64 h h)))))))
	54.8b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g))) (.f64 (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a)) (cbrt.f64 -1/2)))
	48.0b	(+.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 (/.f64 2 a) (/.f64 -1 g)))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	39.5b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (*.f64 2 a))))
	35.8b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))))
	35.3b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (/.f64 (sqrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h))))) a))) (cbrt.f64 -1/2)))
	49.5b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (/.f64 (.f64 h h) a))) (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	45.4b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (neg.f64 g) g))) (.f64 (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a)) (cbrt.f64 -1/2)))
	53.9b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (*.f64 2 a))))
	34.8b	(+.f64 (.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))) (cbrt.f64 (/.f64 (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) a))) (cbrt.f64 -1/2)))
	43.9b	(+.f64 (/.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3) (pow.f64 g 3)))) (cbrt.f64 (+.f64 (.f64 g g) (-.f64 (.f64 g (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (.f64 h h))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))

Compiler

Compiled 2297 to 1013 computations (55.9% saved)

regimes3.1s (33.3%)

Accuracy

Total 1.6b remaining (5%)

Threshold costs 0b (0%)

Compiler

Compiled 69425 to 40132 computations (42.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	57
1	41	57
2	54	57
3	65	57
4	70	57
5	71	57
6	70	57

end1.0ms (0%)

Compiler: Compiled 39 to 23 computations (41% saved)

sample2.2s (23.9%)

Algorithm

1×

intervals

Results

1.3s	7605×	body	256	valid
97.0ms	1238×	body	128	nan
33.0ms	395×	body	128	valid

Compiler

Compiled 808 to 451 computations (44.2% saved)

Details

analyze548.0ms (6%)

sample56.0ms (0.6%)

simplify224.0ms (2.4%)

prune6.0ms (0.1%)

localize18.0ms (0.2%)

rewrite197.0ms (2.1%)

series261.0ms (2.8%)

simplify98.0ms (1.1%)

prune165.0ms (1.8%)

localize21.0ms (0.2%)

rewrite244.0ms (2.7%)

series235.0ms (2.6%)

simplify113.0ms (1.2%)

prune210.0ms (2.3%)

localize25.0ms (0.3%)

rewrite269.0ms (2.9%)

series168.0ms (1.8%)

simplify123.0ms (1.3%)

prune192.0ms (2.1%)

localize22.0ms (0.2%)

rewrite236.0ms (2.6%)

series221.0ms (2.4%)

simplify108.0ms (1.2%)

prune171.0ms (1.9%)

regimes3.1s (33.3%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample2.2s (23.9%)

Profiling