Details

analyze246.0ms

Algorithm

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
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
10.1%	64.7%	25.1%	8
17.2%	32.8%	50.1%	9
23%	26.9%	50.1%	10
26.8%	23.1%	50.1%	11
31.6%	18.3%	50.1%	12
35.2%	14.7%	50.1%	13
37.5%	12.4%	50.1%	14

sample19.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify173.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	4932	18
1	4932	18

prune2.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 0.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
0.0b	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
0.1b	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
0.2b	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-log-exp_binary64`
19×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`log-prod_binary64`
10×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`associate--r+_binary64` `diff-log_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`associate-r_binary64` `associate-l_binary64` `sum-log_binary64`
3×	`sub-neg_binary64` `distribute-lft-out_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-+l-_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `associate-+l+_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

8.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
4.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
5.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
7.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

series210.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
34.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
42.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
86.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

simplify93.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5489	1613

prune76.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 0.0b

Counts

91 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2))
0.3b	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`log-prod_binary64` `associate-+r+_binary64` `cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
10×	`associate-*l/_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64`
4×	`frac-add_binary64` `associate-l_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`distribute-lft-out_binary64` `pow1/3_binary64`
1×	`associate-r_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 71

Calls

4 calls:

8.0ms	(.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2))
11.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series809.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2))
401.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
81.0ms	(cbrt.f64 y)
85.0ms	(cbrt.f64 y)

simplify117.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4938	1187
1	4938	1187

prune88.0ms

Filtered

69 candidates to 83 candidates (-20.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	5	0	5
Picked	0	1	1
Done	0	1	1
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 (+.f64 y 1/2) (+.f64 (.f64 2/3 (log.f64 y)) (log.f64 (cbrt.f64 (sqrt.f64 y))))) (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 y))) (+.f64 y 1/2)))
0.4b	(*.f64 2/3 (log.f64 y))
0.6b	(cbrt.f64 (sqrt.f64 y))
0.6b	(cbrt.f64 (sqrt.f64 y))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

21×	`flip3-+_binary64` `flip-+_binary64`
20×	`associate-*r/_binary64`
16×	`frac-add_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
8×	`frac-times_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `log-prod_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`associate-r_binary64` `associate-*l/_binary64`
3×	`associate-l_binary64`
2×	`pow1/3_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

12.0ms	(+.f64 (.f64 (+.f64 y 1/2) (+.f64 (.f64 2/3 (log.f64 y)) (log.f64 (cbrt.f64 (sqrt.f64 y))))) (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 y))) (+.f64 y 1/2)))
5.0ms	(*.f64 2/3 (log.f64 y))
2.0ms	(cbrt.f64 (sqrt.f64 y))
2.0ms	(cbrt.f64 (sqrt.f64 y))

series545.0ms

Counts

4 → 12

Calls

4 calls:

369.0ms	(+.f64 (.f64 (+.f64 y 1/2) (+.f64 (.f64 2/3 (log.f64 y)) (log.f64 (cbrt.f64 (sqrt.f64 y))))) (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 y))) (+.f64 y 1/2)))
54.0ms	(*.f64 2/3 (log.f64 y))
59.0ms	(cbrt.f64 (sqrt.f64 y))
61.0ms	(cbrt.f64 (sqrt.f64 y))

simplify97.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4949	3034
1	4949	3034

prune126.0ms

Filtered

77 candidates to 96 candidates (-24.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	96	5	101

Merged error: 0.0b

Counts

101 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1)))
0.1b	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 (*.f64 y 3) 3/2))) y)
0.3b	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 (*.f64 y 3) 3/2))
0.6b	(cbrt.f64 (neg.f64 y))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1_binary64`
11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
10×	`cbrt-prod_binary64`
9×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
6×	`log-pow_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-down_binary64` `pow1/3_binary64`
3×	`associate-r_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
2×	`flip3-+_binary64` `rem-log-exp_binary64` `associate-*r/_binary64` `prod-exp_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `log-prod_binary64` `associate-+l+_binary64` `neg-mul-1_binary64` `distribute-lft-in_binary64` `associate-+l-_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 71

Calls

4 calls:

5.0ms	(log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1)))
5.0ms	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 (*.f64 y 3) 3/2))) y)
13.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 (*.f64 y 3) 3/2))
2.0ms	(cbrt.f64 (neg.f64 y))

series749.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1)))
137.0ms	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 (*.f64 y 3) 3/2))) y)
313.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 (*.f64 y 3) 3/2))
89.0ms	(cbrt.f64 (neg.f64 y))

simplify115.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4868	1662
1	4868	1662

prune75.0ms

Filtered

57 candidates to 83 candidates (-45.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	82	6	88

Merged error: 0b

Counts

88 → 6

regimes91.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	64	18
1	64	18

end0.0ms

sample549.0ms

Algorithm

intervals

Results

365.0ms	7998×	body	80	valid
1.0ms	22×	body	80	invalid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid

Details

analyze246.0ms

sample19.0ms

simplify173.0ms

prune2.0ms

localize12.0ms

rewrite25.0ms

series210.0ms

simplify93.0ms

prune76.0ms

localize15.0ms

rewrite24.0ms

series809.0ms

simplify117.0ms

prune88.0ms

localize19.0ms

rewrite27.0ms

series545.0ms

simplify97.0ms

prune126.0ms

localize16.0ms

rewrite26.0ms

series749.0ms

simplify115.0ms

prune75.0ms

regimes91.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample549.0ms

Profiling