Details

sample90.0ms

Algorithm

intervals

Results

28.0ms	581×	body	80	valid
24.0ms	582×	body	80	nan

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	26	9
1	43	9
2	92	9
3	186	9
4	341	9
5	703	9
6	2167	9
7	5001	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Merged error: 0.2b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* t t) 2.0)
0.0b	(exp (/ (* t t) 2.0))
0.0b	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0)))
0.2b	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-cbrt-cube`
14×	`add-exp-log`
13×	`add-sqr-sqrt`
11×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
7×	`exp-prod` `associate-r`
6×	`times-frac` `associate-*l/`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u`
3×	`associate-/r*`
2×	`cbrt-undiv` `flip3--` `div-exp` `*-commutative` `flip--` `div-inv`
1×	`frac-2neg` `clear-num` `sqrt-prod` `rem-exp-log` `associate-/l*` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

5.0ms	(/ (* t t) 2.0)
3.0ms	(exp (/ (* t t) 2.0))
14.0ms	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0)))
9.0ms	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (* t t) 2.0)
21.0ms	(exp (/ (* t t) 2.0))
182.0ms	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0)))
113.0ms	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	463	658
1	1807	565
2	5001	558

prune302.0ms

Filtered

97 candidates to 75 candidates (77.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	8	98

Merged error: 0.0b

Counts

98 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (* t t) 2.0))
0.0b	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0)) (exp (/ (* t t) 2.0)))
0.3b	(* (- (* x 0.5) y) (sqrt z))
0.5b	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube`
17×	`add-exp-log`
16×	`add-sqr-sqrt`
15×	`associate-r`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-l/`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`exp-prod` `sqrt-prod`
5×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `times-frac` `*-commutative` `flip--`
2×	`unswap-sqr`
1×	`div-inv` `rem-exp-log`

Counts

4 → 93

Calls

4 calls:

3.0ms	(exp (/ (* t t) 2.0))
19.0ms	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0)) (exp (/ (* t t) 2.0)))
8.0ms	(* (- (* x 0.5) y) (sqrt z))
11.0ms	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0))

series445.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (/ (* t t) 2.0))
212.0ms	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0)) (exp (/ (* t t) 2.0)))
66.0ms	(* (- (* x 0.5) y) (sqrt z))
146.0ms	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	441	852
1	1914	732
2	5001	718

prune294.0ms

Filtered

105 candidates to 72 candidates (68.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	107	6	113

Merged error: 0b

Counts

113 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (exp (/ (* t t) 2.0)))
0.3b	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0)))
0.3b	(* (- (* x 0.5) y) (sqrt z))
0.3b	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1` `add-cbrt-cube`
30×	`add-exp-log`
27×	`associate-r`
22×	`sqrt-prod`
20×	`pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
18×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`expm1-log1p-u` `flip3--` `*-commutative` `flip--` `log1p-expm1-u` `add-log-exp`
2×	`unswap-sqr`

Counts

4 → 113

Calls

4 calls:

24.0ms	(* (* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (exp (/ (* t t) 2.0)))
12.0ms	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0)))
8.0ms	(* (- (* x 0.5) y) (sqrt z))
17.0ms	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series619.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* (* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (exp (/ (* t t) 2.0)))
170.0ms	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0)))
68.0ms	(* (- (* x 0.5) y) (sqrt z))
153.0ms	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify109.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	562	1337
1	2676	1071
2	5002	1039

prune334.0ms

Filtered

125 candidates to 77 candidates (61.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	125	6	131

Merged error: 0b

Counts

131 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (sqrt (* z 2.0)))
0.2b	(sqrt (sqrt (* z 2.0)))
0.3b	(* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0))))
0.4b	(* (* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0)))) (sqrt (sqrt (* z 2.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

21×	`sqrt-prod`
19×	`pow1`
17×	`add-sqr-sqrt`
14×	`associate-r`
12×	`sqrt-pow1`
11×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`pow-prod-down` `associate-*l/`
4×	`expm1-log1p-u` `pow1/2` `associate-l` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

4.0ms	(sqrt (sqrt (* z 2.0)))
4.0ms	(sqrt (sqrt (* z 2.0)))
12.0ms	(* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0))))
20.0ms	(* (* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0)))) (sqrt (sqrt (* z 2.0))))

series692.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(sqrt (sqrt (* z 2.0)))
195.0ms	(sqrt (sqrt (* z 2.0)))
180.0ms	(* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0))))
117.0ms	(* (* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0)))) (sqrt (sqrt (* z 2.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	383	753
1	1385	657
2	5001	633

prune316.0ms

Filtered

103 candidates to 73 candidates (70.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	103	6	109

Merged error: 0b

Counts

109 → 6

regimes479.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	9
1	19	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

761.0ms	17777×	body	80	valid
730.0ms	17676×	body	80	nan