Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

264×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 27.6b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* a c) (* b d))
27.1b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
80×	`distribute-lft-out`
72×	`associate-l`
56×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`swap-sqr`
8×	`associate-/r*`
7×	`associate-/l*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 102

Calls

2 calls:

13.0ms	(+ (* a c) (* b d))
38.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series125.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ (* a c) (* b d))
89.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify109.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	231	977
1	831	940
2	2778	940
3	5001	939

prune113.0ms

Filtered

108 candidates to 38 candidates (64.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 26.9b

Counts

109 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* a c) (* b d))
17.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
27.1b	(sqrt (+ (* c c) (* d d)))
27.1b	(sqrt (+ (* c c) (* d d)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

258×	`*-un-lft-identity`
102×	`distribute-lft-out`
92×	`associate-l`
80×	`sqrt-prod`
77×	`times-frac`
36×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
20×	`swap-sqr`
11×	`associate-/r*`
7×	`associate-/l*`
6×	`pow1` `add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 166

Calls

4 calls:

13.0ms	(+ (* a c) (* b d))
36.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
16.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* a c) (* b d))
117.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
43.0ms	(sqrt (+ (* c c) (* d d)))

simplify107.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	270	1685
1	837	1616
2	2566	1614
3	5002	1609

prune212.0ms

Filtered

178 candidates to 74 candidates (58.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	173	5	178
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	177	9	186

Merged error: 23.2b

Counts

186 → 9

localize11.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* a c) (* b d))
27.1b	(/ (* 1 (+ (* a c) (* b d))) (+ (* c c) (* d d)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

352×	`*-un-lft-identity`
139×	`associate-l`
136×	`times-frac`
130×	`distribute-lft-out`
74×	`add-sqr-sqrt`
63×	`associate-r`
47×	`add-cube-cbrt`
36×	`swap-sqr`
18×	`unswap-sqr`
17×	`associate-/l*`
9×	`add-exp-log` `*-commutative`
8×	`associate-/r*`
7×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`flip3-+` `div-exp` `flip-+`
2×	`pow1` `cbrt-undiv` `associate-*r/` `prod-exp` `associate-/r/` `associate-/l/`
1×	`+-commutative` `frac-2neg` `1-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv`

Counts

2 → 195

Calls

2 calls:

13.0ms	(+ (* a c) (* b d))
41.0ms	(/ (* 1 (+ (* a c) (* b d))) (+ (* c c) (* d d)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (* a c) (* b d))
89.0ms	(/ (* 1 (+ (* a c) (* b d))) (+ (* c c) (* d d)))

simplify76.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	458	2136
1	1982	2017
2	5001	1972

prune121.0ms

Filtered

201 candidates to 47 candidates (76.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	202	8	210

Merged error: 23.2b

Counts

210 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

27.1b	(sqrt (+ (* c c) (* d d)))
27.1b	(sqrt (+ (* c c) (* d d)))
27.1b	(sqrt (+ (* c c) (* d d)))
27.1b	(sqrt (+ (* c c) (* d d)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
32×	`sqrt-prod`
20×	`distribute-lft-out`
16×	`associate-l`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `sqrt-div` `swap-sqr`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 80

Calls

4 calls:

16.0ms	(sqrt (+ (* c c) (* d d)))
17.0ms	(sqrt (+ (* c c) (* d d)))
19.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))
45.0ms	(sqrt (+ (* c c) (* d d)))

simplify155.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	86	476
1	202	464
2	465	464
3	1174	464
4	3616	464
5	5001	464

prune198.0ms

Filtered

92 candidates to 60 candidates (34.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	92	8	100

Merged error: 23.2b

Counts

100 → 8

regimes140.0ms

Accuracy

2.2% (2.9b remaining)

Error of 26.4b against oracle of 23.5b and baseline of 26.5b

bsearch43.0ms

Steps

Iters	Range		Point
8	3.52254630266601e+87	1.163506504696633e+91	1.0707482603066898e+91

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	18
1	21	18

end0.0ms

sample550.0ms

Algorithm

intervals

Results

323.0ms

8440×

body

valid