Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
27.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

3.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series140.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* c c) (* d d))
32.0ms	(+ (* a c) (* b d))
81.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify127.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4451	477
3	5003	477

prune163.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
13.1b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.3b	(sqrt (+ (* c c) (* d d)))
31.3b	(sqrt (+ (* c c) (* d d)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
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 → 84

Calls

4 calls:

2.0ms	(+ (* a c) (* b d))
14.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* a c) (* b d))
106.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
33.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))

simplify82.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2693	828
3	5001	828

prune264.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
13.1b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.3b	(sqrt (+ (* c c) (* d d)))
31.3b	(sqrt (+ (* c c) (* d d)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
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 → 84

Calls

4 calls:

2.0ms	(+ (* a c) (* b d))
14.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* a c) (* b d))
109.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))

simplify80.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2693	828
3	5001	828

prune278.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
13.2b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
31.3b	(sqrt (+ (* c c) (* d d)))
31.3b	(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
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 → 84

Calls

4 calls:

2.0ms	(+ (* a c) (* b d))
10.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* a c) (* b d))
72.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
37.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify70.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	263	883
1	831	838
2	2301	833
3	5001	833

prune270.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 24.5b

regimes126.0ms

Accuracy

-6.8% (3.2b remaining)

Error of 26.0b against oracle of 22.8b and baseline of 25.8b

bsearch37.0ms

Steps

Iters	Range		Point
8	1.0107547841536689e+43	6.323353158608542e+47	3.9280894087478495e+46

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	18
1	21	18

end0.0ms

sample502.0ms

Algorithm

intervals

Results

297.0ms

8440×

body

valid