Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

273×

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize11.0ms

Local error

Found 2 expressions with local error:

1.0b	(+ (* a c) (* b d))
26.9b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

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

series112.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(+ (* a c) (* b d))
80.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify84.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2851	412
3	5003	412

prune130.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* a c) (* b d))
16.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.8b	(sqrt (+ (* c c) (* d d)))
30.8b	(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))
11.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(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))
107.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))

simplify81.0ms

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

prune267.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* a c) (* b d))
16.5b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
30.8b	(sqrt (+ (* c c) (* d d)))
30.8b	(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)))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* a c) (* b d))
76.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
34.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify72.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

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

prune281.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 23.2b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* a c) (* b d))
16.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.8b	(sqrt (+ (* c c) (* d d)))
30.8b	(sqrt (+ (* c c) (* d d)))

rewrite23.0ms

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:

3.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* a c) (* b d))
108.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify81.0ms

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

prune269.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 23.2b

regimes183.0ms

Accuracy

39% (1.9b remaining)

Error of 24.6b against oracle of 22.7b and baseline of 25.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	38
1	31	38
2	31	38

end0.0ms

sample506.0ms

Algorithm

intervals

Results

293.0ms

8480×

body

valid