Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

269×

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: 26.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* a c) (* b d))
26.0b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite13.0ms

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:

3.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series114.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(+ (* a c) (* b d))
82.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify81.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (22.0ms)

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

prune146.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* a c) (* b d))
14.9b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.9b	(sqrt (+ (* c c) (* d d)))
30.9b	(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` `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))
9.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series216.0ms

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)))

simplify82.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (24.0ms)

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

prune281.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* b d) (* a c))
26.0b	(/ (+ (* b d) (* a c)) (+ (* c c) (* d d)))

rewrite13.0ms

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:

4.0ms	(+ (* b d) (* a c))
9.0ms	(/ (+ (* b d) (* a c)) (+ (* c c) (* d d)))

series108.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* b d) (* a c))
77.0ms	(/ (+ (* b d) (* a c)) (+ (* c c) (* d d)))

simplify82.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (22.0ms)

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

prune136.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* b d) (* a c))
14.9b	(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
30.9b	(sqrt (+ (* c c) (* d d)))
30.9b	(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` `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	(+ (* b d) (* a c))
9.0ms	(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* b d) (* a c))
107.0ms	(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))

simplify84.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2709	828
3	5001	828

prune275.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.4b

regimes203.0ms

Accuracy

0% (3.1b remaining)

Error of 26.9b against oracle of 23.8b and baseline of 26.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample492.0ms

Algorithm

intervals

Results

287.0ms

8488×

body

valid