Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

272×

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: 29.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* a c) (* b d))
28.6b	(/ (+ (* 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)))

series114.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify83.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (23.0ms)

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

prune149.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 28.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
18.6b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.4b	(sqrt (+ (* c c) (* d d)))
31.4b	(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:

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

series213.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* a c) (* b d))
106.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify81.0ms

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

prune290.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 25.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
18.7b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
31.4b	(sqrt (+ (* c c) (* d d)))
31.4b	(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)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* a c) (* b d))
78.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
35.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify75.0ms

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

prune304.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ (* a c) (* b d))
0.8b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
28.0b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`flip3-+` `flip-+`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

3 → 126

Calls

3 calls:

2.0ms	(+ (* a c) (* b d))
11.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
11.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series222.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* a c) (* b d))
131.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
54.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify58.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	480	1744
1	2237	1592
2	5003	1505

prune248.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.6b

regimes203.0ms

Accuracy

29.2% (2.2b remaining)

Error of 25.6b against oracle of 23.5b and baseline of 26.5b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	19
1	20	19

end0.0ms

sample517.0ms

Algorithm

intervals

Results

295.0ms

8457×

body

valid