Details

sample21.0ms

Algorithm

intervals

Results

8.0ms

271×

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: 27.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(+ (* a c) (* b d))
27.1b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite50.0ms

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:

8.0ms	(+ (* c c) (* d d))
10.0ms	(+ (* a c) (* b d))
31.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series130.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* c c) (* d d))
30.0ms	(+ (* a c) (* b d))
75.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify130.0ms

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

prune171.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* a c) (* b d))
16.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.1b	(sqrt (+ (* c c) (* d d)))
29.1b	(sqrt (+ (* c c) (* d d)))

rewrite59.0ms

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:

7.0ms	(+ (* a c) (* b d))
34.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
8.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* a c) (* b d))
103.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
32.0ms	(sqrt (+ (* c c) (* d d)))
33.0ms	(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

prune271.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(+ (* a c) (* b d))
0.5b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
26.8b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

8.0ms	(+ (* c c) (* d d))
7.0ms	(+ (* a c) (* b d))
24.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
33.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* c c) (* d d))
32.0ms	(+ (* a c) (* b d))
121.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
52.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify67.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	518	1821
1	2632	1656
2	5001	1569

prune275.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* a c) (* b d))
16.6b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
29.1b	(sqrt (+ (* c c) (* d d)))
29.1b	(sqrt (+ (* c c) (* d d)))

rewrite50.0ms

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:

7.0ms	(+ (* a c) (* b d))
22.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
8.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

series170.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* a c) (* b d))
72.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
33.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(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

prune264.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.8b

regimes151.0ms

Accuracy

5.2% (3.0b remaining)

Error of 26.1b against oracle of 23.2b and baseline of 26.3b

bsearch39.0ms

Steps

Iters	Range		Point
9	1.5573442921053222e+108	1.6915545349539934e+113	2.182311556201444e+112

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	18
1	21	18

end0.0ms

sample554.0ms

Algorithm

intervals

Results

273.0ms

8510×

body

valid