Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

279×

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: 30.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.6b	(+ (* a c) (* b d))
29.4b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite42.0ms

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:

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

series105.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify84.0ms

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

prune131.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 29.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* a c) (* b d))
18.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
32.5b	(sqrt (+ (* c c) (* d d)))
32.5b	(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:

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

series206.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* a c) (* b d))
108.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(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

prune272.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 27.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* a c) (* b d))
18.5b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
32.5b	(sqrt (+ (* c c) (* d d)))
32.5b	(sqrt (+ (* c c) (* d d)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

7.0ms	(+ (* a c) (* b d))
55.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
8.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* a c) (* b d))
104.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
32.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify54.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	385	911
1	1913	826
2	5002	802

prune282.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 27.1b

localize17.0ms

Local error

Found 4 expressions with local error:

16.3b	(* (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) (/ (cbrt (+ (* a c) (* b d))) (+ (* c c) (* d d))))
19.1b	(cbrt (+ (* a c) (* b d)))
19.1b	(cbrt (+ (* a c) (* b d)))
19.1b	(cbrt (+ (* a c) (* b d)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
25×	`add-sqr-sqrt`
24×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
19×	`cbrt-prod`
16×	`add-exp-log` `frac-times` `flip3-+` `flip-+`
12×	`associate-*l/`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 102

Calls

4 calls:

104.0ms	(* (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) (/ (cbrt (+ (* a c) (* b d))) (+ (* c c) (* d d))))
4.0ms	(cbrt (+ (* a c) (* b d)))
5.0ms	(cbrt (+ (* a c) (* b d)))
5.0ms	(cbrt (+ (* a c) (* b d)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) (/ (cbrt (+ (* a c) (* b d))) (+ (* c c) (* d d))))
99.0ms	(cbrt (+ (* a c) (* b d)))
100.0ms	(cbrt (+ (* a c) (* b d)))
101.0ms	(cbrt (+ (* a c) (* b d)))

simplify65.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	619	1916
1	2341	1727
2	5002	1638

prune367.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 27.1b

regimes167.0ms

Accuracy

29.1% (2.0b remaining)

Error of 25.1b against oracle of 23.1b and baseline of 25.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	25
1	22	25

end0.0ms

sample552.0ms

Algorithm

intervals

Results

272.0ms

8493×

body

valid