Details

sample36.0ms

Algorithm

intervals

Results

25.0ms

272×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.8b	(+ (* a c) (* b d))
25.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite19.0ms

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:

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

series146.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* c c) (* d d))
36.0ms	(+ (* a c) (* b d))
83.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify134.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4451	477
3	5003	477

prune177.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 25.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* a c) (* b d))
16.0b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.2b	(sqrt (+ (* c c) (* d d)))
31.2b	(sqrt (+ (* c c) (* d d)))

rewrite30.0ms

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))
12.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
5.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a c) (* b d))
111.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
40.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify84.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (25.0ms)

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

prune288.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* a c) (* b d))
16.2b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
31.2b	(sqrt (+ (* c c) (* d d)))
31.2b	(sqrt (+ (* c c) (* d d)))

rewrite44.0ms

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:

3.0ms	(+ (* a c) (* b d))
27.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
4.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* a c) (* b d))
112.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
42.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify55.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (41.0ms)

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

prune306.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(/ 1 (+ (* c c) (* d d)))
0.8b	(+ (* a c) (* b d))
24.9b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `1-exp` `associate-*l/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 97

Calls

4 calls:

3.0ms	(+ (* c c) (* d d))
6.0ms	(/ 1 (+ (* c c) (* d d)))
3.0ms	(+ (* a c) (* b d))
22.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* c c) (* d d))
42.0ms	(/ 1 (+ (* c c) (* d d)))
35.0ms	(+ (* a c) (* b d))
85.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

simplify54.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	393	853
1	2037	749
2	5003	720

prune242.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 22.5b

regimes216.0ms

Accuracy

26.3% (2.3b remaining)

Error of 25.8b against oracle of 23.5b and baseline of 26.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	26
1	28	26
2	28	26

end0.0ms

sample998.0ms

Algorithm

intervals

Results

775.0ms

8457×

body

valid