Details

sample31.0ms

Algorithm

intervals

Results

20.0ms

275×

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: 26.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(+ (* a c) (* b d))
26.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite17.0ms

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:

2.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* a c) (* b d))
10.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series138.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* c c) (* d d))
32.0ms	(+ (* a c) (* b d))
78.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify129.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (29.0ms)

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

prune170.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* a c) (* b d))
17.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.7b	(sqrt (+ (* c c) (* d d)))
28.7b	(sqrt (+ (* c c) (* d d)))

rewrite25.0ms

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))))
6.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* a c) (* b d))
106.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify80.0ms

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

prune276.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(+ (* a c) (* b d))
0.7b	(/ 1 (+ (* c c) (* d d)))
26.0b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

rewrite36.0ms

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:

2.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* a c) (* b d))
5.0ms	(/ 1 (+ (* c c) (* d d)))
23.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* c c) (* d d))
38.0ms	(+ (* a c) (* b d))
37.0ms	(/ 1 (+ (* c c) (* d d)))
81.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

simplify55.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (46.0ms)

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

prune233.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 23.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (/ 1 (sqrt (+ (* c c) (* d d)))))
17.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.7b	(sqrt (+ (* c c) (* d d)))
28.7b	(sqrt (+ (* c c) (* d d)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative`

Counts

4 → 161

Calls

4 calls:

43.0ms	(* (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (/ 1 (sqrt (+ (* c c) (* d 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)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (/ 1 (sqrt (+ (* c c) (* d d)))))
110.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify75.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	578	2493
1	2760	2257
2	5001	2142

prune413.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.8b

regimes152.0ms

Accuracy

0% (2.9b remaining)

Error of 26.0b against oracle of 23.1b and baseline of 26.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample857.0ms

Algorithm

intervals

Results

630.0ms

8450×

body

valid