Details

sample27.0ms

Algorithm

intervals

Results

14.0ms

434×

body

valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	55	7
2	101	7
3	182	7
4	335	7
5	731	7
6	1828	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
5.1b	(- (+ (* x x) (* y y)) (* z z))
25.4b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`times-frac` `associate-/l*`
3×	`pow1` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `sum-log` `flip--` `associate-/l/`
1×	`+-commutative` `sub-neg` `frac-2neg` `flip3-+` `div-sub` `prod-exp` `associate--l+` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv`

Counts

3 → 52

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
5.0ms	(- (+ (* x x) (* y y)) (* z z))
9.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series146.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
41.0ms	(- (+ (* x x) (* y y)) (* z z))
79.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	337	520
1	1492	454
2	5001	446

prune157.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 11.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
9.7b	(/ (pow x 2) y)
10.0b	(/ (pow z 2) y)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
49×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
37×	`add-cube-cbrt`
25×	`unpow-prod-down`
16×	`associate-/l*`
13×	`add-exp-log`
9×	`unpow2` `sqr-pow`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`div-exp` `associate-/r*`
5×	`difference-of-squares`
3×	`pow1`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `diff-log` `pow-exp` `clear-num` `frac-sub` `div-inv` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `flip3-+` `associate--l+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

3 → 121

Calls

3 calls:

21.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
5.0ms	(/ (pow x 2) y)
5.0ms	(/ (pow z 2) y)

series79.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
18.0ms	(/ (pow x 2) y)
19.0ms	(/ (pow z 2) y)

simplify47.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	410	766
1	1420	699
2	5002	687

prune327.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
0.2b	(* (fabs z) (/ (fabs z) y))
9.7b	(/ (pow x 2) y)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

34×	`times-frac`
33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `associate-r`
12×	`unpow-prod-down`
10×	`add-cbrt-cube`
8×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`div-exp` `unpow2` `sqr-pow`
3×	`associate-r/` `associate-l` `associate-/r`
2×	`cbrt-undiv` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow-prod-down` `pow-exp` `associate--l+` `clear-num` `sum-log` `*-commutative` `flip--` `flip-+`

Counts

3 → 97

Calls

3 calls:

11.0ms	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
6.0ms	(* (fabs z) (/ (fabs z) y))
5.0ms	(/ (pow x 2) y)

series83.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
19.0ms	(* (fabs z) (/ (fabs z) y))
19.0ms	(/ (pow x 2) y)

simplify55.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	419	684
1	1790	608
2	5002	601

prune284.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (* (fabs x) (/ (fabs x) y))) (* (fabs z) (/ (fabs z) y)))
0.2b	(* (fabs z) (/ (fabs z) y))
0.2b	(* (fabs x) (/ (fabs x) y))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`associate-r`
20×	`times-frac`
19×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
4×	`associate-*r/` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `diff-log` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `div-inv`
1×	`sub-neg` `flip3--` `flip3-+` `associate--l+` `sum-log` `flip--` `flip-+`

Counts

3 → 80

Calls

3 calls:

5.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (* (fabs z) (/ (fabs z) y)))
7.0ms	(* (fabs z) (/ (fabs z) y))
7.0ms	(* (fabs x) (/ (fabs x) y))

series78.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (* (fabs z) (/ (fabs z) y)))
19.0ms	(* (fabs z) (/ (fabs z) y))
22.0ms	(* (fabs x) (/ (fabs x) y))

simplify59.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	431	712
1	2125	619
2	5001	611

prune239.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	11
1	17	11

end0.0ms

sample744.0ms

Algorithm

intervals

Results

463.0ms

13622×

body

valid