Details

sample54.0ms

Algorithm

intervals

Results

41.0ms

429×

body

valid

simplify57.0ms

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: 27.9b

localize9.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (+ (* x x) (* y y)) (* z z))
25.9b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

17.0ms	(- (+ (* x x) (* y y)) (* z z))
30.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series115.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (+ (* x x) (* y y)) (* z z))
76.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	275	450
1	1168	388
2	5001	380

prune118.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
0.0b	(+ y (/ (pow x 2) y))
7.7b	(/ (pow z 2) y)
11.6b	(/ (pow x 2) y)

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

117.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
11.0ms	(+ y (/ (pow x 2) y))
4.0ms	(/ (pow z 2) y)
4.0ms	(/ (pow x 2) y)

series100.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
28.0ms	(+ y (/ (pow x 2) y))
17.0ms	(/ (pow z 2) y)
18.0ms	(/ (pow x 2) y)

simplify46.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	419	838
1	1459	771
2	5002	759

prune319.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y))
0.0b	(+ y (* (fabs x) (/ (fabs x) y)))
0.1b	(* (fabs x) (/ (fabs x) y))
7.7b	(/ (pow z 2) y)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`times-frac`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`unpow-prod-down` `associate-r`
11×	`add-cbrt-cube` `add-log-exp`
8×	`associate-/l*`
6×	`pow1`
5×	`unpow2` `difference-of-squares` `sqr-pow`
4×	`div-exp`
3×	`associate-l` `associate-/r*`
2×	`cbrt-undiv` `flip3-+` `diff-log` `prod-exp` `sum-log` `frac-sub` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `associate--l+` `clear-num` `-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 114

Calls

4 calls:

21.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y))
2.0ms	(+ y (* (fabs x) (/ (fabs x) y)))
7.0ms	(* (fabs x) (/ (fabs x) y))
4.0ms	(/ (pow z 2) y)

series106.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (/ (pow z 2) y))
19.0ms	(+ y (* (fabs x) (/ (fabs x) y)))
19.0ms	(* (fabs x) (/ (fabs x) y))
21.0ms	(/ (pow z 2) y)

simplify69.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	452	909
1	1875	824
2	5001	817

prune314.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* (fabs x) (/ (fabs x) y)))
0.0b	(- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y)))
0.1b	(* (fabs x) (/ (fabs x) y))
0.1b	(* z (/ z y))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

2.0ms	(+ y (* (fabs x) (/ (fabs x) y)))
12.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y)))
8.0ms	(* (fabs x) (/ (fabs x) y))
7.0ms	(* z (/ z y))

series104.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ y (* (fabs x) (/ (fabs x) y)))
46.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y)))
21.0ms	(* (fabs x) (/ (fabs x) y))
18.0ms	(* z (/ z y))

simplify68.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	444	694
1	2180	622
2	5001	618

prune230.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes68.0ms

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	15	9
1	15	9

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

13627×

body

valid