Details

sample26.0ms

Algorithm

intervals

Results

14.0ms

450×

body

valid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
4.9b	(- (+ (* x x) (* y y)) (* z z))
27.3b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite50.0ms

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:

2.0ms	(+ (* x x) (* y y))
16.0ms	(- (+ (* x x) (* y y)) (* z z))
30.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series151.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* x x) (* y y))
43.0ms	(- (+ (* x x) (* y y)) (* z z))
81.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (32.0ms)

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

prune150.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.8b

localize10.0ms

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))
10.3b	(/ (pow x 2) y)
10.4b	(/ (pow z 2) y)

rewrite144.0ms

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:

120.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
11.0ms	(+ y (/ (pow x 2) y))
4.0ms	(/ (pow x 2) y)
4.0ms	(/ (pow z 2) y)

series108.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
27.0ms	(+ y (/ (pow x 2) y))
18.0ms	(/ (pow x 2) y)
21.0ms	(/ (pow z 2) y)

simplify45.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (34.0ms)

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

prune331.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
0.0b	(+ y (/ (pow x 2) y))
0.2b	(* z (/ z y))
10.3b	(/ (pow x 2) y)

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `times-frac`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-r`
12×	`unpow-prod-down`
11×	`add-cbrt-cube` `add-log-exp`
8×	`associate-/l*`
6×	`pow1`
4×	`div-exp` `unpow2` `sqr-pow`
3×	`associate-r/` `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` `pow-prod-down` `pow-exp` `associate--l+` `clear-num` `*-commutative` `flip--` `distribute-lft-out`

Counts

4 → 109

Calls

4 calls:

110.0ms	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
15.0ms	(+ y (/ (pow x 2) y))
7.0ms	(* z (/ z y))
4.0ms	(/ (pow x 2) y)

series108.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
27.0ms	(+ y (/ (pow x 2) y))
19.0ms	(* z (/ z y))
21.0ms	(/ (pow x 2) y)

simplify54.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	428	638
1	1829	584
2	5001	581

prune272.0ms

Pruning

8 alts after pruning (8 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))
0.2b	(* z (/ z y))

rewrite34.0ms

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)))
7.0ms	(* (fabs x) (/ (fabs x) y))
7.0ms	(* z (/ z y))

series109.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ y (* (fabs x) (/ (fabs x) y)))
49.0ms	(- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y)))
19.0ms	(* (fabs x) (/ (fabs x) y))
19.0ms	(* z (/ z y))

simplify61.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (53.0ms)

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

prune236.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms

sample708.0ms

Algorithm

intervals

Results

443.0ms

13670×

body

valid