Details

sample26.0ms

Algorithm

intervals

Results

14.0ms

448×

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: 29.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
3.0b	(- (+ (* x x) (* y y)) (* z z))
27.8b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite52.0ms

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))
33.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series141.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* x x) (* y y))
38.0ms	(- (+ (* x x) (* y y)) (* z z))
76.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

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

prune149.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.4b

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))
7.8b	(/ (pow z 2) y)
9.1b	(/ (pow x 2) y)

rewrite148.0ms

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:

123.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
12.0ms	(+ y (/ (pow x 2) y))
4.0ms	(/ (pow z 2) y)
4.0ms	(/ (pow x 2) y)

series103.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
26.0ms	(+ y (/ (pow x 2) y))
21.0ms	(/ (pow z 2) y)
18.0ms	(/ (pow x 2) y)

simplify45.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (35.0ms)

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

prune312.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
0.0b	(+ y (* x (/ x y)))
0.2b	(* x (/ x y))
7.8b	(/ (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 (* x (/ x y))) (/ (pow z 2) y))
2.0ms	(+ y (* x (/ x y)))
7.0ms	(* x (/ x y))
4.0ms	(/ (pow z 2) y)

series103.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
26.0ms	(+ y (* x (/ x y)))
17.0ms	(* x (/ x y))
21.0ms	(/ (pow z 2) y)

simplify57.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	447	721
1	1850	663
2	5002	660

prune257.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (* x (/ x y))) (* (fabs z) (/ (fabs z) y)))
0.0b	(+ y (* x (/ x y)))
0.1b	(* (fabs z) (/ (fabs z) y))
0.2b	(* x (/ x 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:

15.0ms	(- (+ y (* x (/ x y))) (* (fabs z) (/ (fabs z) y)))
2.0ms	(+ y (* x (/ x y)))
7.0ms	(* (fabs z) (/ (fabs z) y))
7.0ms	(* x (/ x y))

series104.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (+ y (* x (/ x y))) (* (fabs z) (/ (fabs z) y)))
25.0ms	(+ y (* x (/ x y)))
18.0ms	(* (fabs z) (/ (fabs z) y))
18.0ms	(* x (/ x y))

simplify57.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	440	645
1	2155	578
2	5001	574

prune229.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes57.0ms

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	16	9
1	16	9

end0.0ms

sample744.0ms

Algorithm

intervals

Results

465.0ms

13783×

body

valid