Details

sample26.0ms

Algorithm

intervals

Results

14.0ms

419×

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize10.0ms

Local error

Found 2 expressions with local error:

5.2b	(- (+ (* x x) (* y y)) (* z z))
27.6b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite15.0ms

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:

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

series122.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (+ (* x x) (* y y)) (* z z))
79.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (28.0ms)

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

prune120.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 11.4b

localize12.0ms

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))
9.0b	(/ (pow x 2) y)
11.9b	(/ (pow z 2) y)

rewrite44.0ms

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:

21.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
9.0ms	(+ y (/ (pow x 2) y))
5.0ms	(/ (pow x 2) y)
5.0ms	(/ (pow z 2) y)

series107.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
31.0ms	(+ y (/ (pow x 2) y))
18.0ms	(/ (pow x 2) y)
19.0ms	(/ (pow z 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

prune366.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
0.0b	(+ y (/ (pow x 2) y))
0.2b	(* (fabs z) (/ (fabs z) y))
9.0b	(/ (pow x 2) y)

rewrite34.0ms

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:

11.0ms	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
9.0ms	(+ y (/ (pow x 2) y))
6.0ms	(* (fabs z) (/ (fabs z) y))
5.0ms	(/ (pow x 2) y)

series108.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
26.0ms	(+ y (/ (pow x 2) y))
23.0ms	(* (fabs z) (/ (fabs z) y))
19.0ms	(/ (pow x 2) y)

simplify53.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	429	756
1	1830	680
2	5002	673

prune341.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

85×	`times-frac`
59×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
13×	`associate-r` `associate-/r*`
11×	`add-log-exp`
6×	`pow1` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`associate-r/` `associate-l` `associate-/l`
2×	`flip3-+` `diff-log` `prod-exp` `sum-log` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow-prod-down` `associate--l+` `clear-num` `associate-/r/` `*-commutative` `flip--` `distribute-lft-out`

Counts

4 → 130

Calls

4 calls:

11.0ms	(+ y (/ x (/ y x)))
14.0ms	(- (+ y (/ x (/ y x))) (* (fabs z) (/ (fabs z) y)))
11.0ms	(* (fabs z) (/ (fabs z) y))
6.0ms	(/ x (/ y x))

series105.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ x (/ y x)))
44.0ms	(- (+ y (/ x (/ y x))) (* (fabs z) (/ (fabs z) y)))
18.0ms	(* (fabs z) (/ (fabs z) y))
18.0ms	(/ x (/ y x))

simplify77.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	600	968
1	2992	886
2	5001	874

prune376.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes106.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample761.0ms

Algorithm

intervals

Results

484.0ms

13528×

body

valid