Details

sample28.0ms

Algorithm

intervals

Results

15.0ms

434×

body

valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	7
1	59	6
2	111	6
3	204	6
4	369	6
5	839	6
6	2168	6
7	5001	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.5b	(fma x x (- (* y y) (* z z)))
5.0b	(- (* y y) (* z z))
25.4b	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-/l*`
8×	`add-exp-log` `add-cbrt-cube`
5×	`div-inv` `add-log-exp`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `flip--` `fma-udef` `associate-/l/` `difference-of-squares`

Counts

3 → 99

Calls

3 calls:

1.0ms	(fma x x (- (* y y) (* z z)))
4.0ms	(- (* y y) (* z z))
6.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

series186.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(fma x x (- (* y y) (* z z)))
34.0ms	(- (* y y) (* z z))
96.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify58.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	466	1096
1	1881	1029
2	5001	1026

prune345.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.5b

localize11.0ms

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)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

189×	`*-un-lft-identity`
148×	`times-frac`
138×	`add-sqr-sqrt`
126×	`add-cube-cbrt`
112×	`prod-diff`
61×	`unpow-prod-down`
30×	`distribute-lft-out`
21×	`unpow2` `sqr-pow`
16×	`associate-/l*`
13×	`add-exp-log`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`div-exp` `associate-/r*` `div-inv`
5×	`difference-of-squares`
4×	`fma-neg`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `diff-log` `pow-exp` `clear-num` `frac-sub` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `flip3-+` `associate--l+` `sum-log` `flip--` `flip-+`

Counts

3 → 243

Calls

3 calls:

23.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
5.0ms	(/ (pow x 2) y)
5.0ms	(/ (pow z 2) y)

series83.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
20.0ms	(/ (pow x 2) y)
21.0ms	(/ (pow z 2) y)

simplify119.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	957	4380
1	3231	3066
2	5002	2874

prune438.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.6b

localize11.0ms

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)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
34×	`*-un-lft-identity` `times-frac`
30×	`add-cube-cbrt`
13×	`add-exp-log` `associate-r`
12×	`unpow-prod-down`
10×	`add-cbrt-cube`
8×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`fma-neg` `div-exp` `prod-diff` `unpow2` `sqr-pow`
3×	`expm1-log1p-u` `associate-r/` `associate-l` `associate-/r` `log1p-expm1-u`
2×	`cbrt-undiv` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out` `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 → 111

Calls

3 calls:

12.0ms	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
10.0ms	(* (fabs z) (/ (fabs z) y))
5.0ms	(/ (pow x 2) y)

series91.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(- (+ y (/ (pow x 2) y)) (* (fabs z) (/ (fabs z) y)))
20.0ms	(* (fabs z) (/ (fabs z) y))
20.0ms	(/ (pow x 2) y)

simplify64.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	452	821
1	1890	722
2	5001	710

prune338.0ms

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))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
26×	`associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
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`
3×	`expm1-log1p-u` `fma-neg` `prod-diff` `log1p-expm1-u`
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 → 92

Calls

3 calls:

6.0ms	(- (+ 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))

series89.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify72.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	464	847
1	2242	730
2	5001	713

prune302.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes78.0ms

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

sample750.0ms

Algorithm

intervals

Results

470.0ms

13622×

body

valid