Details

sample30.0ms

Algorithm

intervals

Results

12.0ms

405×

body

valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
3.0b	(- (+ (* x x) (* y y)) (* z z))
24.3b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`times-frac` `associate-/l*`
3×	`pow1` `expm1-log1p-u` `fma-neg` `prod-diff` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `sum-log` `flip--` `associate-/l/`
1×	`+-commutative` `sub-neg` `fma-def` `frac-2neg` `flip3-+` `div-sub` `prod-exp` `associate--l+` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv`

Counts

3 → 65

Calls

3 calls:

7.0ms	(+ (* x x) (* y y))
44.0ms	(- (+ (* x x) (* y y)) (* z z))
75.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series151.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* x x) (* y y))
44.0ms	(- (+ (* x x) (* y y)) (* z z))
81.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	365	571
1	1599	486
2	5002	469

prune172.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 6.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
5.4b	(/ (pow x 2) y)
9.8b	(/ (pow z 2) y)

rewrite224.0ms

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:

192.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
8.0ms	(/ (pow x 2) y)
8.0ms	(/ (pow z 2) y)

series80.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
19.0ms	(/ (pow x 2) y)
20.0ms	(/ (pow z 2) y)

simplify106.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (72.0ms)

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

prune354.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
0.1b	(* z (/ z y))
5.4b	(/ (pow x 2) y)

rewrite199.0ms

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:

173.0ms	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
13.0ms	(* z (/ z y))
8.0ms	(/ (pow x 2) y)

series82.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
19.0ms	(* z (/ z y))
20.0ms	(/ (pow x 2) y)

simplify61.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	451	667
1	1889	597
2	5002	591

prune258.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

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:

33.0ms	(- (+ y (* x (/ x y))) (* z (/ z y)))
13.0ms	(* z (/ z y))
13.0ms	(* x (/ x y))

series82.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(- (+ y (* x (/ x y))) (* z (/ z y)))
19.0ms	(* z (/ z y))
19.0ms	(* x (/ x y))

simplify62.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	462	544
1	2217	475
2	5001	468

prune203.0ms

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 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	20	8
2	20	8

end0.0ms

sample813.0ms

Algorithm

intervals

Results

441.0ms

13645×

body

valid