Details

sample22.0ms

Algorithm

intervals

Results

9.0ms	311×	body	80	valid
1.0ms	6×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	4×	body	1280	valid
0.0ms	3×	body	160	valid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	6
1	51	5
2	172	5
3	481	5
4	1241	5
5	3102	5
6	5001	5

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 2.0 3.0) z)
0.0b	(* 6.0 (- (/ 2.0 3.0) z))
0.2b	(fma (- y x) (* 6.0 (- (/ 2.0 3.0) z)) x)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
118×	`*-un-lft-identity`
117×	`prod-diff`
114×	`add-cube-cbrt`
92×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
13×	`fma-neg`
10×	`div-inv`
6×	`associate-r`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`difference-of-squares`
3×	`expm1-log1p-u` `sub-neg` `associate-l` `log1p-expm1-u`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 186

Calls

3 calls:

13.0ms	(- (/ 2.0 3.0) z)
35.0ms	(* 6.0 (- (/ 2.0 3.0) z))
0.0ms	(fma (- y x) (* 6.0 (- (/ 2.0 3.0) z)) x)

series111.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(- (/ 2.0 3.0) z)
41.0ms	(* 6.0 (- (/ 2.0 3.0) z))
51.0ms	(fma (- y x) (* 6.0 (- (/ 2.0 3.0) z)) x)

simplify57.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	453	2251
1	1592	1519
2	5002	1387

prune288.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 6.0 (fma (sqrt (/ 2.0 3.0)) (sqrt (/ 2.0 3.0)) (- z)))
0.2b	(fma (- y x) (* 6.0 (fma (sqrt (/ 2.0 3.0)) (sqrt (/ 2.0 3.0)) (- z))) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l` `fma-udef`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

6.0ms	(* 6.0 (fma (sqrt (/ 2.0 3.0)) (sqrt (/ 2.0 3.0)) (- z)))
0.0ms	(fma (- y x) (* 6.0 (fma (sqrt (/ 2.0 3.0)) (sqrt (/ 2.0 3.0)) (- z))) x)

series298.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(* 6.0 (fma (sqrt (/ 2.0 3.0)) (sqrt (/ 2.0 3.0)) (- z)))
187.0ms	(fma (- y x) (* 6.0 (fma (sqrt (/ 2.0 3.0)) (sqrt (/ 2.0 3.0)) (- z))) x)

simplify76.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	162	388
1	659	314
2	3184	292
3	5002	282

prune123.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 2.0 3.0) z)
0.0b	(* (- y x) 6.0)
0.0b	(+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z)))
0.3b	(* (* (- y x) 6.0) (- (/ 2.0 3.0) z))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
195×	`prod-diff`
191×	`*-un-lft-identity`
185×	`add-cube-cbrt`
146×	`times-frac`
82×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
16×	`div-inv`
13×	`fma-neg`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*l/`
9×	`associate-r`
8×	`flip3--` `flip--` `add-log-exp`
6×	`associate-l`
5×	`sub-neg` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `distribute-lft-out--`
2×	`associate-r/` `-commutative`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 304

Calls

4 calls:

16.0ms	(- (/ 2.0 3.0) z)
10.0ms	(* (- y x) 6.0)
16.0ms	(+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z)))
44.0ms	(* (* (- y x) 6.0) (- (/ 2.0 3.0) z))

series167.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (/ 2.0 3.0) z)
30.0ms	(* (- y x) 6.0)
69.0ms	(+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z)))
44.0ms	(* (* (- y x) 6.0) (- (/ 2.0 3.0) z))

simplify115.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1016	3937
1	4362	2939
2	5001	2939

prune704.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
0.6b	(cbrt z)
61.0b	(fma (- (cbrt z)) (* (cbrt z) (cbrt z)) (* (cbrt z) (* (cbrt z) (cbrt z))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt z)
0.0ms	(cbrt z)
1.0ms	(cbrt z)
0.0ms	(fma (- (cbrt z)) (* (cbrt z) (cbrt z)) (* (cbrt z) (* (cbrt z) (cbrt z))))

series1.0s

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt z)
170.0ms	(cbrt z)
173.0ms	(cbrt z)
508.0ms	(fma (- (cbrt z)) (* (cbrt z) (cbrt z)) (* (cbrt z) (* (cbrt z) (cbrt z))))

simplify41.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	62	267
1	152	229
2	714	219
3	5001	201

prune256.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes174.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	20
1	24	20

end0.0ms

sample556.0ms

Algorithm

intervals

Results

280.0ms	9493×	body	80	valid
27.0ms	227×	body	640	valid
20.0ms	153×	body	1280	valid
15.0ms	192×	body	320	valid
6.0ms	117×	body	160	valid