Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	250×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	3×	body	1280	valid
0.0ms	1×	body	2560	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
11.2b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

13.0ms	(/ (- t x) (- a z))
0.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series144.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- t x) (- a z))
92.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune208.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
11.1b	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

6.0ms	(/ 1 (- a z))
24.0ms	(* (- t x) (/ 1 (- a z)))
0.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series180.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ 1 (- a z))
53.0ms	(* (- t x) (/ 1 (- a z)))
92.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify41.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	350	602
1	1497	525
2	5001	481

prune269.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
11.2b	(fma (- y z) (* 1 (/ (- t x) (- a z))) x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

12.0ms	(/ (- t x) (- a z))
0.0ms	(fma (- y z) (* 1 (/ (- t x) (- a z))) x)

series140.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- t x) (- a z))
90.0ms	(fma (- y z) (* 1 (/ (- t x) (- a z))) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	272	462
1	803	434
2	2854	432
3	5002	429

prune206.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (- a z))
0.0b	(- (/ t (- a z)) (/ x (- a z)))
0.0b	(/ t (- a z))
11.2b	(fma (- y z) (* 1 (- (/ t (- a z)) (/ x (- a z)))) x)

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
693×	`times-frac`
441×	`prod-diff`
413×	`add-cube-cbrt`
149×	`distribute-lft-out--`
143×	`difference-of-squares`
94×	`associate-/r/`
48×	`flip3--` `flip--`
47×	`div-inv`
21×	`fma-neg`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-out--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `diff-log` `frac-sub` `fma-udef` `sub-div`

Counts

4 → 581

Calls

4 calls:

5.0ms	(/ x (- a z))
74.0ms	(- (/ t (- a z)) (/ x (- a z)))
6.0ms	(/ t (- a z))
0.0ms	(fma (- y z) (* 1 (- (/ t (- a z)) (/ x (- a z)))) x)

series289.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ x (- a z))
108.0ms	(- (/ t (- a z)) (/ x (- a z)))
31.0ms	(/ t (- a z))
121.0ms	(fma (- y z) (* 1 (- (/ t (- a z)) (/ x (- a z)))) x)

simplify179.0ms

Algorithm

egg-herbie

Counts

593 → 593

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	1253	15718
1	3354	11728
2	5002	11636

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.6b

regimes275.0ms

Accuracy

18.2% (7.6b remaining)

Error of 12.9b against oracle of 5.3b and baseline of 14.6b

bsearch71.0ms

Steps

Iters	Range		Point
6	7.867046341610554e+209	6.299026182130298e+210	1.2029316985791688e+210
6	-4.356485418338831e+232	-1.0295582727544921e+232	-1.4882279988111647e+232

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	11
1	30	11

end0.0ms

sample734.0ms

Algorithm

intervals

Results

263.0ms	7794×	body	80	valid
61.0ms	460×	body	640	valid
40.0ms	435×	body	320	valid
39.0ms	255×	body	1280	valid
23.0ms	280×	body	160	valid
3.0ms	14×	body	2560	valid