Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	249×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	2560	valid

simplify90.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1907	5
6	4560	5
7	5001	5

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
13.8b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite13.0ms

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:

9.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series151.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (- y x) (- a t))
93.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify69.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	269	450
1	734	425
2	2488	423
3	5002	423

prune231.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- y x) (/ 1 (- a t)))
13.9b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite31.0ms

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:

7.0ms	(/ 1 (- a t))
20.0ms	(* (- y x) (/ 1 (- a t)))
1.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series196.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ 1 (- a t))
56.0ms	(* (- y x) (/ 1 (- a t)))
97.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify52.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	351	602
1	1495	525
2	5001	481

prune309.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
13.8b	(fma (pow (/ (- y x) (- a t)) 1) (- z t) x)

rewrite13.0ms

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:

9.0ms	(/ (- y x) (- a t))
1.0ms	(fma (pow (/ (- y x) (- a t)) 1) (- z t) x)

series151.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- y x) (- a t))
96.0ms	(fma (pow (/ (- y x) (- a t)) 1) (- z t) x)

simplify93.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	271	462
1	770	434
2	2923	432
3	5001	432

prune239.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
4.4b	(+ (* (- z t) (/ (- y x) (- a t))) x)
4.4b	(* (- z t) (/ (- y x) (- a t)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

13.0ms	(/ (- y x) (- a t))
14.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
19.0ms	(* (- z t) (/ (- y x) (- a t)))

series353.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- y x) (- a t))
161.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
139.0ms	(* (- z t) (/ (- y x) (- a t)))

simplify56.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	490	904
1	2049	854
2	5001	852

prune352.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.8b

regimes290.0ms

Accuracy

14.2% (7.6b remaining)

Error of 11.4b against oracle of 3.7b and baseline of 12.6b

bsearch111.0ms

Steps

Iters	Range		Point
8	3.13830469290173e-74	3.2986477011150946e-70	3.1844700299462174e-74
8	-1.5114205842447585e-95	-1.7858658813908628e-99	-1.976117772983193e-99

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	25
1	35	25

end0.0ms

sample742.0ms

Algorithm

intervals

Results

281.0ms	7761×	body	80	valid
62.0ms	505×	body	640	valid
42.0ms	461×	body	320	valid
39.0ms	254×	body	1280	valid
16.0ms	259×	body	160	valid
3.0ms	15×	body	2560	valid