Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	246×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	11×	body	1280	valid
1.0ms	11×	body	320	valid
0.0ms	7×	body	160	valid
0.0ms	2×	body	2560	valid

simplify93.0ms

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: 11.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
14.8b	(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)

series155.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- y x) (- a t))
99.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (25.0ms)

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

prune231.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- y x))
0.3b	(/ 1 (/ (- a t) (- y x)))
14.7b	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `flip--` `div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

3 → 214

Calls

3 calls:

8.0ms	(/ (- a t) (- y x))
12.0ms	(/ 1 (/ (- a t) (- y x)))
1.0ms	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

series476.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (- a t) (- y x))
280.0ms	(/ 1 (/ (- a t) (- y x)))
139.0ms	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

simplify82.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	633	1907
1	2810	1722
2	5002	1551

prune514.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- y x))
2.7b	(+ (/ (- z t) (/ (- a t) (- y x))) x)
4.5b	(/ (- z t) (/ (- a t) (- y x)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

610×	`times-frac`
572×	`*-un-lft-identity`
570×	`add-sqr-sqrt`
200×	`add-cube-cbrt`
185×	`distribute-lft-out--` `difference-of-squares`
160×	`fma-def`
36×	`associate-/r*`
26×	`associate-/r/`
14×	`flip3--` `flip--` `div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 440

Calls

3 calls:

9.0ms	(/ (- a t) (- y x))
66.0ms	(+ (/ (- z t) (/ (- a t) (- y x))) x)
17.0ms	(/ (- z t) (/ (- a t) (- y x)))

series605.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ (- a t) (- y x))
195.0ms	(+ (/ (- z t) (/ (- a t) (- y x))) x)
350.0ms	(/ (- z t) (/ (- a t) (- y x)))

simplify122.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	1036	3079
1	4296	3003
2	5002	3001

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- y x))
2.7b	(- (/ t (/ (- a t) (- y x))) x)
3.6b	(/ z (/ (- a t) (- y x)))
4.0b	(/ t (/ (- a t) (- y x)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

1086×	`times-frac`
959×	`add-sqr-sqrt`
952×	`*-un-lft-identity`
526×	`add-cube-cbrt`
294×	`prod-diff`
215×	`difference-of-squares`
213×	`distribute-lft-out--`
98×	`fma-neg`
67×	`associate-/r*`
48×	`associate-/r/`
27×	`div-inv`
23×	`flip3--` `flip--`
16×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 752

Calls

4 calls:

9.0ms	(/ (- a t) (- y x))
54.0ms	(- (/ t (/ (- a t) (- y x))) x)
12.0ms	(/ z (/ (- a t) (- y x)))
13.0ms	(/ t (/ (- a t) (- y x)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (- a t) (- y x))
164.0ms	(- (/ t (/ (- a t) (- y x))) x)
175.0ms	(/ z (/ (- a t) (- y x)))
291.0ms	(/ t (/ (- a t) (- y x)))

simplify136.0ms

Algorithm

egg-herbie

Counts

764 → 764

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1565	10157
1	5002	8230

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.5b

regimes319.0ms

Accuracy

12.5% (6.2b remaining)

Error of 9.8b against oracle of 3.5b and baseline of 10.7b

bsearch150.0ms

Steps

Iters	Range	Point
6	5.5729737854534255e+225	8.310748197800496e+226	5.014268344444687e+226
10	9.96385176578107e-174	1.0745767130010427e-161	1.8788542726561286e-162
4	-3.5480952993547097e-40	-2.5734052351795068e-40	-3.3348818478163845e-40

Iters

Range

Point

5.5729737854534255e+225

8.310748197800496e+226

5.014268344444687e+226

9.96385176578107e-174

1.0745767130010427e-161

1.8788542726561286e-162

-3.5480952993547097e-40

-2.5734052351795068e-40

-3.3348818478163845e-40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	42
1	46	42

end0.0ms

sample746.0ms

Algorithm

intervals

Results

286.0ms	7786×	body	80	valid
62.0ms	455×	body	640	valid
45.0ms	427×	body	320	valid
40.0ms	248×	body	1280	valid
18.0ms	275×	body	160	valid
4.0ms	18×	body	2560	valid