Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	260×	body	80	valid
1.0ms	14×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	6×	body	1280	valid
0.0ms	9×	body	160	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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: 9.3b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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:

22.0ms	(/ (- y x) (- a t))
0.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series115.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- y x) (- a t))
72.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (16.0ms)

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

prune179.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* (- y x) (/ 1 (- a t)))
13.0b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite61.0ms

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:

11.0ms	(/ 1 (- a t))
44.0ms	(* (- y x) (/ 1 (- a t)))
0.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series162.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ 1 (- a t))
47.0ms	(* (- y x) (/ 1 (- a t)))
86.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify39.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (31.0ms)

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

prune252.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.7b	(+ (* (- z t) (/ (- y x) (- a t))) x)
4.2b	(* (- z t) (/ (- y x) (- a t)))

rewrite106.0ms

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:

23.0ms	(/ (- y x) (- a t))
22.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
56.0ms	(* (- z t) (/ (- y x) (- a t)))

series288.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (- y x) (- a t))
133.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
110.0ms	(* (- z t) (/ (- y x) (- a t)))

simplify56.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (46.0ms)

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

prune327.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- y x))
1.0b	(/ 1 (/ (- a t) (- y x)))
13.0b	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

rewrite61.0ms

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:

22.0ms	(/ (- a t) (- y x))
28.0ms	(/ 1 (/ (- a t) (- y x)))
0.0ms	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

series359.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (- a t) (- y x))
205.0ms	(/ 1 (/ (- a t) (- y x)))
112.0ms	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

simplify68.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (46.0ms)

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

prune342.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.6b

regimes272.0ms

Accuracy

22.6% (8.5b remaining)

Error of 12.2b against oracle of 3.7b and baseline of 14.7b

bsearch64.0ms

Steps

Iters	Range		Point
4	3.8190548211291673e-104	7.035383739695766e-104	5.946387785554189e-104
9	-1.1608156537149954e-39	-6.177652776114809e-49	-6.280468323025652e-49

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	11
1	32	11
2	32	11

end0.0ms

sample750.0ms

Algorithm

intervals

Results

238.0ms	7822×	body	80	valid
52.0ms	474×	body	640	valid
38.0ms	268×	body	1280	valid
32.0ms	405×	body	320	valid
15.0ms	278×	body	160	valid
2.0ms	15×	body	2560	valid