Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	253×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	9×	body	1280	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	2560	valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
18.0b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite12.0ms

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:

57.0ms	(/ (- y x) (- a t))
94.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify64.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (22.0ms)

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

prune222.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- y x) (/ 1 (- a t)))
18.0b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite28.0ms

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 t))
18.0ms	(* (- y x) (/ 1 (- a t)))
1.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series186.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 1 (- a t))
53.0ms	(* (- y x) (/ 1 (- a t)))
93.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (38.0ms)

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

prune296.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.2b	(+ (* (- z t) (/ (- y x) (- a t))) x)
7.5b	(* (- z t) (/ (- y x) (- a t)))

rewrite45.0ms

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:

9.0ms	(/ (- y x) (- a t))
13.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
17.0ms	(* (- z t) (/ (- y x) (- a t)))

series358.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (- y x) (- a t))
156.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
144.0ms	(* (- z t) (/ (- y x) (- a t)))

simplify62.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (51.0ms)

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

prune386.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
1.6b	(* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))))
9.3b	(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-r`
10×	`cbrt-prod` `flip3--` `flip--`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-/r/`
6×	`pow1` `frac-times` `add-log-exp`
5×	`associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u`
3×	`associate-*r/` `distribute-lft-out--` `difference-of-squares`
2×	`times-frac` `pow1/3` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 94

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
26.0ms	(* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))))
40.0ms	(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

series793.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (- a t))
159.0ms	(cbrt (- a t))
305.0ms	(* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))))
162.0ms	(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

simplify83.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	693	1461
1	2676	1237
2	5002	1163

prune419.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.0b

regimes378.0ms

Accuracy

18.3% (7.0b remaining)

Error of 11.0b against oracle of 4.0b and baseline of 12.6b

bsearch132.0ms

Steps

Iters	Range		Point
10	1.1760743530227632e-196	1.4523660772846177e-185	8.422180820851575e-190
9	-5.983843157753064e-147	-2.547368294171095e-152	-2.0356593442717544e-150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	37
1	35	37

end0.0ms

sample721.0ms

Algorithm

intervals

Results

269.0ms	7738×	body	80	valid
64.0ms	540×	body	640	valid
43.0ms	429×	body	320	valid
37.0ms	242×	body	1280	valid
17.0ms	268×	body	160	valid
3.0ms	14×	body	2560	valid