Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	239×	body	80	valid
2.0ms	18×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	8×	body	1280	valid
0.0ms	7×	body	160	valid

simplify89.0ms

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: 12.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
15.4b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite19.0ms

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

series146.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (- y x) (- a t))
88.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify66.0ms

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

prune241.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* (- y x) (/ 1 (- a t)))
15.4b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite35.0ms

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))
25.0ms	(* (- y x) (/ 1 (- a t)))
0.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series193.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ 1 (- a t))
60.0ms	(* (- y x) (/ 1 (- a t)))
96.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (41.0ms)

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

prune325.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.3b

localize14.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (/ (- y x) (- a t)))
8.4b	(cbrt (/ (- y x) (- a t)))
8.4b	(cbrt (/ (- y x) (- a t)))
15.4b	(fma (* (* (cbrt (/ (- y x) (- a t))) (cbrt (/ (- y x) (- a t)))) (cbrt (/ (- y x) (- a t)))) (- z t) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 136

Calls

4 calls:

6.0ms	(cbrt (/ (- y x) (- a t)))
11.0ms	(cbrt (/ (- y x) (- a t)))
6.0ms	(cbrt (/ (- y x) (- a t)))
0.0ms	(fma (* (* (cbrt (/ (- y x) (- a t))) (cbrt (/ (- y x) (- a t)))) (cbrt (/ (- y x) (- a t)))) (- z t) x)

series609.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt (/ (- y x) (- a t)))
177.0ms	(cbrt (/ (- y x) (- a t)))
163.0ms	(cbrt (/ (- y x) (- a t)))
97.0ms	(fma (* (* (cbrt (/ (- y x) (- a t))) (cbrt (/ (- y x) (- a t)))) (cbrt (/ (- y x) (- a t)))) (- z t) x)

simplify83.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	334	1561
1	719	1499
2	2375	1469
3	5002	1439

prune630.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (/ 1 (- a t)))
8.4b	(cbrt (/ (- y x) (- a t)))
8.4b	(cbrt (/ (- y x) (- a t)))
15.4b	(fma (* (* (cbrt (/ (- y x) (- a t))) (* (cbrt (- y x)) (cbrt (/ 1 (- a t))))) (cbrt (/ (- y x) (- a t)))) (- z t) x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

83×	`cbrt-prod`
81×	`add-sqr-sqrt` `*-un-lft-identity`
65×	`times-frac`
35×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 126

Calls

4 calls:

4.0ms	(cbrt (/ 1 (- a t)))
6.0ms	(cbrt (/ (- y x) (- a t)))
6.0ms	(cbrt (/ (- y x) (- a t)))
0.0ms	(fma (* (* (cbrt (/ (- y x) (- a t))) (* (cbrt (- y x)) (cbrt (/ 1 (- a t))))) (cbrt (/ (- y x) (- a t)))) (- z t) x)

series840.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (/ 1 (- a t)))
408.0ms	(cbrt (/ (- y x) (- a t)))
172.0ms	(cbrt (/ (- y x) (- a t)))
100.0ms	(fma (* (* (cbrt (/ (- y x) (- a t))) (* (cbrt (- y x)) (cbrt (/ 1 (- a t))))) (cbrt (/ (- y x) (- a t)))) (- z t) x)

simplify117.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	474	1416
1	1064	1354
2	3894	1322
3	5001	1316

prune641.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.3b

regimes484.0ms

Accuracy

66.7% (2.7b remaining)

Error of 9.3b against oracle of 6.6b and baseline of 14.7b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	73
1	49	73

end0.0ms

sample731.0ms

Algorithm

intervals

Results

272.0ms	7751×	body	80	valid
70.0ms	508×	body	640	valid
46.0ms	292×	body	1280	valid
36.0ms	393×	body	320	valid
17.0ms	271×	body	160	valid
4.0ms	22×	body	2560	valid