Details

sample26.0ms

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

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1493	6
6	3393	6
7	5002	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
3.2b	(+ x (/ (* (- y x) (- z t)) (- a t)))
20.2b	(/ (* (- y x) (- z t)) (- a t))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

9.0ms	(* (- y x) (- z t))
7.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
12.0ms	(/ (* (- y x) (- z t)) (- a t))

series299.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* (- y x) (- z t))
149.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
113.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	468	583
1	2162	534
2	5003	534

prune243.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
3.2b	(+ x (/ (- y x) (/ (- a t) (- z t))))
3.9b	(/ (- y x) (/ (- a t) (- z t)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

8.0ms	(/ (- a t) (- z t))
40.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
18.0ms	(/ (- y x) (/ (- a t) (- z t)))

series402.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- a t) (- z t))
153.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
202.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify102.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	1030	3053
1	4263	2984
2	5003	2984

prune624.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- z t))
0.2b	(* (- a t) (/ 1 (- z t)))
3.9b	(/ (- y x) (* (- a t) (/ 1 (- z t))))
5.6b	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
37×	`times-frac`
32×	`add-exp-log`
26×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-cbrt-cube`
11×	`div-exp`
10×	`associate-/r/` `distribute-lft-out--` `difference-of-squares`
8×	`prod-exp` `associate-/l*`
7×	`pow1` `flip3--` `flip--`
6×	`cbrt-undiv` `associate-/r*` `add-log-exp`
5×	`associate-l`
4×	`frac-times` `associate-*l/` `cbrt-unprod`
3×	`rec-exp` `1-exp` `div-inv` `unswap-sqr`
2×	`frac-2neg` `div-sub` `associate-*r/` `clear-num` `un-div-inv` `associate-/l/`
1×	`+-commutative` `associate-+r-` `pow-flip` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `distribute-lft-out` `inv-pow`

Counts

4 → 142

Calls

4 calls:

6.0ms	(/ 1 (- z t))
16.0ms	(* (- a t) (/ 1 (- z t)))
14.0ms	(/ (- y x) (* (- a t) (/ 1 (- z t))))
9.0ms	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1 (- z t))
47.0ms	(* (- a t) (/ 1 (- z t)))
205.0ms	(/ (- y x) (* (- a t) (/ 1 (- z t))))
152.0ms	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	559	960
1	2445	832
2	5001	785

prune339.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.2b	(+ x (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (/ (cbrt (- a t)) (cbrt (- z t))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

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

series603.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- a t))
147.0ms	(cbrt (- a t))
147.0ms	(cbrt (- a t))
162.0ms	(+ x (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (/ (cbrt (- a t)) (cbrt (- z t))))))

simplify37.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	263	689
1	815	633
2	5001	624

prune284.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.0b

regimes305.0ms

Accuracy

8.7% (7.5b remaining)

Error of 11.5b against oracle of 4.1b and baseline of 12.2b

bsearch171.0ms

Steps

Iters	Range		Point
8	3.13830469290173e-74	3.2986477011150946e-70	3.1844700299462174e-74
4	3.096283894884496e-232	5.29997947542898e-232	3.1326586772354107e-232
9	2.3420034209605466e-278	2.5087460293450125e-273	1.1990666976977664e-273
8	-1.5114205842447585e-95	-1.7858658813908628e-99	-1.976117772983193e-99

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	59
1	55	59
2	58	59
3	58	59

end0.0ms

sample748.0ms

Algorithm

intervals

Results

276.0ms	7761×	body	80	valid
65.0ms	505×	body	640	valid
47.0ms	254×	body	1280	valid
44.0ms	461×	body	320	valid
17.0ms	259×	body	160	valid
3.0ms	15×	body	2560	valid