Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	244×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	10×	body	1280	valid
1.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	2560	valid

simplify63.0ms

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: 22.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.9b	(+ x (/ (* (- y x) (- z t)) (- a t)))
15.0b	(/ (* (- y x) (- z t)) (- a t))

rewrite96.0ms

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:

39.0ms	(* (- y x) (- z t))
21.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
33.0ms	(/ (* (- y x) (- z t)) (- a t))

series271.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* (- y x) (- z t))
137.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
101.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

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

prune278.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
2.7b	(/ (- y x) (/ (- a t) (- z t)))
2.9b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite163.0ms

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:

22.0ms	(/ (- a t) (- z t))
36.0ms	(/ (- y x) (/ (- a t) (- z t)))
84.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series355.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (- a t) (- z t))
174.0ms	(/ (- y x) (/ (- a t) (- z t)))
137.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify103.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (22.0ms)

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

prune644.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.2b	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
2.8b	(/ (/ (- a t) (- z t)) (- y x))
5.1b	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

1933×	`times-frac`
1483×	`*-un-lft-identity`
1480×	`add-sqr-sqrt`
624×	`add-cube-cbrt`
428×	`distribute-lft-out--` `difference-of-squares`
171×	`associate-/r*`
65×	`associate-/r/`
39×	`associate-/l*`
34×	`div-inv`
33×	`flip3--` `flip--`
32×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`div-exp`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
3×	`rec-exp` `frac-2neg` `1-exp` `div-sub` `clear-num` `associate-/l/`
2×	`distribute-lft-out`
1×	`+-commutative` `pow-flip` `flip3-+` `sum-log` `flip-+` `inv-pow`

Counts

4 → 946

Calls

4 calls:

25.0ms	(/ (- a t) (- z t))
65.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
42.0ms	(/ (/ (- a t) (- z t)) (- y x))
200.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

series689.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (- a t) (- z t))
263.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
186.0ms	(/ (/ (- a t) (- z t)) (- y x))
196.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

simplify154.0ms

Algorithm

egg-herbie

Counts

958 → 958

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2354	13203
1	5001	11834

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- z t))
0.2b	(* (- a t) (/ 1 (- z t)))
2.7b	(/ (- y x) (* (- a t) (/ 1 (- z t))))
5.1b	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

rewrite125.0ms

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:

14.0ms	(/ 1 (- z t))
45.0ms	(* (- a t) (/ 1 (- z t)))
34.0ms	(/ (- y x) (* (- a t) (/ 1 (- z t))))
27.0ms	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1 (- z t))
47.0ms	(* (- a t) (/ 1 (- z t)))
178.0ms	(/ (- y x) (* (- a t) (/ 1 (- z t))))
139.0ms	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (57.0ms)

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

prune312.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.1b

regimes234.0ms

Accuracy

18% (6.3b remaining)

Error of 10.7b against oracle of 4.4b and baseline of 12.1b

bsearch85.0ms

Steps

Iters	Range		Point
7	2.3279773334482045e-122	1.2315084140625416e-120	4.0034989804875424e-122
10	-3.7429501962479706e-117	-4.619021105644525e-127	-1.9571495574965582e-126

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	13
1	35	13

end0.0ms

sample782.0ms

Algorithm

intervals

Results

239.0ms	7725×	body	80	valid
50.0ms	469×	body	640	valid
40.0ms	452×	body	320	valid
40.0ms	278×	body	1280	valid
16.0ms	277×	body	160	valid
6.0ms	20×	body	2560	valid