Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	231×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	7×	body	1280	valid
0.0ms	6×	body	160	valid
0.0ms	2×	body	2560	valid

simplify68.0ms

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: 23.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.4b	(+ x (/ (* (- y x) (- z t)) (- a t)))
16.3b	(/ (* (- y x) (- z t)) (- a t))

rewrite88.0ms

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:

36.0ms	(* (- y x) (- z t))
20.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
29.0ms	(/ (* (- y x) (- z t)) (- a t))

series514.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* (- y x) (- z t))
354.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
123.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

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

prune239.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.8b	(/ (- y x) (/ (- a t) (- z t)))
2.4b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite154.0ms

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:

21.0ms	(/ (- a t) (- z t))
36.0ms	(/ (- y x) (/ (- a t) (- z t)))
80.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series428.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- a t) (- z t))
207.0ms	(/ (- y x) (/ (- a t) (- z t)))
170.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify96.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (20.0ms)

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

prune575.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.6b	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
1.6b	(/ (/ (- a t) (- z t)) (- y x))
6.0b	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

rewrite425.0ms

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:

23.0ms	(/ (- a t) (- z t))
61.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
40.0ms	(/ (/ (- a t) (- z t)) (- y x))
211.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

series718.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (- a t) (- z t))
310.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
167.0ms	(/ (/ (- a t) (- z t)) (- y x))
189.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

simplify150.0ms

Algorithm

egg-herbie

Counts

958 → 958

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2354	13203
1	5001	11834

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- z t))
0.2b	(* (- a t) (/ 1 (- z t)))
1.8b	(/ (- y x) (* (- a t) (/ 1 (- z t))))
4.3b	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

rewrite117.0ms

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:

12.0ms	(/ 1 (- z t))
43.0ms	(* (- a t) (/ 1 (- z t)))
32.0ms	(/ (- y x) (* (- a t) (/ 1 (- z t))))
25.0ms	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1 (- z t))
51.0ms	(* (- a t) (/ 1 (- z t)))
218.0ms	(/ (- y x) (* (- a t) (/ 1 (- z t))))
175.0ms	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (51.0ms)

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

prune306.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.1b

regimes255.0ms

Accuracy

18.7% (6.2b remaining)

Error of 10.4b against oracle of 4.2b and baseline of 11.8b

bsearch79.0ms

Steps

Iters	Range		Point
7	5.179480132863119e-140	2.278289265728706e-138	1.3607551715756482e-139
8	-1.1061742222619595e-161	-4.0338442708892566e-165	-7.063037459851844e-164

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	19
1	36	19

end0.0ms

sample754.0ms

Algorithm

intervals

Results

237.0ms	7758×	body	80	valid
50.0ms	481×	body	640	valid
38.0ms	422×	body	320	valid
36.0ms	254×	body	1280	valid
15.0ms	272×	body	160	valid
3.0ms	19×	body	2560	valid