Details

sample49.0ms

Algorithm

intervals

Results

19.0ms	258×	body	80	valid
3.0ms	12×	body	640	valid
2.0ms	9×	body	1280	valid
2.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid

simplify69.0ms

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: 25.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
3.2b	(+ x (/ (* (- y x) (- z t)) (- a t)))
19.2b	(/ (* (- y x) (- z t)) (- a t))

rewrite42.0ms

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:

17.0ms	(* (- y x) (- z t))
10.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
12.0ms	(/ (* (- y x) (- z t)) (- a t))

series313.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* (- y x) (- z t))
153.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
117.0ms	(/ (* (- 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

prune232.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
3.2b	(+ x (/ (- y x) (/ (- a t) (- z t))))
3.5b	(/ (- y x) (/ (- a t) (- z t)))

rewrite110.0ms

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:

10.0ms	(/ (- a t) (- z t))
59.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
23.0ms	(/ (- y x) (/ (- a t) (- z t)))

series400.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- a t) (- z t))
153.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
195.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify104.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (23.0ms)

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

prune652.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.4b	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
3.5b	(/ (/ (- a t) (- z t)) (- y x))
4.1b	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

rewrite348.0ms

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:

14.0ms	(/ (- a t) (- z t))
42.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
24.0ms	(/ (/ (- a t) (- z t)) (- y x))
171.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

series705.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (- a t) (- z t))
320.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
161.0ms	(/ (/ (- a t) (- z t)) (- y x))
176.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

simplify172.0ms

Algorithm

egg-herbie

Counts

958 → 958

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2354	13203
1	5001	11834

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.7b

localize14.0ms

Local error

Found 4 expressions with local error:

4.1b	(+ x (/ (/ 1 (* (cbrt (/ (- a t) (- z t))) (cbrt (/ (- a t) (- z t))))) (/ (cbrt (/ (- a t) (- z t))) (- y x))))
4.9b	(cbrt (/ (- a t) (- z t)))
4.9b	(cbrt (/ (- a t) (- z t)))
4.9b	(cbrt (/ (- a t) (- z t)))

rewrite516.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

494.0ms	(+ x (/ (/ 1 (* (cbrt (/ (- a t) (- z t))) (cbrt (/ (- a t) (- z t))))) (/ (cbrt (/ (- a t) (- z t))) (- y x))))
5.0ms	(cbrt (/ (- a t) (- z t)))
5.0ms	(cbrt (/ (- a t) (- z t)))
5.0ms	(cbrt (/ (- a t) (- z t)))

series1.3s

Counts

4 → 12

Calls

4 calls:

171.0ms	(+ x (/ (/ 1 (* (cbrt (/ (- a t) (- z t))) (cbrt (/ (- a t) (- z t))))) (/ (cbrt (/ (- a t) (- z t))) (- y x))))
310.0ms	(cbrt (/ (- a t) (- z t)))
301.0ms	(cbrt (/ (- a t) (- z t)))
505.0ms	(cbrt (/ (- a t) (- z t)))

simplify150.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 3 (129.0ms)

Iter	Nodes	Cost
0	393	1681
1	996	1617
2	4575	1575
3	5001	1536

prune520.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.7b

regimes261.0ms

Accuracy

3.7% (7.2b remaining)

Error of 11.2b against oracle of 4.0b and baseline of 11.5b

bsearch98.0ms

Steps

Iters	Range		Point
7	1.657212411741948e-221	4.429970766605036e-220	3.690197812148326e-221
10	-9.782577084891276e-55	-2.1595657253418903e-66	-2.1819830922564002e-66

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	20
1	36	20

end0.0ms

sample704.0ms

Algorithm

intervals

Results

267.0ms	7778×	body	80	valid
53.0ms	441×	body	640	valid
42.0ms	418×	body	320	valid
41.0ms	277×	body	1280	valid
16.0ms	263×	body	160	valid
3.0ms	15×	body	2560	valid