Details

sample30.0ms

Algorithm

intervals

Results

10.0ms	258×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	13×	body	160	valid
1.0ms	5×	body	1280	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 25.7b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
3.6b	(+ x (/ (* (- y x) (- z t)) (- a t)))
18.6b	(/ (* (- y x) (- z t)) (- a t))

rewrite30.0ms

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))

series295.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* (- y x) (- z t))
147.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
110.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify60.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (14.0ms)

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

prune226.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	12	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Merged error: 3.6b

Counts

91 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.3b	(/ (- y x) (/ (- a t) (- z t)))
3.6b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite81.0ms

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))
15.0ms	(/ (- y x) (/ (- a t) (- z t)))
41.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series395.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- a t) (- z t))
194.0ms	(/ (- y x) (/ (- a t) (- z t)))
153.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify115.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (28.0ms)

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

prune554.0ms

Filtered

283 candidates to 172 candidates (60.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	275	8	283
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	285	10	295

Merged error: 3.5b

Counts

295 → 10

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.3b	(* (- y x) (/ (- z t) (- a t)))
3.6b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 119

Calls

3 calls:

7.0ms	(/ (- z t) (- a t))
19.0ms	(* (- y x) (/ (- z t) (- a t)))
3.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series306.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- z t) (- a t))
111.0ms	(* (- y x) (/ (- z t) (- a t)))
149.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify66.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	476	869
1	2018	820
2	5001	820

prune255.0ms

Filtered

128 candidates to 87 candidates (68.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	128	10	138

Merged error: 3.5b

Counts

138 → 10

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)))
1.3b	(/ (/ (- a t) (- z t)) (- y x))
5.0b	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

rewrite267.0ms

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:

8.0ms	(/ (- a t) (- z t))
39.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
15.0ms	(/ (/ (- a t) (- z t)) (- y x))
110.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

series668.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (- a t) (- z t))
299.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
153.0ms	(/ (/ (- a t) (- z t)) (- y x))
171.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

simplify180.0ms

Algorithm

egg-herbie

Counts

958 → 958

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2354	13203
1	5001	11834

prune1.2s

Filtered

958 candidates to 359 candidates (37.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	954	4	958
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	956	12	968

Merged error: 3.5b

Counts

968 → 12

regimes239.0ms

Accuracy

11.8% (6.5b remaining)

Error of 10.8b against oracle of 4.3b and baseline of 11.7b

bsearch105.0ms

Steps

Iters	Range		Point
11	1.3636951528383244e-120	2.1620732516896606e-97	1.3782715591853007e-120
9	-2.441408133185532e-87	-2.422168701536519e-92	-2.8458411894470345e-92

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	19
1	36	19

end0.0ms

sample727.0ms

Algorithm

intervals

Results

281.0ms	7853×	body	80	valid
62.0ms	487×	body	640	valid
44.0ms	428×	body	320	valid
39.0ms	243×	body	1280	valid
18.0ms	278×	body	160	valid
4.0ms	20×	body	2560	valid