Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	254×	body	80	valid
2.0ms	13×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	7×	body	1280	valid
1.0ms	8×	body	160	valid
0.0ms	2×	body	2560	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 25.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
3.0b	(+ x (/ (* (- y x) (- z t)) (- a t)))
20.2b	(/ (* (- y x) (- z t)) (- a t))

rewrite32.0ms

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))
8.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
12.0ms	(/ (* (- y x) (- z t)) (- a t))

series295.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* (- y x) (- z t))
149.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
111.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify58.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

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

prune218.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Merged error: 3.8b

Counts

91 → 8

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.8b	(/ (- y x) (/ (- a t) (- z t)))
3.0b	(+ x (/ (- 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))
15.0ms	(/ (- y x) (/ (- a t) (- z t)))
42.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series391.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- a t) (- z t))
195.0ms	(/ (- y x) (/ (- a t) (- z t)))
150.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify109.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (23.0ms)

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

prune548.0ms

Filtered

283 candidates to 172 candidates (60.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	275	8	283
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	280	11	291

Merged error: 3.7b

Counts

291 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.2b	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
1.8b	(/ (/ (- a t) (- z t)) (- y x))
4.7b	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

rewrite271.0ms

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))
41.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
16.0ms	(/ (/ (- a t) (- z t)) (- y x))
116.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

series660.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (- a t) (- z t))
289.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
148.0ms	(/ (/ (- a t) (- z t)) (- y x))
167.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

simplify170.0ms

Algorithm

egg-herbie

Counts

958 → 958

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2354	13203
1	5001	11834

prune1.2s

Filtered

958 candidates to 359 candidates (37.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	956	2	958
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	956	13	969

Merged error: 3.7b

Counts

969 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y x))
0.6b	(cbrt (- y x))
0.6b	(/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))
9.4b	(+ x (* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

728×	`times-frac`
603×	`add-sqr-sqrt` `*-un-lft-identity`
470×	`cbrt-prod`
271×	`add-cube-cbrt`
166×	`distribute-lft-out--` `difference-of-squares`
46×	`associate-/r*`
19×	`associate-/r/`
12×	`flip3--` `flip--`
10×	`div-inv`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`cbrt-undiv` `div-exp`
2×	`pow1/3` `associate-/l/`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+`

Counts

4 → 480

Calls

4 calls:

3.0ms	(cbrt (- y x))
3.0ms	(cbrt (- y x))
22.0ms	(/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))
3.0ms	(+ x (* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))))

series591.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- y x))
145.0ms	(cbrt (- y x))
144.0ms	(/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))
153.0ms	(+ x (* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

492 → 492

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1424	8144
1	5002	7979

prune1.5s

Filtered

492 candidates to 327 candidates (66.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	491	1	492
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	491	14	505

Merged error: 3.7b

Counts

505 → 14

regimes269.0ms

Accuracy

20.3% (6.0b remaining)

Error of 10.0b against oracle of 4.0b and baseline of 11.5b

bsearch98.0ms

Steps

Iters	Range		Point
8	1.348603620070444e-171	8.218237891668852e-169	8.010570145934274e-170
9	-1.125446630178774e-171	-1.924081377858164e-177	-1.5372855936714785e-173

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	13
1	34	13

end0.0ms

sample741.0ms

Algorithm

intervals

Results

295.0ms	7832×	body	80	valid
65.0ms	455×	body	640	valid
49.0ms	425×	body	320	valid
48.0ms	276×	body	1280	valid
16.0ms	227×	body	160	valid
4.0ms	19×	body	2560	valid