Details

sample37.0ms

Algorithm

intervals

Results

17.0ms

267×

body

valid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	25	8
1	39	8
2	64	8
3	115	8
4	207	8
5	465	8
6	1337	8
7	5001	8

prune4.0ms

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: 7.6b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* y z) x)
0.0b	(- (* t z) x)
0.0b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
10.2b	(/ (- (* y z) x) (- (* t z) x))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

184×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
78×	`add-cube-cbrt`
72×	`prod-diff`
65×	`times-frac`
42×	`associate-l`
36×	`distribute-lft-out--` `difference-of-squares`
26×	`unswap-sqr`
24×	`fma-neg` `associate-r`
11×	`associate-/r` `associate-/l`
10×	`distribute-lft-out`
8×	`add-exp-log` `*-commutative` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
3×	`div-sub`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`associate-+r-`

Counts

4 → 257

Calls

4 calls:

11.0ms	(- (* y z) x)
11.0ms	(- (* t z) x)
38.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
30.0ms	(/ (- (* y z) x) (- (* t z) x))

series287.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (* y z) x)
33.0ms	(- (* t z) x)
150.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
76.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify123.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	750	2521
1	2809	1994
2	5001	1919

prune662.0ms

Filtered

269 candidates to 140 candidates (52.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	260	9	269
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	261	9	270

Merged error: 0.6b

Counts

270 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* t z) x)
0.0b	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
0.3b	(/ 1 (- (* t z) x))
10.0b	(* (- (* y z) x) (/ 1 (- (* t z) x)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

187×	`*-un-lft-identity`
146×	`add-sqr-sqrt`
72×	`times-frac`
71×	`add-cube-cbrt`
51×	`associate-l`
39×	`associate-r`
36×	`prod-diff`
34×	`distribute-lft-out--`
32×	`associate-/r*`
28×	`distribute-lft-out`
26×	`frac-times`
24×	`difference-of-squares`
20×	`associate-/l*`
19×	`add-exp-log` `unswap-sqr`
17×	`flip3--` `flip--`
13×	`associate-*r/` `add-cbrt-cube`
12×	`fma-neg`
7×	`pow1`
6×	`clear-num` `associate-/r/` `add-log-exp`
5×	`frac-2neg` `div-exp` `*-commutative`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `un-div-inv` `div-inv`
2×	`rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `inv-pow`

Counts

4 → 272

Calls

4 calls:

10.0ms	(- (* t z) x)
35.0ms	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
16.0ms	(/ 1 (- (* t z) x))
34.0ms	(* (- (* y z) x) (/ 1 (- (* t z) x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(- (* t z) x)
128.0ms	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
26.0ms	(/ 1 (- (* t z) x))
64.0ms	(* (- (* y z) x) (/ 1 (- (* t z) x)))

simplify129.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	771	2504
1	3619	2100
2	5003	1988

prune546.0ms

Filtered

284 candidates to 142 candidates (50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	280	4	284
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	284	9	293

Merged error: 0.6b

Counts

293 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* t z) x)
0.1b	(/ (+ x 1.0) (+ (/ (- (* y z) x) (- (* t z) x)) x))
0.2b	(/ 1 (/ (+ x 1.0) (+ (/ (- (* y z) x) (- (* t z) x)) x)))
10.2b	(/ (- (* y z) x) (- (* t z) x))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

274×	`*-un-lft-identity`
208×	`add-sqr-sqrt`
195×	`times-frac`
115×	`add-cube-cbrt`
45×	`distribute-lft-out`
37×	`associate-/r*`
36×	`prod-diff`
34×	`distribute-lft-out--` `difference-of-squares`
29×	`associate-l`
25×	`associate-/r/`
21×	`unswap-sqr`
20×	`associate-/l*`
19×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`fma-neg` `associate-r`
9×	`div-exp`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l/` `add-log-exp`
5×	`pow1` `cbrt-undiv` `clear-num`
4×	`expm1-log1p-u` `frac-2neg` `*-commutative` `log1p-expm1-u`
3×	`flip3--` `flip--` `remove-double-div`
2×	`rec-exp` `1-exp`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `inv-pow`

Counts

4 → 319

Calls

4 calls:

10.0ms	(- (* t z) x)
37.0ms	(/ (+ x 1.0) (+ (/ (- (* y z) x) (- (* t z) x)) x))
46.0ms	(/ 1 (/ (+ x 1.0) (+ (/ (- (* y z) x) (- (* t z) x)) x)))
21.0ms	(/ (- (* y z) x) (- (* t z) x))

series336.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(- (* t z) x)
122.0ms	(/ (+ x 1.0) (+ (/ (- (* y z) x) (- (* t z) x)) x))
130.0ms	(/ 1 (/ (+ x 1.0) (+ (/ (- (* y z) x) (- (* t z) x)) x)))
59.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify142.0ms

Algorithm

egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	909	3848
1	4067	3414
2	5001	3414

prune661.0ms

Filtered

331 candidates to 174 candidates (52.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	328	3	331
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	332	8	340

Merged error: 0.6b

Counts

340 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* t z) x)
0.0b	(/ (* (cbrt 1) (cbrt 1)) (+ x 1.0))
0.1b	(* (/ (* (cbrt 1) (cbrt 1)) (+ x 1.0)) (* (cbrt 1) (+ (/ (- (* y z) x) (- (* t z) x)) x)))
10.2b	(/ (- (* y z) x) (- (* t z) x))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

695×	`add-sqr-sqrt`
552×	`*-un-lft-identity`
389×	`cbrt-prod`
365×	`times-frac`
280×	`unswap-sqr`
241×	`associate-l`
225×	`add-cube-cbrt`
135×	`associate-/l*`
106×	`associate-r`
84×	`swap-sqr`
82×	`associate-*r/`
78×	`frac-times`
73×	`add-cbrt-cube`
69×	`distribute-lft-out`
46×	`cbrt-unprod`
42×	`flip3-+` `flip-+`
39×	`associate-*l/`
36×	`prod-diff`
34×	`distribute-lft-out--` `difference-of-squares`
32×	`add-exp-log`
23×	`associate-/r*`
22×	`*-commutative`
21×	`cbrt-undiv`
12×	`fma-neg` `prod-exp`
9×	`pow1`
8×	`distribute-rgt-in` `distribute-lft-in`
7×	`div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`frac-2neg` `clear-num`
4×	`+-commutative` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `pow-prod-down` `flip--` `div-inv`
2×	`associate-/l/`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 712

Calls

4 calls:

10.0ms	(- (* t z) x)
20.0ms	(/ (* (cbrt 1) (cbrt 1)) (+ x 1.0))
102.0ms	(* (/ (* (cbrt 1) (cbrt 1)) (+ x 1.0)) (* (cbrt 1) (+ (/ (- (* y z) x) (- (* t z) x)) x)))
21.0ms	(/ (- (* y z) x) (- (* t z) x))

series242.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (* t z) x)
25.0ms	(/ (* (cbrt 1) (cbrt 1)) (+ x 1.0))
132.0ms	(* (/ (* (cbrt 1) (cbrt 1)) (+ x 1.0)) (* (cbrt 1) (+ (/ (- (* y z) x) (- (* t z) x)) x)))
60.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify170.0ms

Algorithm

egg-herbie

Counts

724 → 724

Iterations

Useful iterations: 1 (62.0ms)

Iter	Nodes	Cost
0	2388	11991
1	5001	11072

prune1.9s

Filtered

724 candidates to 382 candidates (52.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	723	1	724
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	724	8	732

Merged error: 0.6b

Counts

732 → 8

regimes211.0ms

Accuracy

60.6% (2.5b remaining)

Error of 3.2b against oracle of 0.7b and baseline of 7.1b

bsearch131.0ms

Steps

Iters	Range		Point
9	2.5457713080429357e+95	1.4561095946501342e+101	1.8056947966834833e+100
9	-1.1853128331038075e+151	-2.2579433472796912e+145	-1.934585560366914e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	13
1	35	13

end0.0ms

sample545.0ms

Algorithm

intervals

Results

327.0ms

8331×

body

valid