Details

sample32.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	55	18
1	138	18
2	450	18
3	1597	18
4	5001	18

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 25.2b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
24.4b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

957×	`*-un-lft-identity`
608×	`distribute-lft-out`
542×	`associate-l`
220×	`times-frac`
130×	`associate-r`
116×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
22×	`associate-/l*`
15×	`add-exp-log` `add-cbrt-cube`
14×	`*-commutative` `unswap-sqr`
11×	`distribute-lft-out--` `difference-of-squares`
10×	`pow1` `associate-/r*`
8×	`associate-*l/` `associate-/l/`
7×	`flip3-+` `flip-+`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `associate-/r/`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 348

Calls

4 calls:

20.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
28.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
11.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
81.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series437.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
74.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
68.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
251.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify167.0ms

Algorithm

egg-herbie

Counts

360 → 360

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	840	7125
1	4120	6962
2	5001	6962

prune546.0ms

Filtered

360 candidates to 115 candidates (68.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	354	6	360
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	355	6	361

Merged error: 0.0b

Counts

361 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
22.9b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

649×	`*-un-lft-identity`
432×	`distribute-lft-out`
355×	`associate-l`
110×	`times-frac`
39×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
12×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
10×	`pow1` `associate-/r*`
9×	`associate-r`
6×	`associate-*l/`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 219

Calls

4 calls:

19.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
28.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
14.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
66.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series395.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
75.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
68.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
209.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify99.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	534	3617
1	2233	3500
2	5001	3494

prune343.0ms

Filtered

231 candidates to 75 candidates (67.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	232	5	237

Merged error: 0.0b

Counts

237 → 5

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* x 4.16438922228) 3)
0.3b	(* (* x 4.16438922228) (* x 4.16438922228))
19.8b	(/ (* (+ (pow (* x 4.16438922228) 3) (pow 78.6994924154 3)) x) (+ (* (* x 4.16438922228) (* x 4.16438922228)) (- (* 78.6994924154 78.6994924154) (* (* x 4.16438922228) 78.6994924154))))
22.9b	(/ (+ (* (+ (* (+ (/ (* (+ (pow (* x 4.16438922228) 3) (pow 78.6994924154 3)) x) (+ (* (* x 4.16438922228) (* x 4.16438922228)) (- (* 78.6994924154 78.6994924154) (* (* x 4.16438922228) 78.6994924154)))) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite546.0ms

Algorithm

rewrite-expression-head

Rules

1950×	`*-un-lft-identity`
1438×	`associate-l`
738×	`distribute-lft-out`
536×	`times-frac`
360×	`distribute-lft-out--`
207×	`add-sqr-sqrt`
135×	`add-cube-cbrt`
112×	`unpow-prod-down`
103×	`pow-unpow`
102×	`associate-r`
100×	`sum-cubes`
46×	`pow1`
38×	`unswap-sqr`
34×	`associate-/r*`
31×	`*-commutative`
27×	`associate-/l*`
26×	`add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down`
14×	`swap-sqr`
10×	`prod-exp` `cbrt-unprod`
4×	`flip3-+` `associate-/r/` `pow-sqr` `pow-prod-up` `flip-+` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow-pow` `frac-2neg` `pow-plus` `associate-*l/` `pow-exp` `clear-num` `div-inv` `rem-cube-cbrt`
1×	`pow2` `pow-to-exp` `unpow3` `sqr-pow`

Counts

4 → 735

Calls

4 calls:

6.0ms	(pow (* x 4.16438922228) 3)
14.0ms	(* (* x 4.16438922228) (* x 4.16438922228))
143.0ms	(/ (* (+ (pow (* x 4.16438922228) 3) (pow 78.6994924154 3)) x) (+ (* (* x 4.16438922228) (* x 4.16438922228)) (- (* 78.6994924154 78.6994924154) (* (* x 4.16438922228) 78.6994924154))))
296.0ms	(/ (+ (* (+ (* (+ (/ (* (+ (pow (* x 4.16438922228) 3) (pow 78.6994924154 3)) x) (+ (* (* x 4.16438922228) (* x 4.16438922228)) (- (* 78.6994924154 78.6994924154) (* (* x 4.16438922228) 78.6994924154)))) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series567.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(pow (* x 4.16438922228) 3)
26.0ms	(* (* x 4.16438922228) (* x 4.16438922228))
150.0ms	(/ (* (+ (pow (* x 4.16438922228) 3) (pow 78.6994924154 3)) x) (+ (* (* x 4.16438922228) (* x 4.16438922228)) (- (* 78.6994924154 78.6994924154) (* (* x 4.16438922228) 78.6994924154))))
346.0ms	(/ (+ (* (+ (* (+ (/ (* (+ (pow (* x 4.16438922228) 3) (pow 78.6994924154 3)) x) (+ (* (* x 4.16438922228) (* x 4.16438922228)) (- (* 78.6994924154 78.6994924154) (* (* x 4.16438922228) 78.6994924154)))) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify191.0ms

Algorithm

egg-herbie

Counts

747 → 747

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1062	13823
1	5001	13237

prune1.0s

Filtered

747 candidates to 153 candidates (79.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	747	0	747
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	747	5	752

Merged error: 0.0b

Counts

752 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

16.8b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.8b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.8b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
17.5b	(* (/ (/ (- x 2.0) (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

17213×	`*-un-lft-identity`
10036×	`distribute-lft-out`
8581×	`associate-l`
4732×	`cbrt-prod`
3905×	`times-frac`
3510×	`associate-/l*`
3190×	`frac-times`
2965×	`add-sqr-sqrt`
2223×	`associate-/r*`
1701×	`add-cube-cbrt`
972×	`associate-/l/`
589×	`distribute-lft-out--` `difference-of-squares`
172×	`clear-num`
171×	`frac-2neg`
159×	`flip3-+` `flip-+`
149×	`associate-r`
110×	`associate-*l/`
96×	`cbrt-div`
90×	`associate-/r/`
68×	`add-cbrt-cube`
45×	`div-inv`
44×	`cbrt-undiv`
30×	`flip3--` `flip--`
29×	`associate-*r/`
25×	`add-exp-log`
21×	`cbrt-unprod` `unswap-sqr`
10×	`un-div-inv`
9×	`div-exp`
6×	`pow1` `prod-exp`
4×	`add-log-exp`
3×	`pow1/3`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 4534

Calls

4 calls:

28.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
34.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
28.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
2.0s	(* (/ (/ (- x 2.0) (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))

series662.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
135.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
134.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
261.0ms	(* (/ (/ (- x 2.0) (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))

simplify2.0s

Algorithm

egg-herbie

Counts

4546 → 4546

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5001	207243

prune5.9s

Filtered

4546 candidates to 868 candidates (80.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	4545	1	4546
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	4546	5	4551

Merged error: 0.0b

Counts

4551 → 5

regimes195.0ms

Accuracy

97.7% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 24.8b

bsearch265.0ms

Steps

Iters	Range		Point
8	1.762913208951331e+54	6.029997523963933e+57	8.292445271328924e+55
8	-1.2745855388170935e+40	-4.213223813186294e+37	-1.257168454610475e+40

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	34
1	75	34
2	75	34

end0.0ms

sample679.0ms

Algorithm

intervals

Results

500.0ms

8014×

body

valid