Details

sample37.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify45.0ms

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 (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: 25.2b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) 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))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

954×	`*-un-lft-identity`
606×	`distribute-lft-out`
539×	`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 → 347

Calls

4 calls:

13.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
11.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
29.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
86.0ms	(/ (* (- 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))

series459.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
72.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
75.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
272.0ms	(/ (* (- 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))

simplify174.0ms

Algorithm

egg-herbie

Counts

359 → 359

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	854	7106
1	4219	6923
2	5002	6923

prune585.0ms

Filtered

359 candidates to 114 candidates (31.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	352	7	359
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	353	7	360

Merged error: 0.0b

Counts

360 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

6.3b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
14.6b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
15.0b	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
18.8b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite605.0ms

Algorithm

rewrite-expression-head

Rules

3909×	`*-un-lft-identity`
2464×	`distribute-lft-out`
1971×	`associate-l`
896×	`sqrt-prod`
728×	`associate-/r*`
667×	`frac-times`
439×	`associate-/l*`
436×	`add-sqr-sqrt`
428×	`times-frac`
291×	`add-cube-cbrt`
149×	`associate-r`
112×	`associate-/l/`
57×	`clear-num` `distribute-lft-out--` `difference-of-squares`
56×	`frac-2neg`
31×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
29×	`associate-*r/`
23×	`associate-*l/`
20×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div` `un-div-inv`
9×	`unswap-sqr`
8×	`associate-/r/`
7×	`pow1`
6×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 1280

Calls

4 calls:

28.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
35.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
282.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
70.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series836.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
136.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
261.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
363.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify389.0ms

Algorithm

egg-herbie

Counts

1292 → 1292

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	1960	33645
1	5002	31633

prune1.3s

Filtered

1292 candidates to 253 candidates (19.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	1289	3	1292
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	1293	6	1299

Merged error: 0b

Counts

1299 → 6

localize33.0ms

Local error

Found 4 expressions with local error:

6.3b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
14.6b	(/ (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (- x 2.0))
15.0b	(* (/ 1 (/ (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (- x 2.0))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
18.8b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

11404×	`*-un-lft-identity`
6504×	`distribute-lft-out`
5224×	`associate-l`
3167×	`associate-/r*`
2753×	`times-frac` `sqrt-prod`
2233×	`frac-times`
2202×	`add-sqr-sqrt`
1236×	`add-cube-cbrt`
994×	`associate-/l*`
444×	`distribute-lft-out--` `difference-of-squares`
162×	`associate-/l/`
149×	`associate-r`
112×	`clear-num`
111×	`frac-2neg`
95×	`associate-/r/`
84×	`flip3-+` `flip-+`
77×	`associate-*l/`
53×	`add-exp-log`
37×	`div-inv`
34×	`flip3--` `flip--`
29×	`associate-*r/` `add-cbrt-cube`
23×	`div-exp`
21×	`unswap-sqr`
14×	`prod-exp`
11×	`cbrt-undiv`
10×	`sqrt-div` `un-div-inv`
7×	`pow1`
6×	`cbrt-unprod`
4×	`rec-exp` `1-exp` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative`

Counts

4 → 3092

Calls

4 calls:

30.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
34.0ms	(/ (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (- x 2.0))
552.0ms	(* (/ 1 (/ (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (- x 2.0))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
65.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series809.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
133.0ms	(/ (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (- x 2.0))
259.0ms	(* (/ 1 (/ (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (- x 2.0))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
342.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify1.2s

Algorithm

egg-herbie

Counts

3104 → 3104

Iterations

Useful iterations: 1 (109.0ms)

Iter	Nodes	Cost
0	4077	108185
1	5001	102743

prune2.8s

Filtered

3104 candidates to 475 candidates (15.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	3104	0	3104
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	3104	6	3110

Merged error: 0b

Counts

3110 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
2.8b	(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
22.1b	(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

471×	`*-un-lft-identity`
258×	`distribute-lft-out`
219×	`associate-l`
105×	`add-sqr-sqrt`
101×	`times-frac`
62×	`associate-r`
48×	`add-cube-cbrt`
40×	`frac-times` `associate-/r*`
25×	`flip3-+` `flip-+` `distribute-lft-out--`
24×	`difference-of-squares`
22×	`associate-/l*`
20×	`associate-*r/`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
8×	`associate-/l/`
6×	`associate-*l/`
5×	`clear-num`
4×	`flip3--` `frac-2neg` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `un-div-inv` `*-commutative`
2×	`cbrt-undiv` `div-exp` `div-inv`
1×	`div-sub`

Counts

4 → 277

Calls

4 calls:

10.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
29.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
30.0ms	(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
82.0ms	(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
75.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
77.0ms	(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
256.0ms	(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify155.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	856	4885
1	4385	4703
2	5001	4703

prune571.0ms

Filtered

289 candidates to 126 candidates (43.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	289	6	295

Merged error: 0b

Counts

295 → 6

regimes215.0ms

Accuracy

96.4% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 24.6b

bsearch450.0ms

Steps

Iters	Range		Point
9	1.0815468575645218e+20	8.37173053923323e+25	8.22351433349814e+25
7	-1.8347284548271936e+73	-2.541648319617525e+71	-2.205791074229281e+72

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	34
1	69	34
2	69	34

end0.0ms

sample692.0ms

Algorithm

intervals

Results

510.0ms

8009×

body

valid