Details

sample49.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

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: 29.5b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
28.4b	(/ (* (- 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))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
8×	`associate-*l/` `associate-/l/`
7×	`flip3-+` `flip-+`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `times-frac` `pow-prod-down` `associate-/r` `-commutative` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `associate-/r/`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

13.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
12.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
30.0ms	(/ (* (- 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))

series678.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
80.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
65.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
481.0ms	(/ (* (- 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))

simplify82.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	663	1251
1	3276	1097
2	5002	1097

prune982.0ms

Filtered

103 candidates to 76 candidates (26.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	7	104

Merged error: 0.0b

Counts

104 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

6.8b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.4b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.5b	(* (/ (- 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))))
21.1b	(/ (+ (* (+ (* (+ (* (+ (* 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)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
108×	`times-frac`
95×	`*-un-lft-identity`
69×	`add-cube-cbrt`
63×	`sqrt-prod`
36×	`associate-l`
24×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`associate-/r/` `associate-/l*`
7×	`pow1`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 205

Calls

4 calls:

14.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
17.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
56.0ms	(* (/ (- 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))))
29.0ms	(/ (+ (* (+ (* (+ (* (+ (* 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)))

series908.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
154.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
276.0ms	(* (/ (- 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))))
390.0ms	(/ (+ (* (+ (* (+ (* (+ (* 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)))

simplify126.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	894	5675
1	3611	5204
2	5001	5070

prune1.3s

Filtered

217 candidates to 140 candidates (35.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	213	4	217
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	214	10	224

Merged error: 0b

Counts

224 → 10

localize32.0ms

Local error

Found 4 expressions with local error:

6.8b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.4b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.5b	(* (/ (- 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) (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))
20.2b	(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
82×	`times-frac`
55×	`add-cube-cbrt`
50×	`add-exp-log`
47×	`sqrt-prod`
39×	`associate-l`
32×	`add-cbrt-cube`
25×	`associate-r`
22×	`prod-exp`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`pow1` `frac-times` `div-exp` `cbrt-unprod`
10×	`flip3-+` `flip-+`
9×	`associate-*r/`
8×	`sqrt-div`
7×	`cbrt-undiv` `associate-*l/`
6×	`associate-/r*` `associate-/r/`
5×	`associate-/l*` `unswap-sqr`
4×	`pow-prod-down` `add-log-exp`
3×	`rec-exp` `1-exp` `un-div-inv` `div-inv`
2×	`*-commutative` `associate-/l/`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `clear-num` `flip--`

Counts

4 → 202

Calls

4 calls:

15.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
17.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
55.0ms	(* (/ (- 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) (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))
33.0ms	(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))

series952.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
162.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
298.0ms	(* (/ (- 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) (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))
399.0ms	(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))

simplify136.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	992	5195
1	4720	4583
2	5001	4559

prune1.3s

Filtered

214 candidates to 132 candidates (38.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	214	10	224

Merged error: 0b

Counts

224 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

16.3b	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.3b	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.4b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.5b	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (* (/ 1 (sqrt (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 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
74×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
60×	`times-frac`
53×	`sqrt-prod`
47×	`add-cbrt-cube`
44×	`add-cube-cbrt`
36×	`associate-l`
34×	`prod-exp`
26×	`div-exp`
18×	`cbrt-unprod`
14×	`cbrt-undiv`
13×	`pow1` `distribute-lft-out--` `difference-of-squares`
12×	`sqrt-div`
8×	`sqrt-pow1`
6×	`associate-/r*`
5×	`frac-times` `associate-r/` `associate-/l`
4×	`rem-sqrt-square` `rec-exp` `flip3-+` `pow1/2` `1-exp` `associate-/r/` `flip-+` `add-log-exp`
3×	`pow-prod-down` `associate-*l/`
2×	`div-inv` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-r` `clear-num` `*-commutative` `flip--`

Counts

4 → 182

Calls

4 calls:

13.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
13.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
18.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
69.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (* (/ 1 (sqrt (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 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))))

series784.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
159.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
162.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
296.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (* (/ 1 (sqrt (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 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))))

simplify135.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	934	5687
1	4723	4432
2	5001	4105

prune996.0ms

Filtered

194 candidates to 113 candidates (41.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	195	9	204

Merged error: 0b

Counts

204 → 9

regimes579.0ms

Accuracy

95.8% (1.0b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 24.8b

bsearch269.0ms

Steps

Iters	Range		Point
5	2.267846025326125e+24	5.282155470912896e+24	5.190246440810936e+24
10	-2.248574206605931e+47	-1.04986181023155e+32	-3.3487753667505475e+37

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	34
1	70	34
2	70	34

end0.0ms

sample900.0ms

Algorithm

intervals

Results

613.0ms

8004×

body

valid

Details

sample49.0ms

simplify40.0ms

prune6.0ms

localize22.0ms

rewrite64.0ms

series678.0ms

simplify82.0ms

prune982.0ms

localize26.0ms

rewrite126.0ms

series908.0ms

simplify126.0ms

prune1.3s

localize32.0ms

rewrite129.0ms

series952.0ms

simplify136.0ms

prune1.3s

localize31.0ms

rewrite127.0ms

series784.0ms

simplify135.0ms

prune996.0ms

regimes579.0ms

bsearch269.0ms

simplify2.0ms

end0.0ms

sample900.0ms

Profiling