Details

sample35.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify41.0ms

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

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: 27.7b

Counts

2 → 1

localize23.0ms

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) 137.519416416) x) y) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
26.8b	(/ (* (- 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:

10.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
12.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
32.0ms	(/ (* (- 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))

series62.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
9.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
10.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
40.0ms	(/ (* (- 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	657	1279
1	3241	1119
2	5002	1119

prune248.0ms

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

localize28.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.7b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.8b	(* (/ (- 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))))
21.3b	(/ (+ (* (+ (* (+ (* (+ (* 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)))

rewrite128.0ms

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:

12.0ms	(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)))
57.0ms	(* (/ (- 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))))
30.0ms	(/ (+ (* (+ (* (+ (* (+ (* 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)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
8.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
43.0ms	(* (/ (- 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))))
49.0ms	(/ (+ (* (+ (* (+ (* (+ (* 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)))

simplify120.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (72.0ms)

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

prune741.0ms

Filtered

217 candidates to 142 candidates (34.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	216	8	224

Merged error: 0.0b

Counts

224 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

15.8b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
15.8b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
15.8b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
21.4b	(* (/ (- 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))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
30×	`times-frac`
25×	`add-exp-log`
24×	`-un-lft-identity` `associate-r*`
22×	`add-cube-cbrt`
20×	`cbrt-prod` `cbrt-div`
18×	`add-cbrt-cube`
17×	`associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

12.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
12.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
12.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
69.0ms	(* (/ (- 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))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
10.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
10.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
44.0ms	(* (/ (- 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))))

simplify100.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	734	4060
1	3167	3554
2	5002	3351

prune681.0ms

Filtered

122 candidates to 102 candidates (16.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	122	8	130

Merged error: 0.0b

Counts

130 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x))
0.3b	(* (- (* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x)) (* 137.519416416 137.519416416)) x)
19.2b	(/ (* (- (* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x)) (* 137.519416416 137.519416416)) x) (- (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416))
26.8b	(/ (* (- x 2.0) (+ (* (+ (/ (* (- (* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x)) (* 137.519416416 137.519416416)) x) (- (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416)) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
28×	`add-exp-log` `add-cbrt-cube`
20×	`associate-*l/`
18×	`pow-prod-down`
12×	`add-sqr-sqrt`
11×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity` `flip3-+` `flip-+` `associate-/l/`
8×	`frac-times`
6×	`flip3--` `times-frac` `associate-/r*` `flip--`
5×	`associate-l`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-r*` `associate-/r/` `pow-sqr` `pow-prod-up` `add-log-exp`
2×	`frac-2neg` `pow-plus` `clear-num` `-commutative` `div-inv` `associate-/l`
1×	`pow2` `swap-sqr` `difference-of-squares` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

14.0ms	(* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x))
16.0ms	(* (- (* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x)) (* 137.519416416 137.519416416)) x)
24.0ms	(/ (* (- (* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x)) (* 137.519416416 137.519416416)) x) (- (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416))
39.0ms	(/ (* (- x 2.0) (+ (* (+ (/ (* (- (* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x)) (* 137.519416416 137.519416416)) x) (- (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416)) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series110.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x))
8.0ms	(* (- (* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x)) (* 137.519416416 137.519416416)) x)
9.0ms	(/ (* (- (* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x)) (* 137.519416416 137.519416416)) x) (- (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416))
89.0ms	(/ (* (- x 2.0) (+ (* (+ (/ (* (- (* (* (+ (* x 4.16438922228) 78.6994924154) x) (* (+ (* x 4.16438922228) 78.6994924154) x)) (* 137.519416416 137.519416416)) x) (- (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416)) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify121.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	865	2362
1	4490	2005
2	5001	2005

prune334.0ms

Filtered

131 candidates to 85 candidates (35.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	131	8	139

Merged error: 0b

Counts

139 → 8

regimes367.0ms

Accuracy

95.9% (1.0b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 24.7b

bsearch57.0ms

Steps

Iters	Range		Point
8	9.489307371361725e+25	2.4226674565005327e+29	2.3876880559927516e+29
10	-1.7554059141447428e+34	-3764032618942745.5	-1.723958632260071e+34

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	33
1	65	33
2	65	33

end0.0ms

sample970.0ms

Algorithm

intervals

Results

675.0ms

8007×

body

valid

Details

sample35.0ms

simplify41.0ms

prune4.0ms

localize23.0ms

rewrite64.0ms

series62.0ms

simplify82.0ms

prune248.0ms

localize28.0ms

rewrite128.0ms

series107.0ms

simplify120.0ms

prune741.0ms

localize33.0ms

rewrite109.0ms

series74.0ms

simplify100.0ms

prune681.0ms

localize31.0ms

rewrite98.0ms

series110.0ms

simplify121.0ms

prune334.0ms

regimes367.0ms

bsearch57.0ms

simplify2.0ms

end0.0ms

sample970.0ms

Profiling