Details

sample39.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify39.0ms

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 (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: 26.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.0b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
25.3b	(/ (* (- 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))

rewrite61.0ms

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:

11.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
12.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
29.0ms	(/ (* (- 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))

series389.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
68.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
63.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
225.0ms	(/ (* (- 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))

simplify90.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	673	1268
1	3351	1088
2	5001	1088

prune400.0ms

Filtered

103 candidates to 75 candidates (72.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	6	104

Merged error: 0.0b

Counts

104 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.0b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
23.9b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

9.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
12.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
10.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
25.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series362.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
70.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
67.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
191.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify71.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	564	1293
1	2414	1159
2	5001	1159

prune377.0ms

Filtered

103 candidates to 75 candidates (72.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	102	7	109

Merged error: 0b

Counts

109 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.3b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.3b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
18.7b	(* (/ (- 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))))

rewrite104.0ms

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:

11.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
11.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
11.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
65.0ms	(* (/ (- 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))))

series616.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
120.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
129.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
240.0ms	(* (/ (- 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 (68.0ms)

Iter	Nodes	Cost
0	706	3952
1	3079	3446
2	5001	3243

prune621.0ms

Filtered

122 candidates to 103 candidates (84.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	122	7	129

Merged error: 0b

Counts

129 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

8.9b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
8.9b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
17.5b	(/ (* (- 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)))
20.7b	(/ (/ (* (- 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))) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
72×	`sqrt-prod`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
22×	`sqrt-div`
18×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
12×	`associate-/r*`
9×	`div-inv` `associate-/l/`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`frac-times` `add-log-exp`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`

Counts

4 → 176

Calls

4 calls:

12.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
11.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
37.0ms	(/ (* (- 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)))
43.0ms	(/ (/ (* (- 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))) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series753.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
71.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
371.0ms	(/ (* (- 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)))
240.0ms	(/ (/ (* (- 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))) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify123.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	792	6140
1	3584	5571
2	5002	5571

prune656.0ms

Filtered

188 candidates to 117 candidates (62.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	189	6	195

Merged error: 0b

Counts

195 → 6

regimes244.0ms

Accuracy

97.3% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 25.1b

bsearch226.0ms

Steps

Iters	Range		Point
9	9.198045984357059e+49	1.0694899092935235e+55	3.796917059623679e+50
5	-1.2514886377233823e+29	-3.8751698555059933e+28	-7.707163920177255e+28

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	26
1	69	26

end0.0ms

sample823.0ms

Algorithm

intervals

Results

637.0ms

8005×

body

valid