Details

sample39.0ms

Algorithm

intervals

Results

20.0ms

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: 24.9b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
24.2b	(/ (* (- 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))

rewrite73.0ms

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 43.3400022514) x) 263.505074721) x) 313.399215894) x)
17.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
33.0ms	(/ (* (- 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))

series467.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
83.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
71.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
259.0ms	(/ (* (- 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))

simplify93.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	667	1310
1	3314	1141
2	5001	1141

prune441.0ms

Filtered

103 candidates to 77 candidates (74.8%)

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: 0b

Counts

104 → 7

localize35.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
15.6b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
15.7b	(* (/ (- 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))))
20.8b	(/ (+ (* (+ (* (+ (* (+ (* 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)))

rewrite135.0ms

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:

13.0ms	(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)))
65.0ms	(* (/ (- 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)))

series844.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
135.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
263.0ms	(* (/ (- 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))))
369.0ms	(/ (+ (* (+ (* (+ (* (+ (* 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)))

simplify132.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	894	5675
1	3611	5204
2	5002	5070

prune879.0ms

Filtered

217 candidates to 141 candidates (65.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	217	7	224

Merged error: 0b

Counts

224 → 7

localize34.0ms

Local error

Found 4 expressions with local error:

15.5b	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
15.5b	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
15.6b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
15.7b	(* (/ (- 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))))))

rewrite130.0ms

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:

14.0ms	(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)))
76.0ms	(* (/ (- 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))))))

series885.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
138.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
351.0ms	(/ (- 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))) (* (/ 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))))))

simplify146.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	934	5683
1	4723	4432
2	5001	4105

prune743.0ms

Filtered

194 candidates to 114 candidates (58.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	194	7	201

Merged error: 0b

Counts

201 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.3b	(/ 1 (/ (+ (* (+ (* (+ (* (+ 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))))
24.5b	(/ (+ (* (+ (* (+ (* (+ 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)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
41×	`associate-/r/`
38×	`add-sqr-sqrt`
34×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
20×	`frac-times`
18×	`flip3-+` `flip-+`
16×	`associate-/r*`
15×	`flip3--` `flip--`
14×	`div-exp` `associate-*l/`
10×	`associate-*r/`
9×	`pow1`
7×	`cbrt-undiv`
6×	`associate-r` `associate-l` `prod-exp` `div-inv` `associate-/l*`
4×	`cbrt-unprod` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`pow-flip` `inv-pow`

Counts

4 → 159

Calls

4 calls:

14.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
31.0ms	(/ 1 (/ (+ (* (+ (* (+ (* (+ 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))))
32.0ms	(/ (+ (* (+ (* (+ (* (+ 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)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
72.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
251.0ms	(/ 1 (/ (+ (* (+ (* (+ (* (+ 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))))
166.0ms	(/ (+ (* (+ (* (+ (* (+ 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)))

simplify145.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	877	3836
1	4810	3483
2	5002	3482

prune656.0ms

Filtered

171 candidates to 116 candidates (67.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	171	7	178

Merged error: 0b

Counts

178 → 7

regimes341.0ms

Accuracy

95% (1.2b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 24.5b

bsearch240.0ms

Steps

Iters	Range		Point
5	1236178698.9405453	3048118974.682059	3005568268.0445433
10	-1.3002308350545781e+28	-1604508521047215.5	-1.1550559361478097e+28

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	24
1	67	24
2	67	24

end0.0ms

sample720.0ms

Algorithm

intervals

Results

533.0ms

8007×

body

valid