Details

sample39.0ms

Algorithm

intervals

Results

17.0ms	373×	body	80	valid
5.0ms	140×	body	80	nan

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune8.0ms

Filtered

1 candidates to 1 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: 1.9b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
1.9b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
14×	`add-sqr-sqrt`
10×	`add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-log-exp`
7×	`associate-r`
6×	`prod-exp`
4×	`unpow-prod-down` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-def` `times-frac` `associate-l` `associate-/r*` `sum-log` `log1p-expm1-u` `unswap-sqr`
2×	`cbrt-undiv` `pow-to-exp` `flip3-+` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`+-commutative` `associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

3 → 72

Calls

3 calls:

6.0ms	(* a (pow k m))
10.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* a (pow k m))
19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
129.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify56.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	419	575
1	2040	495
2	5002	476

prune266.0ms

Filtered

81 candidates to 63 candidates (77.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.0b

Counts

83 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
0.6b	(cbrt k)
0.6b	(cbrt k)
1.9b	(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
30×	`prod-exp`
16×	`div-exp`
13×	`add-cbrt-cube`
11×	`pow-exp`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow-to-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `pow1/3` `associate-/r*` `cbrt-unprod`
2×	`associate-/r/`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 79

Calls

4 calls:

1.0ms	(cbrt k)
1.0ms	(cbrt k)
1.0ms	(cbrt k)
14.0ms	(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series1.1s

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt k)
354.0ms	(cbrt k)
178.0ms	(cbrt k)
436.0ms	(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify64.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	514	921
1	2446	788
2	5001	734

prune313.0ms

Filtered

91 candidates to 65 candidates (71.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	91	5	96

Merged error: 0.0b

Counts

96 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
0.6b	(cbrt k)
11.7b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
11.7b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `hypot-def`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt k)
1.0ms	(cbrt k)
5.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt k)
181.0ms	(cbrt k)
54.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
50.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify67.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	188	398
1	635	378
2	2448	366
3	5002	362

prune330.0ms

Filtered

74 candidates to 64 candidates (86.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	74	5	79

Merged error: 0.0b

Counts

79 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma k k (fma k 10.0 1.0))
0.1b	(fma k 10.0 1.0)
0.2b	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
2.9b	(/ (fma k k (fma k 10.0 1.0)) a)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
96×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`unpow-prod-down`
19×	`add-exp-log`
16×	`associate-/r*`
14×	`sqr-pow`
11×	`add-cbrt-cube`
10×	`div-exp` `div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `fma-udef`
1×	`associate-/r/`

Counts

4 → 181

Calls

4 calls:

1.0ms	(fma k k (fma k 10.0 1.0))
1.0ms	(fma k 10.0 1.0)
8.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
3.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

series226.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(fma k k (fma k 10.0 1.0))
32.0ms	(fma k 10.0 1.0)
115.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
51.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

simplify88.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	715	1922
1	3280	1854
2	5002	1852

prune571.0ms

Filtered

193 candidates to 150 candidates (77.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	194	4	198

Merged error: 0.0b

Counts

198 → 4

regimes87.0ms

Accuracy

98.4% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.0b

bsearch75.0ms

Steps

Iters	Range		Point
9	8.413343279761259e+131	1.4293573783770087e+139	5.7179340614281354e+135

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	46
1	54	46

end0.0ms

sample1.1s

Algorithm

intervals

Results

571.0ms	12075×	body	80	valid
160.0ms	4315×	body	80	nan