Details

sample47.0ms

Algorithm

intervals

Results

25.0ms	382×	body	80	valid
6.0ms	141×	body	80	nan

simplify104.0ms

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: 2.8b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.8b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

3.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(* a (pow k m))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ 1.0 (* 10.0 k))
60.0ms	(* a (pow k m))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
116.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify62.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	477	629
1	2275	544
2	5001	524

prune254.0ms

Filtered

100 candidates to 79 candidates (79.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	5	102

Merged error: 0.0b

Counts

102 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ 1.0 (* 10.0 k)))
0.7b	(cbrt (+ 1.0 (* 10.0 k)))
0.7b	(cbrt (+ 1.0 (* 10.0 k)))
2.8b	(/ (* a (pow k m)) (fma (* (cbrt (+ 1.0 (* 10.0 k))) (cbrt (+ 1.0 (* 10.0 k)))) (cbrt (+ 1.0 (* 10.0 k))) (* k k)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

5.0ms	(cbrt (+ 1.0 (* 10.0 k)))
2.0ms	(cbrt (+ 1.0 (* 10.0 k)))
2.0ms	(cbrt (+ 1.0 (* 10.0 k)))
5.0ms	(/ (* a (pow k m)) (fma (* (cbrt (+ 1.0 (* 10.0 k))) (cbrt (+ 1.0 (* 10.0 k)))) (cbrt (+ 1.0 (* 10.0 k))) (* k k)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (+ 1.0 (* 10.0 k)))
126.0ms	(cbrt (+ 1.0 (* 10.0 k)))
120.0ms	(cbrt (+ 1.0 (* 10.0 k)))
201.0ms	(/ (* a (pow k m)) (fma (* (cbrt (+ 1.0 (* 10.0 k))) (cbrt (+ 1.0 (* 10.0 k)))) (cbrt (+ 1.0 (* 10.0 k))) (* k k)))

simplify55.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	463	1170
1	1881	1041
2	5002	1013

prune295.0ms

Filtered

82 candidates to 73 candidates (89.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	82	5	87

Merged error: 0.0b

Counts

87 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.2b	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
2.6b	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

3.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
7.0ms	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
13.0ms	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ 1.0 (* 10.0 k))
22.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
62.0ms	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
117.0ms	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

simplify78.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	634	1353
1	2939	1224
2	5001	1204

prune359.0ms

Filtered

147 candidates to 119 candidates (81.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	147	5	152

Merged error: 0.0b

Counts

152 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma k k (fma k 10.0 1.0))
0.0b	(fma k 10.0 1.0)
0.3b	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
3.8b	(/ (fma k k (fma k 10.0 1.0)) a)

rewrite21.0ms

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)

series207.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(fma k k (fma k 10.0 1.0))
30.0ms	(fma k 10.0 1.0)
111.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
45.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

simplify94.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (67.0ms)

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

prune467.0ms

Filtered

193 candidates to 149 candidates (77.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	193	5	198

Merged error: 0.0b

Counts

198 → 5

regimes83.0ms

Accuracy

95.2% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch76.0ms

Steps

Iters	Range		Point
10	3.106786252575419e+128	7.010155340758994e+146	2.2354937785872955e+134

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	42
1	55	42
2	55	42

end0.0ms

sample1.4s

Algorithm

intervals

Results

832.0ms	11882×	body	80	valid
198.0ms	4295×	body	80	nan