Details

sample36.0ms

Algorithm

intervals

Results

16.0ms	390×	body	80	valid
5.0ms	144×	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

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(* a (pow k m))
2.2b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite36.0ms

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:

14.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms	(* a (pow k m))
14.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series193.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
60.0ms	(* a (pow k m))
115.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify55.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (48.0ms)

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

prune232.0ms

Filtered

81 candidates to 63 candidates (77.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
2.2b	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 189

Calls

3 calls:

11.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
25.0ms	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
18.0ms	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

series210.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
63.0ms	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
123.0ms	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

simplify103.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	848	2597
1	4083	2407
2	5002	2378

prune593.0ms

Filtered

198 candidates to 159 candidates (80.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize203.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.1b	(fma 10.0 k 1.0)
0.3b	(/ 1 (fma k k (fma 10.0 k 1.0)))
2.2b	(* (/ 1 (fma k k (fma 10.0 k 1.0))) (* a (pow k m)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-exp-log`
31×	`prod-exp`
27×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
18×	`times-frac`
16×	`associate-l`
10×	`div-exp`
8×	`associate-r`
7×	`pow1` `cbrt-unprod`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
2×	`*-commutative` `div-inv` `sqr-pow`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `fma-udef` `inv-pow`

Counts

4 → 116

Calls

4 calls:

5.0ms	(* a (pow k m))
0.0ms	(fma 10.0 k 1.0)
2.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
14.0ms	(* (/ 1 (fma k k (fma 10.0 k 1.0))) (* a (pow k m)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* a (pow k m))
31.0ms	(fma 10.0 k 1.0)
43.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
109.0ms	(* (/ 1 (fma k k (fma 10.0 k 1.0))) (* a (pow k m)))

simplify62.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	494	796
1	2369	688
2	5001	666

prune296.0ms

Filtered

128 candidates to 79 candidates (61.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b	(/ (* a (pow k m)) (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
17.8b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.8b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.8b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

20.0ms	(/ (* a (pow k m)) (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
6.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series563.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ (* a (pow k m)) (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
106.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
106.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
111.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify59.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	536	1256
1	2110	1102
2	5002	1060

prune348.0ms

Filtered

92 candidates to 78 candidates (84.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

98.6% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.3b

bsearch29.0ms

Steps

Iters	Range		Point
4	7.317339237634592e+150	1.4340110496867217e+151	8.317260679289482e+150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	33
1	51	33
2	51	33

end0.0ms

sample1.0s

Algorithm

intervals

Results

506.0ms	11972×	body	80	valid
145.0ms	4238×	body	80	nan