Details

sample39.0ms

Algorithm

intervals

Results

16.0ms	387×	body	80	valid
6.0ms	162×	body	80	nan

simplify110.0ms

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(+ 1.0 (* 10.0 k))
1.6b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite34.0ms

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:

6.0ms	(* a (pow k m))
10.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.0ms	(+ 1.0 (* 10.0 k))
14.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* a (pow k m))
19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
35.0ms	(+ 1.0 (* 10.0 k))
116.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify60.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (52.0ms)

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

prune279.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(fma 10.0 k 1.0)
0.4b	(/ 1 (fma k k (fma 10.0 k 1.0)))
1.6b	(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

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)))
15.0ms	(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* a (pow k m))
32.0ms	(fma 10.0 k 1.0)
42.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
117.0ms	(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

simplify69.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	512	805
1	2653	698
2	5001	671

prune283.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (sqrt (fma k k (fma 10.0 k 1.0)))) (sqrt (fma k k (fma 10.0 k 1.0))))
1.6b	(* (* a (pow k m)) (/ (/ 1 (sqrt (fma k k (fma 10.0 k 1.0)))) (sqrt (fma k k (fma 10.0 k 1.0)))))
11.5b	(sqrt (fma k k (fma 10.0 k 1.0)))
11.5b	(sqrt (fma k k (fma 10.0 k 1.0)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

498×	`times-frac`
268×	`add-sqr-sqrt`
266×	`add-cube-cbrt` `*-un-lft-identity`
258×	`sqrt-prod`
136×	`associate-r`
83×	`add-exp-log`
35×	`prod-exp`
30×	`div-exp` `add-cbrt-cube`
22×	`associate-/l*`
15×	`pow1` `div-inv`
9×	`cbrt-undiv` `cbrt-unprod`
6×	`sqrt-pow1` `pow1/2` `associate-/r*` `pow-div`
5×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`frac-2neg` `associate-r/` `associate-l` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 390

Calls

4 calls:

11.0ms	(/ (/ 1 (sqrt (fma k k (fma 10.0 k 1.0)))) (sqrt (fma k k (fma 10.0 k 1.0))))
44.0ms	(* (* a (pow k m)) (/ (/ 1 (sqrt (fma k k (fma 10.0 k 1.0)))) (sqrt (fma k k (fma 10.0 k 1.0)))))
1.0ms	(sqrt (fma k k (fma 10.0 k 1.0)))
1.0ms	(sqrt (fma k k (fma 10.0 k 1.0)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (/ 1 (sqrt (fma k k (fma 10.0 k 1.0)))) (sqrt (fma k k (fma 10.0 k 1.0))))
118.0ms	(* (* a (pow k m)) (/ (/ 1 (sqrt (fma k k (fma 10.0 k 1.0)))) (sqrt (fma k k (fma 10.0 k 1.0)))))
54.0ms	(sqrt (fma k k (fma 10.0 k 1.0)))
60.0ms	(sqrt (fma k k (fma 10.0 k 1.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

402 → 402

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1393	5543
1	5001	4670

prune809.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 10.0 k 1.0)
0.0b	(/ (/ (* a (pow k m)) (sqrt (fma k k (fma 10.0 k 1.0)))) (sqrt (fma k k (fma 10.0 k 1.0))))
11.5b	(sqrt (fma k k (fma 10.0 k 1.0)))
11.5b	(sqrt (fma k k (fma 10.0 k 1.0)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
60×	`sqrt-prod`
51×	`add-sqr-sqrt`
49×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-/l*`
9×	`div-exp`
8×	`div-inv`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `fma-udef` `associate-/l/`

Counts

4 → 137

Calls

4 calls:

0.0ms	(fma 10.0 k 1.0)
9.0ms	(/ (/ (* a (pow k m)) (sqrt (fma k k (fma 10.0 k 1.0)))) (sqrt (fma k k (fma 10.0 k 1.0))))
1.0ms	(sqrt (fma k k (fma 10.0 k 1.0)))
1.0ms	(sqrt (fma k k (fma 10.0 k 1.0)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(fma 10.0 k 1.0)
118.0ms	(/ (/ (* a (pow k m)) (sqrt (fma k k (fma 10.0 k 1.0)))) (sqrt (fma k k (fma 10.0 k 1.0))))
59.0ms	(sqrt (fma k k (fma 10.0 k 1.0)))
58.0ms	(sqrt (fma k k (fma 10.0 k 1.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	596	1889
1	2494	1657
2	5001	1633

prune386.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes73.0ms

Accuracy

98.9% (0.0b remaining)

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

bsearch60.0ms

Steps

Iters	Range		Point
8	6.472113268382579e+91	1.9802750439539387e+95	8.93171350438392e+94

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	38
1	53	38
2	53	38

end0.0ms

sample1.0s

Algorithm

intervals

Results

509.0ms	12128×	body	80	valid
152.0ms	4348×	body	80	nan