Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	363×	body	80	valid
5.0ms	155×	body	80	nan

simplify107.0ms

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: 3.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
3.0b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

2.0ms	(+ 1.0 (* 10.0 k))
11.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
14.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ 1.0 (* 10.0 k))
19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
126.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify51.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	421	510
1	1910	434
2	5001	411

prune204.0ms

Filtered

70 candidates to 55 candidates (78.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma k k (fma 10.0 k 1.0))
0.0b	(fma 10.0 k 1.0)
0.6b	(/ 2 (* (fma k k (fma 10.0 k 1.0)) 2))
2.7b	(* (* a (pow k m)) (/ 2 (* (fma k k (fma 10.0 k 1.0)) 2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
30×	`add-cbrt-cube`
26×	`prod-exp`
12×	`cbrt-unprod`
10×	`div-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`pow1` `cbrt-undiv` `times-frac`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `associate-/l*`
2×	`fma-udef` `div-inv`
1×	`frac-2neg` `associate-r/` `associate-l` `pow-prod-down` `clear-num` `associate-/r` `*-commutative`

Counts

4 → 81

Calls

4 calls:

0.0ms	(fma k k (fma 10.0 k 1.0))
0.0ms	(fma 10.0 k 1.0)
3.0ms	(/ 2 (* (fma k k (fma 10.0 k 1.0)) 2))
14.0ms	(* (* a (pow k m)) (/ 2 (* (fma k k (fma 10.0 k 1.0)) 2)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(fma k k (fma 10.0 k 1.0))
32.0ms	(fma 10.0 k 1.0)
45.0ms	(/ 2 (* (fma k k (fma 10.0 k 1.0)) 2))
120.0ms	(* (* a (pow k m)) (/ 2 (* (fma k k (fma 10.0 k 1.0)) 2)))

simplify62.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	458	680
1	2246	546
2	5001	512

prune236.0ms

Filtered

93 candidates to 61 candidates (65.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

2.3b	(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
8.5b	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
9.4b	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
10.6b	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
19×	`times-frac` `associate-/r*`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`unpow-prod-down` `div-exp`
8×	`exp-neg` `distribute-rgt-neg-out` `associate-/l/`
6×	`cube-prod` `associate-*r/` `prod-exp` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `mul-1-neg` `log-rec` `pow-exp` `un-div-inv` `log1p-expm1-u` `sqr-pow`
2×	`cube-mult` `frac-2neg` `unpow3` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `frac-sub` `flip--` `fma-udef`

Counts

4 → 115

Calls

4 calls:

0.0ms	(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
19.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
20.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
51.0ms	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

series513.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
82.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
77.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
168.0ms	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

simplify98.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	623	1870
1	3219	1577
2	5001	1498

prune577.0ms

Filtered

127 candidates to 92 candidates (72.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

3.8b	(* (/ a k) (/ (pow (pow (/ 1 k) m) -1) k))
8.5b	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
9.4b	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
10.6b	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
122×	`add-sqr-sqrt`
118×	`unpow-prod-down`
83×	`add-exp-log`
72×	`*-un-lft-identity`
70×	`add-cube-cbrt`
67×	`associate-r`
41×	`div-exp`
26×	`add-cbrt-cube`
24×	`pow-exp` `prod-exp`
19×	`associate-/r*`
16×	`unswap-sqr`
14×	`sqr-pow`
13×	`associate-l`
8×	`cbrt-undiv` `exp-neg` `pow-to-exp` `distribute-rgt-neg-out` `associate-/l/`
7×	`associate-*r/` `div-inv`
6×	`pow1` `cube-prod` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `mul-1-neg` `log-rec` `un-div-inv` `log1p-expm1-u`
2×	`cube-mult` `rec-exp` `frac-2neg` `1-exp` `unpow3` `clear-num` `associate-/l*`
1×	`frac-times` `sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-l/` `-commutative` `frac-sub` `flip--`

Counts

4 → 237

Calls

4 calls:

62.0ms	(* (/ a k) (/ (pow (pow (/ 1 k) m) -1) k))
19.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
22.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
47.0ms	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (/ a k) (/ (pow (pow (/ 1 k) m) -1) k))
77.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
78.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
176.0ms	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

simplify67.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1559	2702
1	5002	2369

prune1.2s

Filtered

249 candidates to 175 candidates (70.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes99.0ms

Accuracy

98.5% (0.0b remaining)

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

bsearch38.0ms

Steps

Iters	Range		Point
5	6.176789711974138e+149	2.3062326495713713e+150	1.9661959056847304e+150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	33
1	59	33
2	59	33

end0.0ms

sample981.0ms

Algorithm

intervals

Results

476.0ms	11828×	body	80	valid
151.0ms	4193×	body	80	nan