Details

sample54.0ms

Algorithm

intervals

Results

32.0ms	375×	body	80	valid
8.0ms	115×	body	80	nan

simplify105.0ms

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: 3.7b

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))
3.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite34.0ms

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:

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

series195.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(* a (pow k m))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
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 (49.0ms)

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

prune222.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize198.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
0.0b	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
17.5b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.5b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
72×	`sqrt-prod`
61×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
30×	`add-exp-log`
22×	`sqrt-div`
18×	`associate-/r/` `add-cbrt-cube`
13×	`div-exp` `associate-/l*`
12×	`associate-/r*`
11×	`flip3-+` `flip-+`
9×	`div-inv`
7×	`cbrt-undiv`
6×	`pow1` `prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `cbrt-unprod` `hypot-def`
1×	`associate-/l/`

Counts

4 → 182

Calls

4 calls:

14.0ms	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
34.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
11.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
112.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
50.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
47.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify92.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	773	3508
1	3374	3103
2	5002	3090

prune501.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ (* a (pow k m)) (* (fabs (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
17.5b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
18.1b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
18.1b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

12.0ms	(/ (* a (pow k m)) (* (fabs (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
11.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (* a (pow k m)) (* (fabs (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
51.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
104.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
104.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify67.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	613	1250
1	2678	1085
2	5001	1057

prune403.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.6b	(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)))))
5.9b	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
6.1b	(/ (* 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))))

rewrite89.0ms

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)))))
18.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
21.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
45.0ms	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

series490.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(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)))))
80.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
71.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
162.0ms	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

simplify100.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	623	1864
1	3171	1567
2	5001	1493

prune573.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes117.0ms

Accuracy

99% (0.0b remaining)

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

bsearch26.0ms

Steps

Iters	Range		Point
3	3.2306096308063657e+153	4.3251915665116296e+153	3.945215226703958e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	34
1	54	34
2	54	34

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.0s	12012×	body	80	valid
269.0ms	4179×	body	80	nan