Details

Time bar (total: 19.8s)

sample182.0ms

Algorithm
intervals
Results
66.0ms72×body10240exit
34.0ms52×body1280valid
32.0ms312×body80valid
13.0ms30×body640valid
4.0ms17×body320valid
3.0ms19×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (394.0ms)

IterNodesCost
01929
14729
212429
339527
4233826
done500226

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b
(exp (- (* (- 1.0 eps) x)))
0.0b
(exp (- (* (+ 1.0 eps) x)))
2.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
78×exp-neg
76×frac-times
59×neg-sub0 exp-diff
38×associate-*r/ associate-*l/
30×flip3-+ flip-+
28×flip3-- flip--
19×un-div-inv
12×exp-prod
10×add-sqr-sqrt *-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 add-cbrt-cube
5×add-exp-log
4×expm1-log1p-u associate-*l* log1p-expm1-u rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log
1×sub-neg fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
4 → 165
Calls
4 calls:
80.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
17.0ms
(exp (- (* (- 1.0 eps) x)))
9.0ms
(exp (- (* (+ 1.0 eps) x)))
65.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
42.0ms
(exp (- (* (- 1.0 eps) x)))
30.0ms
(exp (- (* (+ 1.0 eps) x)))
321.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify743.0ms

Counts
177 → 177
Iterations

Useful iterations: done (733.0ms)

IterNodesCost
03747973
113087143
done50006936

prune667.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
0.2b
(/ (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))) 2.0)
6.4b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube add-log-exp
3×pow1 expm1-log1p-u fma-neg prod-diff associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip-- fma-udef associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp associate--l+ clear-num div-inv
Counts
3 → 63
Calls
3 calls:
0.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
23.0ms
(/ (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))) 2.0)
12.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series256.0ms

Counts
3 → 9
Calls
3 calls:
113.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
99.0ms
(/ (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))) 2.0)
44.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify914.0ms

Counts
72 → 72
Iterations

Useful iterations: done (910.0ms)

IterNodesCost
01051309
12631277
211671159
done50011142

prune312.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 2.0)
6.4b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
2 → 39
Calls
2 calls:
5.0ms
(/ (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 2.0)
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series131.0ms

Counts
2 → 6
Calls
2 calls:
89.0ms
(/ (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 2.0)
42.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify2.8s

Counts
45 → 45
Iterations

Useful iterations: done (2.8s)

IterNodesCost
073896
1132881
2509803
34140747
done5000744

prune186.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

6.4b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
6.4b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
8.0b
(sqrt (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))
8.0b
(sqrt (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×add-log-exp
6×pow1 fma-neg prod-diff sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate--l+ fma-udef
Counts
4 → 76
Calls
4 calls:
6.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
6.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
8.0ms
(sqrt (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))
9.0ms
(sqrt (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
61.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
86.0ms
(sqrt (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))
96.0ms
(sqrt (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))

simplify738.0ms

Counts
88 → 88
Iterations

Useful iterations: done (734.0ms)

IterNodesCost
0841666
11991558
28821414
done50001300

prune517.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes167.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.2b against oracle of 0.5b and baseline of 17.1b

bsearch297.0ms

Steps
ItersRangePoint
9
6.998697613329711e-05
1051.5641664341613
42.863550376773794

simplify15.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03450
14848
25148
done5148

end0.0ms

sample9.2s

Algorithm
intervals
Results
3.0s1923×body10240exit
2.7s1680×body1280valid
1.5s9821×body80valid
980.0ms1253×body640valid
259.0ms637×body320valid
79.0ms328×body160valid