Details

Time bar (total: 20.5s)

sample186.0ms

Algorithm
intervals
Results
61.0ms42×body10240exit
33.0ms314×body80valid
31.0ms43×body1280valid
22.0ms46×body640valid
5.0ms16×body320valid
3.0ms14×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5001
42356
3395
2124
147
019

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.4b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
77×exp-neg
76×frac-times
58×neg-sub0 exp-diff
40×associate-*l/
38×associate-*r/
31×flip3-- flip--
28×flip3-+ flip-+
19×un-div-inv
18×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
7×add-exp-log
6×exp-prod associate-*r*
4×expm1-log1p-u log1p-expm1-u
2×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr rem-exp-log
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in times-frac fma-neg diff-log prod-diff neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 171
Calls
4 calls:
19.0ms
(* (+ 1.0 eps) x)
8.0ms
(exp (- (* (- 1.0 eps) x)))
75.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
66.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series408.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (+ 1.0 eps) x)
33.0ms
(exp (- (* (- 1.0 eps) x)))
56.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
277.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify710.0ms

Counts
183 → 183
Iterations
IterNodes
done5001
11386
0405

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
7.8b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (* x x)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
3×fma-neg prod-diff
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log fma-udef log1p-expm1-u
1×sub-neg flip3-- diff-log associate--l+ flip--
Counts
2 → 31
Calls
2 calls:
0.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
6.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (* x x)))

series204.0ms

Counts
2 → 6
Calls
2 calls:
148.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
55.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (* x x)))

simplify642.0ms

Counts
37 → 37
Iterations
IterNodes
done5001
2774
1157
055

prune235.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (pow x 3) 0.6666666666666667 2.0)
0.5b
(expm1 (log1p (fma (pow x 3) 0.6666666666666667 2.0)))
7.8b
(- (expm1 (log1p (fma (pow x 3) 0.6666666666666667 2.0))) (* 1.0 (* x x)))
13.3b
(log1p (fma (pow x 3) 0.6666666666666667 2.0))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
5×expm1-log1p-u
4×pow1 add-cbrt-cube add-exp-log log1p-expm1-u
3×fma-neg prod-diff
2×expm1-udef
1×associate--l- log1p-udef expm1-log1p sub-neg flip3-- diff-log log1p-expm1 fma-udef flip--
Counts
4 → 53
Calls
4 calls:
0.0ms
(fma (pow x 3) 0.6666666666666667 2.0)
0.0ms
(expm1 (log1p (fma (pow x 3) 0.6666666666666667 2.0)))
10.0ms
(- (expm1 (log1p (fma (pow x 3) 0.6666666666666667 2.0))) (* 1.0 (* x x)))
1.0ms
(log1p (fma (pow x 3) 0.6666666666666667 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
142.0ms
(fma (pow x 3) 0.6666666666666667 2.0)
633.0ms
(expm1 (log1p (fma (pow x 3) 0.6666666666666667 2.0)))
211.0ms
(- (expm1 (log1p (fma (pow x 3) 0.6666666666666667 2.0))) (* 1.0 (* x x)))
514.0ms
(log1p (fma (pow x 3) 0.6666666666666667 2.0))

simplify1.2s

Counts
65 → 65
Iterations
IterNodes
done5003
21727
1406
0153

prune481.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (fma (/ (pow x 6) (* 3.0 3.0)) (- 0.2222222222222222) (fma 0.2222222222222222 (pow x 3) (log 3.0))))
0.0b
(fma 0.2222222222222222 (pow x 3) (log 3.0))
0.0b
(/ (pow x 6) (* 3.0 3.0))
13.1b
(fma (/ (pow x 6) (* 3.0 3.0)) (- 0.2222222222222222) (fma 0.2222222222222222 (pow x 3) (log 3.0)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×times-frac associate-/l*
6×unpow-prod-down div-exp
5×log1p-expm1-u
4×expm1-log1p-u pow1 add-log-exp
3×prod-exp
2×pow-to-exp cbrt-undiv pow-exp fma-udef sqr-pow
1×expm1-log1p clear-num associate-/r* frac-2neg cbrt-unprod div-inv expm1-udef
Counts
4 → 66
Calls
4 calls:
1.0ms
(expm1 (fma (/ (pow x 6) (* 3.0 3.0)) (- 0.2222222222222222) (fma 0.2222222222222222 (pow x 3) (log 3.0))))
1.0ms
(fma 0.2222222222222222 (pow x 3) (log 3.0))
18.0ms
(/ (pow x 6) (* 3.0 3.0))
1.0ms
(fma (/ (pow x 6) (* 3.0 3.0)) (- 0.2222222222222222) (fma 0.2222222222222222 (pow x 3) (log 3.0)))

series1.4s

Counts
4 → 12
Calls
4 calls:
566.0ms
(expm1 (fma (/ (pow x 6) (* 3.0 3.0)) (- 0.2222222222222222) (fma 0.2222222222222222 (pow x 3) (log 3.0))))
530.0ms
(fma 0.2222222222222222 (pow x 3) (log 3.0))
68.0ms
(/ (pow x 6) (* 3.0 3.0))
226.0ms
(fma (/ (pow x 6) (* 3.0 3.0)) (- 0.2222222222222222) (fma 0.2222222222222222 (pow x 3) (log 3.0)))

simplify536.0ms

Counts
78 → 78
Iterations
IterNodes
done5001
2788
1241
0119

prune541.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

regimes162.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.2b

bsearch256.0ms

Steps
ItersRangePoint
9
0.6377634613352363
18639768.73979092
326.02657780939904

simplify15.0ms

Iterations
IterNodes
done55
255
149
038

end0.0ms

sample9.1s

Algorithm
intervals
Results
3.3s1938×body10240exit
1.9s9917×body80valid
1.6s1764×body1280valid
841.0ms673×body320valid
714.0ms1287×body640valid
149.0ms299×body160valid