Details

Time bar (total: 6.3s)

sample103.0ms

Algorithm
intervals
Results
25.0ms49×body1280valid
24.0ms59×body10240exit
18.0ms321×body80valid
12.0ms46×body640valid
3.0ms18×body320valid
1.0ms11×body160valid

simplify39.0ms

Counts
1 → 1
Iterations

Useful iterations: 4 (37.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115
done500115

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 eps))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (+ 1.0 eps) x)
2.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
76×exp-neg frac-times
57×neg-sub0 exp-diff
40×associate-*l/
38×associate-*r/
31×flip3-- flip--
29×flip3-+ flip-+
19×un-div-inv
18×add-sqr-sqrt
15×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
7×add-exp-log
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u
3×fma-def
2×pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out difference-of-squares unswap-sqr
1×+-commutative sub-neg times-frac fma-neg diff-log prod-diff sum-log distribute-lft-out--
Counts
4 → 169
Calls
4 calls:
10.0ms
(+ 1.0 (/ 1.0 eps))
66.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
20.0ms
(* (+ 1.0 eps) x)
47.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ 1.0 (/ 1.0 eps))
51.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
34.0ms
(* (+ 1.0 eps) x)
202.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify151.0ms

Counts
181 → 181
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013343889
149833592
250013592
done50013592

prune623.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 1 expressions with local error:

8.2b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series42.0ms

Counts
1 → 3
Calls
1 calls:
41.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify28.0ms

Counts
13 → 13
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04289
113678
272278
3500275
done500275

prune38.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

8.2b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
13.0b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
13.0b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
13.0b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
1.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
146.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
150.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
140.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify76.0ms

Counts
61 → 61
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0190752
1639693
22777627
35001621
done5001621

prune235.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

8.2b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
8.2b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
13.0b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
13.0b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow1/3 fma-udef
Counts
4 → 46
Calls
4 calls:
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
1.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
45.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
143.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
148.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify78.0ms

Counts
58 → 58
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0190620
1639566
22777522
35001514
done5001514

prune247.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

regimes69.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 17.3b

bsearch126.0ms

Steps
ItersRangePoint
9
0.02319676823116778
6068.335987417336
273.9633798024049

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04822
15822
25822
done5822

end0.0ms

sample3.0s

Algorithm
intervals
Results
800.0ms1951×body10240exit
748.0ms1705×body1280valid
561.0ms10034×body80valid
311.0ms1209×body640valid
117.0ms676×body320valid
31.0ms284×body160valid