Details

Time bar (total: 18.7s)

sample277.0ms

Algorithm
intervals
Results
75.0ms42×body640valid
68.0ms64×body10240exit
44.0ms49×body1280valid
39.0ms322×body80valid
8.0ms20×body320valid
2.0ms9×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 4 (345.0ms)

IterNodesCost
01929
14729
212429
339527
4233826
done500226

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.7b

localize44.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.3b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
2.7b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
40×associate-*r/ associate-*l/
31×flip3-- flip--
30×flip3-+ flip-+
20×un-div-inv
16×add-sqr-sqrt
11×*-un-lft-identity
10×associate-*l*
7×pow1 add-cube-cbrt add-cbrt-cube
6×associate-*r*
5×add-exp-log add-log-exp
3×expm1-log1p-u log1p-expm1-u
2×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
1×sub-neg times-frac fma-neg diff-log prod-diff distribute-lft-out distribute-lft-out--
Counts
3 → 159
Calls
3 calls:
54.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
106.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
52.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series451.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
78.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
304.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify904.0ms

Counts
168 → 168
Iterations

Useful iterations: done (895.0ms)

IterNodesCost
03748257
113317383
done50017175

prune644.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
6.6b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
3×fma-neg prod-diff
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube fma-udef log1p-expm1-u
1×sub-neg flip3-- diff-log associate--l+ flip--
Counts
2 → 31
Calls
2 calls:
1.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
11.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series170.0ms

Counts
2 → 6
Calls
2 calls:
113.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
57.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify639.0ms

Counts
37 → 37
Iterations

Useful iterations: done (637.0ms)

IterNodesCost
053544
1138530
2634468
done5000433

prune193.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
6.6b
(+ (* 0.6666666666666667 (pow x 3)) (fma x (* x (- 1.0)) 2.0))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube add-log-exp unswap-sqr
3×associate-*l* prod-exp
2×pow1 expm1-log1p-u log1p-expm1-u sqr-pow
1×+-commutative cube-mult pow-to-exp associate-+r+ fma-def flip3-+ unpow3 pow-exp sum-log *-commutative cbrt-unprod flip-+ fma-udef
Counts
2 → 48
Calls
2 calls:
22.0ms
(* 0.6666666666666667 (pow x 3))
21.0ms
(+ (* 0.6666666666666667 (pow x 3)) (fma x (* x (- 1.0)) 2.0))

series107.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(* 0.6666666666666667 (pow x 3))
54.0ms
(+ (* 0.6666666666666667 (pow x 3)) (fma x (* x (- 1.0)) 2.0))

simplify854.0ms

Counts
54 → 54
Iterations

Useful iterations: done (851.0ms)

IterNodesCost
087607
1231534
2891495
done5000491

prune222.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
0.1b
(* 0.6666666666666667 (pow x 3))
11.4b
(+ (pow (* 0.6666666666666667 (pow x 3)) 3) (pow (fma x (* x (- 1.0)) 2.0) 3))
13.5b
(/ (+ (pow (* 0.6666666666666667 (pow x 3)) 3) (pow (fma x (* x (- 1.0)) 2.0) 3)) (fma (fma x (* x (- 1.0)) 2.0) (- (fma x (* x (- 1.0)) 2.0) (* 0.6666666666666667 (pow x 3))) (* (* 0.6666666666666667 0.6666666666666667) (pow x 6))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
33×*-un-lft-identity
24×associate-*r*
23×add-cube-cbrt
16×add-exp-log
15×times-frac
10×add-cbrt-cube
9×unpow-prod-down cube-prod
8×fma-def unswap-sqr
6×associate-*l* prod-exp add-log-exp
5×sum-cubes distribute-lft-out associate-/l* sqr-pow
4×pow1 expm1-log1p-u log1p-expm1-u
3×cube-mult unpow3 associate-/r*
2×pow-to-exp flip3-+ pow-exp *-commutative cbrt-unprod flip-+ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 128
Calls
4 calls:
14.0ms
(* 0.6666666666666667 (pow x 3))
22.0ms
(* 0.6666666666666667 (pow x 3))
28.0ms
(+ (pow (* 0.6666666666666667 (pow x 3)) 3) (pow (fma x (* x (- 1.0)) 2.0) 3))
87.0ms
(/ (+ (pow (* 0.6666666666666667 (pow x 3)) 3) (pow (fma x (* x (- 1.0)) 2.0) 3)) (fma (fma x (* x (- 1.0)) 2.0) (- (fma x (* x (- 1.0)) 2.0) (* 0.6666666666666667 (pow x 3))) (* (* 0.6666666666666667 0.6666666666666667) (pow x 6))))

series571.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* 0.6666666666666667 (pow x 3))
63.0ms
(* 0.6666666666666667 (pow x 3))
162.0ms
(+ (pow (* 0.6666666666666667 (pow x 3)) 3) (pow (fma x (* x (- 1.0)) 2.0) 3))
275.0ms
(/ (+ (pow (* 0.6666666666666667 (pow x 3)) 3) (pow (fma x (* x (- 1.0)) 2.0) 3)) (fma (fma x (* x (- 1.0)) 2.0) (- (fma x (* x (- 1.0)) 2.0) (* 0.6666666666666667 (pow x 3))) (* (* 0.6666666666666667 0.6666666666666667) (pow x 6))))

simplify1.8s

Counts
140 → 140
Iterations

Useful iterations: 2 (365.0ms)

IterNodesCost
01693890
14133685
219443426
done50003426

prune738.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

regimes122.0ms

Accuracy

96.5% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.5b

bsearch138.0ms

Steps
ItersRangePoint
7
0.4989185846411821
15.006088268796836
10.278504282981798

simplify34.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04192
15692
26492
36592
done6592

end0.0ms

sample8.7s

Algorithm
intervals
Results
2.9s1702×body1280valid
2.6s1919×body10240exit
1.3s10083×body80valid
727.0ms1249×body640valid
363.0ms626×body320valid
71.0ms329×body160valid