Details

Time bar (total: 13.4s)

sample117.0ms

Algorithm
intervals
Results
36.0ms78×body10240exit
27.0ms61×body1280valid
19.0ms331×body80valid
12.0ms43×body640valid
3.0ms18×body320valid
2.0ms15×body160valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 4 (147.0ms)

IterNodesCost
01929
14729
212429
332327
4109126
5464426
done500026

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (- 1.0 eps) x)))
0.0b
(* (+ 1.0 eps) x)
0.0b
(exp (- (* (+ 1.0 eps) x)))
3.6b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
74×exp-neg
72×frac-times
56×neg-sub0 exp-diff
38×associate-*l/
36×associate-*r/
28×flip3-- flip3-+ flip-- flip-+
18×un-div-inv
12×exp-prod
10×add-sqr-sqrt *-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 add-exp-log add-cbrt-cube
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 → 158
Calls
4 calls:
4.0ms
(exp (- (* (- 1.0 eps) x)))
10.0ms
(* (+ 1.0 eps) x)
3.0ms
(exp (- (* (+ 1.0 eps) x)))
31.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series294.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(exp (- (* (- 1.0 eps) x)))
29.0ms
(* (+ 1.0 eps) x)
31.0ms
(exp (- (* (+ 1.0 eps) x)))
206.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.2s

Counts
170 → 170
Iterations

Useful iterations: 2 (461.0ms)

IterNodesCost
03817574
112246798
238956366
done50016366

prune465.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
4.8b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite4.0ms

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:
0.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
3.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series128.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
45.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify1.4s

Counts
37 → 37
Iterations

Useful iterations: done (1.4s)

IterNodesCost
053544
1120518
2420468
32482433
done5001430

prune127.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
4.8b
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×associate-*r*
7×add-exp-log add-cube-cbrt *-un-lft-identity add-log-exp
5×associate-+r+
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-diff prod-exp
2×pow1 expm1-log1p-u sum-log log1p-expm1-u sqr-pow
1×+-commutative cube-mult pow-to-exp associate-+r- sub-neg fma-def flip3-+ diff-log unpow3 pow-exp *-commutative cbrt-unprod flip-+
Counts
2 → 54
Calls
2 calls:
7.0ms
(* 0.6666666666666667 (pow x 3))
10.0ms
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

series87.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(* 0.6666666666666667 (pow x 3))
42.0ms
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

simplify2.4s

Counts
60 → 60
Iterations

Useful iterations: done (2.4s)

IterNodesCost
098684
1240603
2722558
33977532
done5000531

prune161.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize14.0ms

Local error

Found 4 expressions with local error:

4.8b
(+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) (- 2.0 (* 1.0 (pow x 2))))
41.0b
(cbrt (* 0.6666666666666667 (pow x 3)))
41.0b
(cbrt (* 0.6666666666666667 (pow x 3)))
41.0b
(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
5×add-sqr-sqrt add-cube-cbrt associate-+r+ *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cbrt-prod pow1/3 prod-diff
2×sum-log
1×+-commutative associate-+r- sub-neg fma-def flip3-+ diff-log flip-+
Counts
4 → 54
Calls
4 calls:
21.0ms
(+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) (- 2.0 (* 1.0 (pow x 2))))
2.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))

series195.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) (- 2.0 (* 1.0 (pow x 2))))
39.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
43.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
39.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))

simplify1.1s

Counts
66 → 66
Iterations

Useful iterations: 3 (266.0ms)

IterNodesCost
0711126
11771078
2476599
32294566
done5000566

prune211.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes84.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.3b

bsearch135.0ms

Steps
ItersRangePoint
8
1.1588875362171251
7686.007879781806
95.54164031582988

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03664
15264
25864
done5864

end0.0ms

sample3.0s

Algorithm
intervals
Results
858.0ms1963×body10240exit
788.0ms1763×body1280valid
584.0ms9939×body80valid
345.0ms1288×body640valid
112.0ms614×body320valid
39.0ms338×body160valid