Details

Time bar (total: 21.5s)

sample266.0ms

Algorithm
intervals
Results
96.0ms320×body80valid
54.0ms57×body10240exit
50.0ms53×body1280valid
22.0ms35×body640valid
7.0ms19×body320valid
1.0ms6×body160valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (721.0ms)

IterNodesCost
01929
14729
212429
339527
4233826
done500226

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.1b
(exp (- (* (+ 1.0 eps) x)))
0.1b
(exp (- (* (- 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)))))

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
78×exp-neg
76×frac-times
59×neg-sub0 exp-diff
38×associate-*r/ associate-*l/
31×flip3-- flip--
27×flip3-+ flip-+
19×un-div-inv
15×add-sqr-sqrt
12×exp-prod
10×*-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 associate-*l* add-cbrt-cube
5×add-exp-log
4×expm1-log1p-u log1p-expm1-u rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log difference-of-squares
1×sub-neg times-frac fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 167
Calls
4 calls:
129.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
7.0ms
(exp (- (* (+ 1.0 eps) x)))
9.0ms
(exp (- (* (- 1.0 eps) x)))
72.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series452.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
49.0ms
(exp (- (* (+ 1.0 eps) x)))
30.0ms
(exp (- (* (- 1.0 eps) x)))
295.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify987.0ms

Counts
179 → 179
Iterations

Useful iterations: done (974.0ms)

IterNodesCost
03828008
113097178
done50016962

prune837.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
8.0b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite15.0ms

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)
13.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series206.0ms

Counts
2 → 6
Calls
2 calls:
134.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
73.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify674.0ms

Counts
37 → 37
Iterations

Useful iterations: done (672.0ms)

IterNodesCost
053544
1138530
2634468
done5000433

prune212.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
8.0b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite8.0ms

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)
7.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series175.0ms

Counts
2 → 6
Calls
2 calls:
120.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
54.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify688.0ms

Counts
37 → 37
Iterations

Useful iterations: done (686.0ms)

IterNodesCost
053544
1138530
2634468
done5000433

prune176.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
0.0b
(pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)
3.1b
(cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3))
8.0b
(- (cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)) (* 1.0 (pow x 2)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×fma-neg prod-diff
12×unpow-prod-down cube-prod
6×add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u sqr-pow
3×pow-unpow
1×pow-to-exp sub-neg flip3-- pow-pow pow1/3 diff-log pow-exp flip-- rem-cbrt-cube fma-udef rem-cube-cbrt
Counts
4 → 102
Calls
4 calls:
1.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
6.0ms
(pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)
5.0ms
(cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3))
59.0ms
(- (cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)) (* 1.0 (pow x 2)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
169.0ms
(pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)
144.0ms
(cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3))
49.0ms
(- (cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)) (* 1.0 (pow x 2)))

simplify3.9s

Counts
114 → 114
Iterations

Useful iterations: 2 (338.0ms)

IterNodesCost
01161899
13181529
222221298
done50001298

prune500.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes95.0ms

Accuracy

96.7% (0.5b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.7b

bsearch234.0ms

Steps
ItersRangePoint
8
1.4124627081995123
1575.9184687212278
14.67295150394162

simplify11.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03450
15148
25948
done5948

end0.0ms

sample9.1s

Algorithm
intervals
Results
2.6s1858×body10240exit
2.4s10005×body80valid
1.8s1697×body1280valid
1.2s1244×body640valid
257.0ms640×body320valid
71.0ms309×body160valid