Details

Time bar (total: 13.6s)

sample101.0ms

Algorithm
intervals
Results
24.0ms57×body1280valid
23.0ms61×body10240exit
19.0ms306×body80valid
10.0ms41×body640valid
3.0ms16×body320valid
1.0ms12×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 4 (175.0ms)

IterNodesCost
01929
14729
212429
335327
4100826
5451426
done500026

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
31×flip3-- flip3-+ flip-- flip-+
21×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
14×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-lft-out difference-of-squares
1×sub-neg times-frac fma-neg diff-log prod-diff distribute-lft-out--
Counts
4 → 182
Calls
4 calls:
19.0ms
(* (+ 1.0 eps) x)
50.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
66.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
48.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series328.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (+ 1.0 eps) x)
50.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
50.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
200.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.9s

Counts
194 → 194
Iterations

Useful iterations: 2 (922.0ms)

IterNodesCost
04078453
111577571
242557072
done50007072

prune691.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
6.0b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite9.0ms

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

series114.0ms

Counts
2 → 6
Calls
2 calls:
75.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
38.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify2.2s

Counts
37 → 37
Iterations

Useful iterations: done (2.2s)

IterNodesCost
053544
1119518
2387468
32205433
done5000386

prune97.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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))
6.0b
(- (cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)) (* 1.0 (pow x 2)))

rewrite33.0ms

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:
0.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
2.0ms
(pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)
2.0ms
(cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3))
26.0ms
(- (cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)) (* 1.0 (pow x 2)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
108.0ms
(pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)
74.0ms
(cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3))
42.0ms
(- (cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)) (* 1.0 (pow x 2)))

simplify657.0ms

Counts
114 → 114
Iterations

Useful iterations: done (654.0ms)

IterNodesCost
01161899
12601485
27941298
done50011271

prune264.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×cbrt-prod
10×unpow-prod-down
9×add-exp-log
8×associate-*l*
6×cube-prod prod-diff add-cbrt-cube
5×distribute-rgt-in distribute-lft-in
4×pow1 cube-div unswap-sqr sqr-pow
3×expm1-log1p-u pow-unpow associate-*r* prod-exp log1p-expm1-u add-log-exp
2×cube-mult pow-to-exp sub-neg cbrt-div flip3-+ unpow3 associate-*r/ pow-exp flip-+ unpow2
1×flip3-- pow-pow pow1/3 *-commutative flip-- rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
3 → 93
Calls
3 calls:
7.0ms
(pow (+ 2.0 (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))) 3)
33.0ms
(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))
8.0ms
(cbrt (pow (+ 2.0 (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))) 3))

series180.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(pow (+ 2.0 (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))) 3)
78.0ms
(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))
41.0ms
(cbrt (pow (+ 2.0 (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))) 3))

simplify796.0ms

Counts
102 → 102
Iterations

Useful iterations: done (793.0ms)

IterNodesCost
01861981
14261675
213611429
done50011426

prune216.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes48.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.7b

bsearch147.0ms

Steps
ItersRangePoint
10
0.0001820196720056695
1126179.5725289274
178.4372176880553

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03354
14454
25054
done5054

end0.0ms

sample2.9s

Algorithm
intervals
Results
770.0ms1953×body10240exit
713.0ms1697×body1280valid
539.0ms9940×body80valid
319.0ms1285×body640valid
106.0ms646×body320valid
37.0ms333×body160valid