Details

Time bar (total: 25.9s)

sample170.0ms

Algorithm
intervals
Results
45.0ms64×body1280valid
37.0ms49×body640valid
29.0ms45×body10240exit
25.0ms284×body80valid
6.0ms22×body320valid
3.0ms13×body160valid

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (328.0ms)

IterNodesCost
01929
14729
212429
335327
4100826
5451426
done500026

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 eps))
0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 eps) x)
2.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
72×exp-neg frac-times
54×neg-sub0 exp-diff
40×associate-*l/
36×associate-*r/
29×flip3-- flip3-+ flip-- flip-+
18×un-div-inv
15×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt associate-*l*
8×pow1 add-exp-log add-cbrt-cube add-log-exp
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 unswap-sqr
1×+-commutative sub-neg fma-neg diff-log prod-diff sum-log distribute-lft-out-- difference-of-squares
Counts
4 → 161
Calls
4 calls:
25.0ms
(+ 1.0 (/ 1.0 eps))
26.0ms
(* (- 1.0 eps) x)
30.0ms
(* (+ 1.0 eps) x)
65.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series435.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ 1.0 (/ 1.0 eps))
45.0ms
(* (- 1.0 eps) x)
35.0ms
(* (+ 1.0 eps) x)
296.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify3.1s

Counts
173 → 173
Iterations

Useful iterations: done (3.1s)

IterNodesCost
03847578
111006803
240856379
done50006325

prune664.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
5.2b
(- (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)))

series156.0ms

Counts
2 → 6
Calls
2 calls:
109.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
48.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify4.1s

Counts
37 → 37
Iterations

Useful iterations: done (4.1s)

IterNodesCost
053544
1119518
2387468
32205433
done5000386

prune159.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)
0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
2.6b
(cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3))
5.2b
(- (cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)) (* 1.0 (pow x 2)))

rewrite42.0ms

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:
3.0ms
(pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)
0.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
2.0ms
(cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3))
33.0ms
(- (cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)) (* 1.0 (pow x 2)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)
116.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
97.0ms
(cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3))
54.0ms
(- (cbrt (pow (fma 0.6666666666666667 (pow x 3) 2.0) 3)) (* 1.0 (pow x 2)))

simplify986.0ms

Counts
114 → 114
Iterations

Useful iterations: done (982.0ms)

IterNodesCost
01161899
12591485
27961298
done50011271

prune463.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 2.666666666666667 (pow x 6) (fma 8.0 (pow x 3) 8.0))
4.5b
(cbrt (fma 2.666666666666667 (pow x 6) (fma 8.0 (pow x 3) 8.0)))
5.3b
(- (cbrt (fma 2.666666666666667 (pow x 6) (fma 8.0 (pow x 3) 8.0))) (* 1.0 (pow x 2)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×fma-neg prod-diff
5×add-log-exp
3×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- pow1/3 diff-log flip-- fma-udef
Counts
3 → 49
Calls
3 calls:
0.0ms
(fma 2.666666666666667 (pow x 6) (fma 8.0 (pow x 3) 8.0))
1.0ms
(cbrt (fma 2.666666666666667 (pow x 6) (fma 8.0 (pow x 3) 8.0)))
11.0ms
(- (cbrt (fma 2.666666666666667 (pow x 6) (fma 8.0 (pow x 3) 8.0))) (* 1.0 (pow x 2)))

series1.1s

Counts
3 → 9
Calls
3 calls:
131.0ms
(fma 2.666666666666667 (pow x 6) (fma 8.0 (pow x 3) 8.0))
712.0ms
(cbrt (fma 2.666666666666667 (pow x 6) (fma 8.0 (pow x 3) 8.0)))
219.0ms
(- (cbrt (fma 2.666666666666667 (pow x 6) (fma 8.0 (pow x 3) 8.0))) (* 1.0 (pow x 2)))

simplify844.0ms

Counts
58 → 58
Iterations

Useful iterations: done (840.0ms)

IterNodesCost
01311394
13201330
210221226
done50001125

prune354.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

regimes109.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.7b

bsearch304.0ms

Steps
ItersRangePoint
11
0.030249150039395014
3.464226407561616e+19
299.41844014586917

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03559
14059
done4059

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.2s1890×body10240exit
1.7s1758×body1280valid
1.5s10032×body80valid
743.0ms1276×body640valid
311.0ms628×body320valid
116.0ms308×body160valid