Details

Time bar (total: 29.3s)

sample247.0ms

Algorithm
intervals
Results
89.0ms69×body10240exit
45.0ms54×body1280valid
45.0ms348×body80valid
23.0ms42×body640valid
8.0ms22×body320valid
2.0ms9×body160valid

simplify4.3s

Counts
1 → 1
Iterations

Useful iterations: 4 (279.0ms)

IterNodesCost
01929
14729
212429
335327
4100826
5451426
done500026

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 eps) 1.0)
0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 eps) x)
1.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
72×exp-neg frac-times
60×add-sqr-sqrt
55×*-un-lft-identity
54×neg-sub0 exp-diff
49×add-cube-cbrt
40×prod-diff associate-*l/
37×times-frac
36×associate-*r/
30×flip3-- flip--
28×flip3-+ flip-+
18×un-div-inv
14×fma-neg
9×associate-*l*
8×pow1 add-exp-log add-cbrt-cube add-log-exp
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u div-inv
3×difference-of-squares
2×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
1×distribute-lft-out
Counts
4 → 213
Calls
4 calls:
30.0ms
(- (/ 1.0 eps) 1.0)
33.0ms
(* (- 1.0 eps) x)
26.0ms
(* (+ 1.0 eps) x)
63.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series487.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (/ 1.0 eps) 1.0)
48.0ms
(* (- 1.0 eps) x)
42.0ms
(* (+ 1.0 eps) x)
347.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify3.2s

Counts
225 → 225
Iterations

Useful iterations: done (3.2s)

IterNodesCost
04628754
112467604
243747003
done50006989

prune981.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
5.6b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite13.0ms

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)
11.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series176.0ms

Counts
2 → 6
Calls
2 calls:
110.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
65.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify3.4s

Counts
37 → 37
Iterations

Useful iterations: done (3.4s)

IterNodesCost
053544
1119518
2387468
32205433
done5000386

prune176.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)) (cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
10.7b
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
10.7b
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
10.7b
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
20.0ms
(* (cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)) (cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
1.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
1.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
1.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
309.0ms
(* (cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)) (cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
251.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
263.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
193.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

simplify2.4s

Counts
93 → 93
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01522510
13452345
210142175
334111750
done50021679

prune426.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

2.2b
(expm1 (log1p (cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))))
10.7b
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
10.7b
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
10.7b
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×expm1-log1p expm1-udef
Counts
4 → 50
Calls
4 calls:
0.0ms
(expm1 (log1p (cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))))
1.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
1.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
1.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
454.0ms
(expm1 (log1p (cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))))
254.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
232.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
216.0ms
(cbrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

simplify874.0ms

Counts
62 → 62
Iterations

Useful iterations: done (871.0ms)

IterNodesCost
01231726
13171649
210291544
done50001276

prune350.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes115.0ms

Accuracy

96.5% (0.6b remaining)

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

bsearch281.0ms

Steps
ItersRangePoint
10
6.100620313640196e-08
81116161.23870511
331.75996649696236

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03046
14146
24346
done4346

end0.0ms

sample9.5s

Algorithm
intervals
Results
3.2s10027×body80valid
2.4s1957×body10240exit
1.9s1775×body1280valid
952.0ms1287×body640valid
304.0ms612×body320valid
73.0ms303×body160valid