Details

Time bar (total: 10.7s)

sample32.0ms

Algorithm
intervals
Results
13.0ms87×body1280valid
4.0ms43×body640valid
3.0ms176×body80valid
2.0ms27×body320valid
1.0ms16×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
066
1116
2186
3266
4496
51076
62466
77026
824266
done50006

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
3.8b
(- (exp (* a x)) 1.0)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt *-un-lft-identity
2×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
1×sub-neg exp-prod flip3-- exp-to-pow diff-log flip-- rem-exp-log distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
1.0ms
(exp (* a x))
4.0ms
(- (exp (* a x)) 1.0)

series52.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(exp (* a x))
40.0ms
(- (exp (* a x)) 1.0)

simplify3.0s

Counts
30 → 30
Iterations

Useful iterations: 4 (974.0ms)

IterNodesCost
053263
1116248
2312232
31006228
44638226
done5000226

prune74.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
4.8b
(* (* 1/6 (pow a 3)) x)
8.1b
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
9.1b
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt add-cbrt-cube
10×pow1
9×add-cube-cbrt *-un-lft-identity associate-*r* prod-exp
7×associate-*l*
6×add-log-exp
5×cbrt-unprod
4×associate-*r/
3×flip3-+ pow-prod-down *-commutative flip-+
2×distribute-rgt-in distribute-lft-in unswap-sqr
1×+-commutative pow-to-exp pow-exp sum-log
Counts
4 → 74
Calls
4 calls:
7.0ms
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
10.0ms
(* (* 1/6 (pow a 3)) x)
11.0ms
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
3.0ms
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

series316.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
29.0ms
(* (* 1/6 (pow a 3)) x)
120.0ms
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
64.0ms
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

simplify712.0ms

Counts
86 → 86
Iterations

Useful iterations: done (709.0ms)

IterNodesCost
01371638
14041524
216971362
done50011360

prune216.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.2b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))))
4.8b
(* (* 1/6 (pow a 3)) x)
8.1b
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
9.1b
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
17×add-cbrt-cube
16×prod-exp
12×cbrt-unprod
10×pow-prod-down
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity associate-*r*
6×associate-*r/ add-log-exp
5×distribute-rgt-in distribute-lft-in associate-*l*
3×flip3-+ *-commutative flip-+
1×+-commutative pow-to-exp pow-exp sum-log unswap-sqr
Counts
4 → 80
Calls
4 calls:
21.0ms
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))))
10.0ms
(* (* 1/6 (pow a 3)) x)
11.0ms
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
4.0ms
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

series345.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))))
27.0ms
(* (* 1/6 (pow a 3)) x)
126.0ms
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
64.0ms
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

simplify804.0ms

Counts
92 → 92
Iterations

Useful iterations: done (801.0ms)

IterNodesCost
01592085
14911966
221221552
done50001550

prune253.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.2b

localize23.0ms

Local error

Found 4 expressions with local error:

9.1b
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
20.1b
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))
20.1b
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))
20.1b
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-div associate-*l/ add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ add-cbrt-cube flip-+
3×cbrt-prod pow1/3
1×+-commutative sum-log
Counts
4 → 44
Calls
4 calls:
4.0ms
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
5.0ms
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))
8.0ms
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))
5.0ms
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))

series945.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
289.0ms
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))
293.0ms
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))
298.0ms
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))

simplify455.0ms

Counts
56 → 56
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
01192098
13331866
211861699
done50001699

prune329.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.2b

regimes95.0ms

Accuracy

50% (12.0b remaining)

Error of 14.4b against oracle of 2.4b and baseline of 26.4b

bsearch100.0ms

Steps
ItersRangePoint
10
0.0005333266348582408
7738264586.128652
6913276300.677357
7
-4.233477147491156e+82
-6.388473830684138e+80
-1.8775905144238698e+82

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03161
14345
done4345

end0.0ms

sample906.0ms

Algorithm
intervals
Results
416.0ms2689×body1280valid
125.0ms1271×body640valid
102.0ms5525×body80valid
49.0ms760×body320valid
19.0ms433×body160valid