Details

Time bar (total: 11.8s)

sample32.0ms

Algorithm
intervals
Results
11.0ms79×body1280valid
6.0ms42×body640valid
3.0ms185×body80valid
1.0ms24×body320valid
1.0ms17×body160valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
066
1116
2186
3266
4496
51076
62466
77026
824296
done50016

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
4.5b
(- (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)

series49.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(exp (* a x))
37.0ms
(- (exp (* a x)) 1.0)

simplify2.9s

Counts
30 → 30
Iterations

Useful iterations: 4 (1.8s)

IterNodesCost
053263
1116248
2312232
31006228
44632226
done5000226

prune77.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
4.0b
(* (* 1/6 (pow a 3)) x)
9.2b
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
9.5b
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

rewrite35.0ms

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)
3.0ms
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
12.0ms
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
32.0ms
(* (* 1/6 (pow a 3)) x)
59.0ms
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
123.0ms
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

simplify890.0ms

Counts
86 → 86
Iterations

Useful iterations: done (888.0ms)

IterNodesCost
01371638
14041524
216951362
done50011360

prune226.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.4b

localize22.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))))
4.0b
(* (* 1/6 (pow a 3)) x)
9.2b
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
9.5b
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

rewrite50.0ms

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:
22.0ms
(* (* (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)
4.0ms
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
12.0ms
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))))
32.0ms
(* (* 1/6 (pow a 3)) x)
64.0ms
(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
121.0ms
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

simplify1.1s

Counts
92 → 92
Iterations

Useful iterations: 2 (397.0ms)

IterNodesCost
01592085
14911966
221251552
done50001552

prune247.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.4b

localize28.0ms

Local error

Found 4 expressions with local error:

9.5b
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
17.2b
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))
17.2b
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))
17.2b
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt cbrt-div *-un-lft-identity associate-*l/ add-cbrt-cube
4×flip3-+ flip-+ add-log-exp
3×cbrt-prod pow1/3 associate-*r* associate-*l*
2×associate-*r/
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 55
Calls
4 calls:
12.0ms
(* x (+ (* 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)))
5.0ms
(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)))

series979.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
291.0ms
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))
280.0ms
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))
287.0ms
(cbrt (* (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))) (pow (cbrt x) 3)))

simplify590.0ms

Counts
67 → 67
Iterations

Useful iterations: 2 (143.0ms)

IterNodesCost
01362307
13722047
212891880
done50011880

prune341.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.4b

regimes171.0ms

Accuracy

87.7% (2.9b remaining)

Error of 5.3b against oracle of 2.4b and baseline of 26.2b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03561
14761
done4761

end0.0ms

sample902.0ms

Algorithm
intervals
Results
420.0ms2649×body1280valid
133.0ms1371×body640valid
100.0ms5510×body80valid
49.0ms781×body320valid
17.0ms391×body160valid