Details

Time bar (total: 21.5s)

sample62.0ms

Algorithm
intervals
Results
29.0ms77×body1280valid
12.0ms50×body640valid
8.0ms169×body80valid
4.0ms26×body320valid
2.0ms22×body160valid

simplify17.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
17.0ms
(/ (- (exp x) 1) x)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize17.0ms

Local error

Found 1 expressions with local error:

6.0b
(- (exp x) 1)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×*-un-lft-identity
3×add-log-exp
2×difference-of-squares
1×pow1 sub-neg flip3-- add-cbrt-cube diff-log difference-of-sqr-1 add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out--
Counts
1 → 17
Calls
1 calls:
Slowest
8.0ms
(- (exp x) 1)

series15.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
15.0ms
(- (exp x) 1)

simplify332.0ms

Counts
10 → 20
Calls
10 calls:
Slowest
212.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
23.0ms
(/ (exp (exp x)) (exp 1))
22.0ms
(- (sqrt (exp x)) 1)
15.0ms
(- (exp x) 1)
13.0ms
(- (exp x) 1)

prune156.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ (+ x (* (* x x) (+ (* x 1/6) 1/2))) x)
0.3b
(* x 1/6)
0.1b
(* (* x x) (+ (* x 1/6) 1/2))
0.0b
(+ (* x 1/6) 1/2)

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube add-exp-log
11×pow1
9×times-frac
6×associate-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16
3×associate-/r* flip3-+ flip-+ associate-/l*
2×associate-*r/ *-commutative unswap-sqr associate-/l/
1×distribute-rgt-in cbrt-undiv +-commutative clear-num sum-log frac-2neg distribute-lft-in div-exp div-inv
Counts
4 → 85
Calls
4 calls:
Slowest
34.0ms
(/ (+ x (* (* x x) (+ (* x 1/6) 1/2))) x)
31.0ms
(* (* x x) (+ (* x 1/6) 1/2))
6.0ms
(+ (* x 1/6) 1/2)
5.0ms
(* x 1/6)

series246.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
86.0ms
(* (* x x) (+ (* x 1/6) 1/2))
79.0ms
(/ (+ x (* (* x x) (+ (* x 1/6) 1/2))) x)
58.0ms
(+ (* x 1/6) 1/2)
23.0ms
(* x 1/6)

simplify6.2s

Counts
63 → 97
Calls
63 calls:
Slowest
324.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
276.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
246.0ms
(/ (* (* (+ x (* (* x x) (+ (* x 1/6) 1/2))) (+ x (* (* x x) (+ (* x 1/6) 1/2)))) (+ x (* (* x x) (+ (* x 1/6) 1/2)))) (* (* x x) x))
241.0ms
(+ (* (* x 1/6) (* x 1/6)) (- (* 1/2 1/2) (* (* x 1/6) 1/2)))
230.0ms
(/ (* (cbrt (+ x (* (* x x) (+ (* x 1/6) 1/2)))) (cbrt (+ x (* (* x x) (+ (* x 1/6) 1/2))))) (* (cbrt x) (cbrt x)))

prune703.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

5.9b
(- (* (exp x) (exp x)) (* 1 1))
0.0b
(* (exp x) (exp x))
0.0b
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
0.0b
(+ (exp x) 1)

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
26×add-sqr-sqrt
24×add-cube-cbrt
18×exp-prod
16×times-frac
11×pow1
8×add-cbrt-cube add-log-exp
6×add-exp-log distribute-lft-out difference-of-squares
4×associate-/r* pow-prod-down pow-sqr pow-prod-up insert-posit16 associate-/l*
3×swap-sqr associate-*r* associate-*l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×pow2 cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg pow-plus diff-log div-sub div-exp prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 104
Calls
4 calls:
Slowest
49.0ms
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
26.0ms
(- (* (exp x) (exp x)) (* 1 1))
14.0ms
(* (exp x) (exp x))
6.0ms
(+ (exp x) 1)

series126.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
26.0ms
(- (* (exp x) (exp x)) (* 1 1))
22.0ms
(* (exp x) (exp x))
14.0ms
(+ (exp x) 1)

simplify5.6s

Counts
101 → 116
Calls
101 calls:
Slowest
635.0ms
(/ (* (* (- (* (exp x) (exp x)) (* 1 1)) (- (* (exp x) (exp x)) (* 1 1))) (- (* (exp x) (exp x)) (* 1 1))) (* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1)))
404.0ms
(/ (- (pow (exp x) 2) 1) (+ (exp x) 1))
330.0ms
(/ (- (pow (exp x) 2) 1) (+ (exp x) 1))
268.0ms
(/ (exp (* (exp x) (exp x))) (exp (* 1 1)))
244.0ms
(- (pow (* (exp x) (exp x)) 3) (pow (* 1 1) 3))

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

6.0b
(- (* 1 1) (* (exp x) 1))
5.9b
(- (* (exp x) (exp x)) (* 1 1))
0.0b
(pow (exp x) 3)
0.0b
(* (exp x) (exp x))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
21×exp-prod
20×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
12×pow1
8×add-log-exp
7×add-cbrt-cube
4×pow-pow pow-prod-down add-exp-log pow-sqr pow-prod-up insert-posit16
3×pow-unpow unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l*
2×sub-neg flip3-- diff-log flip--
1×pow2 cube-mult pow-to-exp pow-plus distribute-rgt-out-- unpow3 pow-exp prod-exp *-commutative cbrt-unprod rem-cube-cbrt difference-of-squares unswap-sqr sqr-pow
Counts
4 → 90
Calls
4 calls:
Slowest
26.0ms
(* (exp x) (exp x))
23.0ms
(- (* (exp x) (exp x)) (* 1 1))
10.0ms
(- (* 1 1) (* (exp x) 1))
7.0ms
(pow (exp x) 3)

series115.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
38.0ms
(- (* (exp x) (exp x)) (* 1 1))
31.0ms
(pow (exp x) 3)
25.0ms
(- (* 1 1) (* (exp x) 1))
21.0ms
(* (exp x) (exp x))

simplify2.4s

Counts
69 → 102
Calls
69 calls:
Slowest
293.0ms
(/ (exp (* (exp x) (exp x))) (exp (* 1 1)))
261.0ms
(* (exp (* (cbrt x) (cbrt x))) (exp (* (cbrt x) (cbrt x))))
229.0ms
(+ (* 2 x) (+ (* 4/3 (pow x 3)) (* 2 (pow x 2))))
183.0ms
(pow (* (cbrt (exp x)) (cbrt (exp x))) 3)
178.0ms
(* (* (* (exp x) (exp x)) (exp x)) (* (* (exp x) (exp x)) (exp x)))

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 20.4b

bsearch75.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s2291×body1280valid
587.0ms1736×body640valid
322.0ms5346×body80valid
155.0ms808×body320valid
55.0ms445×body160valid