Details

Time bar (total: 16.9s)

sample74.0ms

Algorithm
intervals
Results
35.0ms82×body1280valid
16.0ms51×body640valid
10.0ms180×body80valid
4.0ms20×body320valid
1.0ms11×body160valid

simplify19.0ms

Calls
1 calls:
Slowest
19.0ms
(/ (- (exp x) 1) x)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize9.0ms

Local error

Found 2 expressions with local error:

3.5b
(- (exp x) 1)
0.0b
(/ (- (exp x) 1) x)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×associate-/l*
3×*-un-lft-identity add-cube-cbrt
2×pow1 flip3-- add-cbrt-cube difference-of-sqr-1 add-exp-log insert-posit16 flip-- add-log-exp associate-/l/
1×clear-num sub-neg frac-2neg div-sub div-inv
Calls
2 calls:
Slowest
15.0ms
(/ (- (exp x) 1) x)
6.0ms
(- (exp x) 1)

series93.0ms

Calls
2 calls:
Slowest
52.0ms
(/ (- (exp x) 1) x)
41.0ms
(- (exp x) 1)

simplify555.0ms

Calls
13 calls:
Slowest
185.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
103.0ms
(* -1 (/ (- 1 (exp x)) x))
58.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
58.0ms
(- (* (exp x) (exp x)) (* 1 1))
39.0ms
(- (pow (exp x) 3) (pow 1 3))

prune271.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.4b
(* 1/6 x)
0.1b
(* x (+ (* 1/6 x) 1/2))
0.0b
(+ (* 1/6 x) 1/2)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×pow1 add-cbrt-cube associate-*r* add-exp-log insert-posit16 add-log-exp
2×flip3-+ associate-*r/ *-commutative flip-+
1×distribute-rgt-in +-commutative distribute-lft-in
Calls
3 calls:
Slowest
6.0ms
(* x (+ (* 1/6 x) 1/2))
2.0ms
(+ (* 1/6 x) 1/2)
0.0ms
(* 1/6 x)

series159.0ms

Calls
3 calls:
Slowest
88.0ms
(* x (+ (* 1/6 x) 1/2))
44.0ms
(+ (* 1/6 x) 1/2)
27.0ms
(* 1/6 x)

simplify545.0ms

Calls
16 calls:
Slowest
266.0ms
(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
59.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))
57.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))
57.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))
17.0ms
(- (* 1/6 x) 1/2)

prune272.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

3.5b
(- (* (exp x) (exp x)) (* 1 1))
0.0b
(* (exp x) (exp x))
0.0b
(/ (/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1)) x)
0.0b
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
22×associate-/l*
9×pow1
8×add-cbrt-cube difference-of-squares
6×add-exp-log add-log-exp
4×associate-/r/ insert-posit16
3×associate-/r* div-sub associate-*r* associate-*l* div-inv associate-/l/
2×clear-num frac-2neg flip3-+ flip3-- flip-+ flip--
1×pow2 cbrt-undiv sub-neg pow-plus diff-log div-exp pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod
Calls
4 calls:
Slowest
18.0ms
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
17.0ms
(/ (/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1)) x)
12.0ms
(* (exp x) (exp x))
10.0ms
(- (* (exp x) (exp x)) (* 1 1))

series211.0ms

Calls
4 calls:
Slowest
98.0ms
(/ (/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1)) x)
73.0ms
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
26.0ms
(- (* (exp x) (exp x)) (* 1 1))
14.0ms
(* (exp x) (exp x))

simplify5.8s

Calls
82 calls:
Slowest
680.0ms
(/ (* (* (- (* (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)))
288.0ms
(/ (- (pow (exp x) 2) 1) (* x (+ (exp x) 1)))
279.0ms
(/ (- (pow (exp x) 2) 1) (* x (+ (exp x) 1)))
209.0ms
(+ (* 2 x) (+ (* 4/3 (pow x 3)) (* 2 (pow x 2))))
176.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))

prune690.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (sqrt (exp x)) 1)
0.0b
(/ (+ (sqrt (exp x)) 1) (/ x (- (sqrt (exp x)) 1)))
0.0b
(/ x (- (sqrt (exp x)) 1))
0.0b
(+ (sqrt (exp x)) 1)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×times-frac
16×*-un-lft-identity add-cube-cbrt
11×associate-/r* associate-/r/
6×flip3-- add-cbrt-cube add-exp-log div-inv flip--
4×pow1 difference-of-sqr-1 insert-posit16 add-log-exp
3×associate-/l*
2×clear-num frac-2neg flip3-+ sqrt-prod flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg div-exp
Calls
4 calls:
Slowest
17.0ms
(/ (+ (sqrt (exp x)) 1) (/ x (- (sqrt (exp x)) 1)))
10.0ms
(- (sqrt (exp x)) 1)
4.0ms
(+ (sqrt (exp x)) 1)
3.0ms
(/ x (- (sqrt (exp x)) 1))

series208.0ms

Calls
4 calls:
Slowest
99.0ms
(/ (+ (sqrt (exp x)) 1) (/ x (- (sqrt (exp x)) 1)))
60.0ms
(/ x (- (sqrt (exp x)) 1))
32.0ms
(- (sqrt (exp x)) 1)
17.0ms
(+ (sqrt (exp x)) 1)

simplify4.2s

Calls
70 calls:
Slowest
376.0ms
(/ (* (cbrt (+ (sqrt (exp x)) 1)) (cbrt (+ (sqrt (exp x)) 1))) (/ x (- (pow (sqrt (exp x)) 3) (pow 1 3))))
296.0ms
(/ (* (cbrt (+ (sqrt (exp x)) 1)) (cbrt (+ (sqrt (exp x)) 1))) (/ x (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1))))
238.0ms
(/ (sqrt (+ (sqrt (exp x)) 1)) (/ x (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1))))
211.0ms
(/ 1 (/ x (- (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1))))
196.0ms
(/ (* (* (+ (sqrt (exp x)) 1) (+ (sqrt (exp x)) 1)) (+ (sqrt (exp x)) 1)) (* (* (/ x (- (sqrt (exp x)) 1)) (/ x (- (sqrt (exp x)) 1))) (/ x (- (sqrt (exp x)) 1))))

prune795.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 19.9b

bsearch47.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
974.0ms2283×body1280valid
659.0ms5406×body80valid
595.0ms1715×body640valid
247.0ms787×body320valid
53.0ms406×body160valid