Details

Time bar (total: 4.7m)

sample98.0ms

Algorithm
intervals
Results
30.0ms81×body10240exit
27.0ms64×body1280valid
17.0ms57×body640valid
7.0ms32×body320valid
5.0ms83×body80valid
2.0ms20×body160valid

simplify39.0ms

Calls
1 calls:
Slowest
39.0ms
(/ (exp x) (- (exp x) 1))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.0b

localize17.0ms

Local error

Found 2 expressions with local error:

4.8b
(- (exp x) 1)
0.3b
(/ (exp x) (- (exp x) 1))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×*-un-lft-identity
21×times-frac
14×add-cube-cbrt
10×difference-of-squares
7×associate-/r*
5×difference-of-sqr-1 add-exp-log distribute-lft-out--
4×add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-- div-exp associate-/r/ insert-posit16 flip--
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-inv
Calls
2 calls:
Slowest
27.0ms
(/ (exp x) (- (exp x) 1))
16.0ms
(- (exp x) 1)

series60.0ms

Calls
2 calls:
Slowest
35.0ms
(/ (exp x) (- (exp x) 1))
26.0ms
(- (exp x) 1)

simplify1.8s

Calls
69 calls:
Slowest
455.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
223.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
65.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
64.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
37.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (sqrt (exp x)) 1))

prune594.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 2 expressions with local error:

0.3b
(* 1/12 x)
0.0b
(+ (* 1/12 x) (+ (/ 1 x) 1/2))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
10×distribute-lft-out
7×add-log-exp
6×add-sqr-sqrt associate-*l*
4×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
3×sum-log associate-*r*
2×+-commutative associate-+r+ insert-posit16 div-inv
1×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Calls
2 calls:
Slowest
63.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
10.0ms
(* 1/12 x)

series57.0ms

Calls
2 calls:
Slowest
30.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
27.0ms
(* 1/12 x)

simplify1.2s

Calls
24 calls:
Slowest
385.0ms
(* (exp (* 1/12 x)) (* (exp (/ 1 x)) (exp 1/2)))
299.0ms
(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
215.0ms
(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
38.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
36.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune311.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

4.7b
(- (* (exp x) (exp x)) (* 1 1))
0.3b
(/ (exp x) (/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1)))
0.2b
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
0.0b
(* (exp x) (exp x))

rewrite433.0ms

Algorithm
rewrite-expression-head
Rules
2422×add-sqr-sqrt
2393×*-un-lft-identity
1906×times-frac
1035×difference-of-squares
691×unswap-sqr
580×add-cube-cbrt
532×swap-sqr
369×*-commutative
297×distribute-lft-out
253×distribute-lft-out--
250×associate-/r*
141×associate-*l*
121×associate-/l*
78×associate-/r/
26×associate-*r*
18×exp-prod add-exp-log
13×add-cbrt-cube
11×pow1
7×div-exp
6×div-inv add-log-exp
5×flip3-+ flip-+
4×cbrt-undiv pow-prod-down prod-exp pow-sqr pow-prod-up insert-posit16 associate-/l/
3×clear-num frac-2neg flip3-- flip--
1×pow2 sub-neg pow-plus diff-log div-sub cbrt-unprod
Calls
4 calls:
Slowest
155.0ms
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
129.0ms
(/ (exp x) (/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1)))
64.0ms
(- (* (exp x) (exp x)) (* 1 1))
16.0ms
(* (exp x) (exp x))

series223.0ms

Calls
4 calls:
Slowest
82.0ms
(/ (exp x) (/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1)))
76.0ms
(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
50.0ms
(- (* (exp x) (exp x)) (* 1 1))
14.0ms
(* (exp x) (exp x))

simplify4.3m

Calls
2461 calls:
Slowest
1.3s
(/ (cbrt (exp x)) (/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1)))
1.3s
(/ (exp x) (/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1)))
903.0ms
(/ (* (exp x) (+ (exp x) 1)) (- (pow (exp x) 2) 1))
838.0ms
(/ (sqrt (exp x)) (/ (- (* (exp x) (exp x)) 1) (cbrt (+ (exp x) 1))))
831.0ms
(/ (* (exp x) (+ (exp x) 1)) (- (pow (exp x) 2) 1))

prune13.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize52.0ms

Local error

Found 4 expressions with local error:

4.7b
(- (* (exp x) (exp x)) (* 1 1))
4.7b
(- (* (exp x) (exp x)) (* 1 1))
4.7b
(- (* (exp x) (exp x)) (* 1 1))
0.3b
(/ (exp x) (/ (* (* (cbrt (- (* (exp x) (exp x)) (* 1 1))) (cbrt (- (* (exp x) (exp x)) (* 1 1)))) (cbrt (- (* (exp x) (exp x)) (* 1 1)))) (+ (exp x) 1)))

rewrite3.8s

Algorithm
rewrite-expression-head
Rules
16612×add-sqr-sqrt
15294×*-un-lft-identity
11330×times-frac
9656×cbrt-prod
7753×associate-*l*
7020×difference-of-squares
6954×swap-sqr
5054×unswap-sqr
3452×add-cube-cbrt
2836×*-commutative
2196×associate-*r*
1988×distribute-lft-out--
1626×associate-/r*
1617×distribute-lft-out
445×associate-/r/
407×associate-/l*
54×cbrt-div
44×add-cbrt-cube
30×flip3-- flip--
28×frac-times add-exp-log
26×associate-/l/
23×cbrt-undiv
18×cbrt-unprod
14×div-exp associate-*l/
10×add-log-exp
8×associate-*r/
6×prod-exp
5×div-inv
4×pow1 flip3-+ flip-+ insert-posit16
3×sub-neg diff-log
2×clear-num frac-2neg
Calls
4 calls:
Slowest
2.9s
(/ (exp x) (/ (* (* (cbrt (- (* (exp x) (exp x)) (* 1 1))) (cbrt (- (* (exp x) (exp x)) (* 1 1)))) (cbrt (- (* (exp x) (exp x)) (* 1 1)))) (+ (exp x) 1)))
77.0ms
(- (* (exp x) (exp x)) (* 1 1))
66.0ms
(- (* (exp x) (exp x)) (* 1 1))
56.0ms
(- (* (exp x) (exp x)) (* 1 1))

series170.0ms

Calls
4 calls:
Slowest
78.0ms
(/ (exp x) (/ (* (* (cbrt (- (* (exp x) (exp x)) (* 1 1))) (cbrt (- (* (exp x) (exp x)) (* 1 1)))) (cbrt (- (* (exp x) (exp x)) (* 1 1)))) (+ (exp x) 1)))
33.0ms
(- (* (exp x) (exp x)) (* 1 1))
29.0ms
(- (* (exp x) (exp x)) (* 1 1))
29.0ms
(- (* (exp x) (exp x)) (* 1 1))