Details

Time bar (total: 9.6m)

sample522.0ms

Algorithm
intervals
Results
145.0ms49×body1280valid
127.0ms60×body640valid
97.0ms210×body80valid
87.0ms31×body320valid
39.0ms12×body160valid

simplify518.0ms

Calls
1 calls:
Slowest
517.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune71.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.8b

localize93.0ms

Local error

Found 4 expressions with local error:

13.8b
(/ (/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t)))) (fma (/ k t) (/ k t) 2))
3.4b
(/ (* t (tan k)) (* (/ l t) (/ l t)))
2.6b
(/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t))))
0.3b
(* (/ l t) (/ l t))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
293×times-frac
110×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
71×associate-/r/ div-inv
42×associate-/l*
34×add-cbrt-cube add-exp-log
24×associate-*r/
23×frac-times associate-*l/
16×cbrt-undiv div-exp
12×associate-/r*
9×pow1
4×expm1-log1p-u associate-*r* associate-*l* prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-/l/
1×pow2 pow-plus pow-prod-down tan-quot *-commutative pow-prod-up
Calls
4 calls:
Slowest
53.0ms
(/ (/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t)))) (fma (/ k t) (/ k t) 2))
36.0ms
(/ (* t (tan k)) (* (/ l t) (/ l t)))
27.0ms
(/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t))))
8.0ms
(* (/ l t) (/ l t))

series1.5s

Calls
4 calls:
Slowest
924.0ms
(/ (/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t)))) (fma (/ k t) (/ k t) 2))
308.0ms
(/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t))))
232.0ms
(/ (* t (tan k)) (* (/ l t) (/ l t)))
38.0ms
(* (/ l t) (/ l t))

simplify3.1m

Calls
385 calls:
Slowest
4.2s
(/ (/ (* (* (/ 2 (sin k)) (/ 2 (sin k))) (/ 2 (sin k))) (/ (* (* (* t (tan k)) (* t (tan k))) (* t (tan k))) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2)))
4.0s
(/ (/ (* (* (/ 2 (sin k)) (/ 2 (sin k))) (/ 2 (sin k))) (/ (* (* (* t (tan k)) (* t (tan k))) (* t (tan k))) (* (* (* (/ l t) (/ l t)) (* (/ l t) (/ l t))) (* (/ l t) (/ l t))))) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2)))
3.3s
(/ (/ (cbrt (/ 2 (sin k))) (/ (* t (tan k)) (* (/ l t) (/ l t)))) (sqrt (fma (/ k t) (/ k t) 2)))
2.5s
(/ (* (* (/ 2 (sin k)) (/ 2 (sin k))) (/ 2 (sin k))) (* (* (/ (* t (tan k)) (* (/ l t) (/ l t))) (/ (* t (tan k)) (* (/ l t) (/ l t)))) (/ (* t (tan k)) (* (/ l t) (/ l t)))))
2.4s
(/ (/ (* (* (/ 2 (sin k)) (/ 2 (sin k))) (/ 2 (sin k))) (* (* (/ (* t (tan k)) (* (/ l t) (/ l t))) (/ (* t (tan k)) (* (/ l t) (/ l t)))) (/ (* t (tan k)) (* (/ l t) (/ l t))))) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2)))

prune8.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.9b

localize41.0ms

Local error

Found 4 expressions with local error:

10.8b
(* (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l)) (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
8.3b
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))
2.6b
(/ (tan k) (/ l t))
0.6b
(cbrt (/ 2 (sin k)))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
2177×times-frac
901×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
480×cbrt-prod
376×associate-*r*
330×div-inv
127×associate-/l*
57×associate-/r/
47×add-exp-log
41×add-cbrt-cube
19×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
9×pow1 associate-*l/
7×associate-/r*
5×frac-times
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down associate-*r/
2×clear-num frac-2neg associate-/l/
1×cbrt-div pow1/3 associate-*l* tan-quot *-commutative
Calls
4 calls:
Slowest
83.0ms
(* (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l)) (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
22.0ms
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))
7.0ms
(/ (tan k) (/ l t))
1.0ms
(cbrt (/ 2 (sin k)))

series3.2s

Calls
4 calls:
Slowest
1.3s
(* (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l)) (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
963.0ms
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))
594.0ms
(cbrt (/ 2 (sin k)))
357.0ms
(/ (tan k) (/ l t))

simplify5.9m

Calls
1332 calls:
Slowest
3.6s
(* (* (* (* (/ (cbrt (/ 2 (sin k))) t) (/ (cbrt (/ 2 (sin k))) t)) (/ (cbrt (/ 2 (sin k))) t)) (* (* (* (/ (cbrt (/ 2 (sin k))) t) l) (* (/ (cbrt (/ 2 (sin k))) t) l)) (* (/ (cbrt (/ 2 (sin k))) t) l))) (/ (* (* (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t)))) (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t)))) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))))
3.1s
(/ (/ (sqrt (cbrt (/ 2 (sin k)))) (/ (tan k) (/ l t))) (sqrt (fma (/ k t) (/ k t) 2)))
2.8s
(* (* (* (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l)) (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l))) (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l))) (/ (/ (/ 2 (sin k)) (/ (* (* (tan k) (tan k)) (tan k)) (* (* (/ l t) (/ l t)) (/ l t)))) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))))
2.4s
(* (* (* (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l)) (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l))) (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l))) (/ (* (* (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t)))) (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t)))) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))))
2.4s
(* (* (* (* (/ (cbrt (/ 2 (sin k))) t) (/ (cbrt (/ 2 (sin k))) t)) (/ (cbrt (/ 2 (sin k))) t)) (* (* (* (/ (cbrt (/ 2 (sin k))) t) l) (* (/ (cbrt (/ 2 (sin k))) t) l)) (* (/ (cbrt (/ 2 (sin k))) t) l))) (/ (/ (/ 2 (sin k)) (/ (* (* (tan k) (tan k)) (tan k)) (* (* (/ l t) (/ l t)) (/ l t)))) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))))

prune11.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.6b

localize43.0ms

Local error

Found 4 expressions with local error:

14.2b
(cbrt (/ l t))
14.2b
(cbrt (/ l t))
14.2b
(cbrt (/ l t))
10.6b
(sqrt (fma (/ k t) (/ k t) 2))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
1×rem-sqrt-square pow1/2
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma (/ k t) (/ k t) 2))
1.0ms
(cbrt (/ l t))
1.0ms
(cbrt (/ l t))
1.0ms
(cbrt (/ l t))

series190.0ms

Calls
4 calls:
Slowest
57.0ms
(cbrt (/ l t))
56.0ms
(cbrt (/ l t))
55.0ms
(cbrt (/ l t))
23.0ms
(sqrt (fma (/ k t) (/ k t) 2))

simplify1.5s

Calls
31 calls:
Slowest
395.0ms
(exp (* 1/3 (- (log (/ 1 t)) (log (/ 1 l)))))
156.0ms
(exp (* 1/3 (- (log (/ -1 t)) (log (/ -1 l)))))
154.0ms
(exp (* 1/3 (- (log (/ -1 t)) (log (/ -1 l)))))
153.0ms
(exp (* 1/3 (- (log (/ -1 t)) (log (/ -1 l)))))
148.0ms
(exp (* 1/3 (- (log (/ 1 t)) (log (/ 1 l)))))

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.6b

localize19.0ms

Local error

Found 4 expressions with local error:

24.4b
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
24.4b
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
24.4b
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
9.8b
(* (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l)) (* (cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))) (cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
2943×times-frac
1740×cbrt-prod
1198×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
417×div-inv
72×associate-/r/
19×cbrt-div associate-*l/
17×frac-times
16×pow1 add-exp-log
12×add-cbrt-cube
11×associate-*r/
8×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×associate-*r* associate-*l* *-commutative
Calls
4 calls:
Slowest
58.0ms
(* (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l)) (* (cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))) (cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))))
5.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
5.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
5.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))

series1.9s

Calls
4 calls:
Slowest
636.0ms
(* (* (/ (cbrt (/ 2 (sin k))) t) (* (/ (cbrt (/ 2 (sin k))) t) l)) (* (cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))) (cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))))
436.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
433.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
432.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))