Details

Time bar (total: 8.2m)

sample428.0ms

Algorithm
intervals
Results
186.0ms64×body1280valid
104.0ms59×body640valid
65.0ms180×body80valid
36.0ms22×body320valid
13.0ms16×body160valid

simplify210.0ms

Calls
1 calls:
Slowest
210.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.8b

localize36.0ms

Local error

Found 4 expressions with local error:

14.7b
(/ (/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t)))) (fma (/ k t) (/ k t) 2))
3.0b
(/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t))))
2.8b
(/ (* t (tan k)) (* (/ l t) (/ l t)))
0.2b
(* (/ l t) (/ l t))

rewrite36.0ms

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
12.0ms
(/ (/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t)))) (fma (/ k t) (/ k t) 2))
8.0ms
(/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t))))
7.0ms
(/ (* t (tan k)) (* (/ l t) (/ l t)))
4.0ms
(* (/ l t) (/ l t))

series1.0s

Calls
4 calls:
Slowest
681.0ms
(/ (/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t)))) (fma (/ k t) (/ k t) 2))
212.0ms
(/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t))))
129.0ms
(/ (* t (tan k)) (* (/ l t) (/ l t)))
14.0ms
(* (/ l t) (/ l t))

simplify1.5m

Calls
385 calls:
Slowest
1.3s
(/ (/ (* (* (/ 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)))
1.2s
(/ (/ (* (* (/ 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)))
1.2s
(/ (/ (* (* (/ 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)))
1.2s
(/ (* (* (/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t)))) (/ (/ 2 (sin k)) (/ (* t (tan k)) (* (/ l t) (/ l t))))) (/ (/ 2 (sin k)) (/ (* 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)))
1.0s
(/ (* (* (/ 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)))))

prune4.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.6b

localize46.0ms

Local error

Found 4 expressions with local error:

13.6b
(* (* (/ (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)))
6.8b
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))
3.4b
(/ (tan k) (/ l t))
0.9b
(/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t)))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
2392×times-frac
1000×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
548×cbrt-prod
380×div-inv
376×associate-*r*
134×associate-/l*
66×associate-/r/
52×add-exp-log
44×add-cbrt-cube
24×associate-/r*
22×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
9×pow1 associate-*l/
5×frac-times
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down associate-*r/ associate-/l/
1×cbrt-div associate-*l* tan-quot *-commutative
Calls
4 calls:
Slowest
37.0ms
(* (* (/ (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)))
15.0ms
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))
8.0ms
(/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t)))
4.0ms
(/ (tan k) (/ l t))

series1.7s

Calls
4 calls:
Slowest
813.0ms
(* (* (/ (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)))
482.0ms
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))
279.0ms
(/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t)))
128.0ms
(/ (tan k) (/ l t))

simplify3.6m

Calls
1593 calls:
Slowest
1.5s
(* (* (* (* (/ (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))))
1.3s
(* (* (* (* (/ (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))))
1.3s
(* (* (* (* (/ (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))))
1.3s
(* (* (* (* (/ (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))))
985.0ms
(+ (+ (log (/ (cbrt (/ 2 (sin k))) t)) (log (* (/ (cbrt (/ 2 (sin k))) t) l))) (log (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))))

prune12.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

localize7.0ms

Local error

Found 4 expressions with local error:

6.8b
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))
6.7b
(* (* (/ (cbrt (/ 2 (sin k))) t) l) (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
4.7b
(* (/ (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))))
3.4b
(/ (tan k) (/ l t))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
2177×times-frac
901×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
476×cbrt-prod
377×associate-*r*
330×div-inv
127×associate-/l*
57×associate-/r/
49×add-exp-log
43×add-cbrt-cube
19×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
11×pow1
10×associate-*l/
7×associate-/r*
6×frac-times associate-*r/
5×associate-*l*
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg *-commutative associate-/l/
1×tan-quot
Calls
4 calls:
Slowest
39.0ms
(* (/ (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))))
20.0ms
(* (* (/ (cbrt (/ 2 (sin k))) t) l) (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
10.0ms
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))
4.0ms
(/ (tan k) (/ l t))

series2.1s

Calls
4 calls:
Slowest
1.0s
(* (* (/ (cbrt (/ 2 (sin k))) t) l) (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
584.0ms
(* (/ (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))))
370.0ms
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))
94.0ms
(/ (tan k) (/ l t))

simplify2.5m

Calls
1337 calls:
Slowest
968.0ms
(* (* (* (/ (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)))))
885.0ms
(* (* (* (/ (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) (/ l t)) (/ (tan k) (/ l t))) (/ (tan k) (/ l t)))) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2)))))
873.0ms
(* (* (* (/ (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)))))
739.0ms
(* (* (* (* (/ (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))))
726.0ms
(* (* (* (/ (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))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))) (* (* (/ (cbrt (/ 2 (sin k))) t) l) (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))) (* (* (/ (cbrt (/ 2 (sin k))) t) l) (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))))

prune10.7s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.9b

localize17.0ms

Local error

Found 4 expressions with local error:

28.0b
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
28.0b
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
28.0b
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
6.8b
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
4127×times-frac
2012×cbrt-prod
1687×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
602×div-inv
124×associate-/l*
104×associate-/r/
13×add-exp-log
11×add-cbrt-cube
6×cbrt-undiv div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div associate-/r* pow1/3
1×clear-num frac-2neg associate-/l/
Calls
4 calls:
Slowest
10.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
10.0ms
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))
4.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
4.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))

series1.6s

Calls
4 calls:
Slowest
436.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
428.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
426.0ms
(cbrt (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
350.0ms
(/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))