Details

Time bar (total: 6.6m)

sample460.0ms

Algorithm
intervals
Results
170.0ms69×body1280valid
96.0ms195×body80valid
89.0ms52×body640valid
67.0ms35×body320valid
13.0ms17×body160valid

simplify299.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
299.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.5b

localize72.0ms

Local error

Found 4 expressions with local error:

12.0b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
8.6b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
2.2b
(/ t (* (/ l t) (/ l t)))
0.2b
(* (/ l t) (/ l t))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
243×add-cbrt-cube add-exp-log
106×cbrt-undiv div-exp
86×prod-exp cbrt-unprod
77×times-frac
62×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
23×associate-*r*
16×pow1 associate-/l*
14×associate-*l*
13×swap-sqr
9×associate-*r/ associate-/r/ div-inv
5×frac-times associate-*l/
4×expm1-log1p-u pow-prod-down tan-quot insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×clear-num associate-/r* frac-2neg *-commutative
1×pow2 pow-plus pow-sqr pow-prod-up associate-/l/
Counts
4 → 250
Calls
4 calls:
Slowest
76.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
46.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
22.0ms
(* (/ l t) (/ l t))
10.0ms
(/ t (* (/ l t) (/ l t)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
891.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
246.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
43.0ms
(/ t (* (/ l t) (/ l t)))
36.0ms
(* (/ l t) (/ l t))

simplify1.0m

Counts
239 → 262
Calls
239 calls:
Slowest
2.1s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (* (/ l t) (/ l t))) (* (/ l t) (/ l t))))))
2.0s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))
1.9s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
1.9s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))
1.8s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))

prune4.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.3b

localize46.0ms

Local error

Found 4 expressions with local error:

12.0b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.5b
(/ (sin k) (/ l t))
3.5b
(/ (sin k) (/ l t))
0.2b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
364×times-frac
196×add-cbrt-cube add-exp-log
180×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
117×cbrt-undiv div-exp
42×prod-exp cbrt-unprod
36×associate-/r*
34×div-inv
22×associate-/l*
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r/
1×associate-/l/
Counts
4 → 358
Calls
4 calls:
Slowest
70.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
22.0ms
(/ (sin k) (/ l t))
20.0ms
(/ (sin k) (/ l t))
7.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
824.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
91.0ms
(/ (sin k) (/ l t))
84.0ms
(/ (sin k) (/ l t))
65.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

simplify1.4m

Counts
488 → 370
Calls
488 calls:
Slowest
2.7s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (* (* (cos k) (cos k)) (cos k))))
1.9s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.8s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.7s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (* t (/ (sin k) (/ l t)))) (* t (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.6s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (* t (/ (sin k) (/ l t)))) (* t (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))

prune5.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.9b

localize70.0ms

Local error

Found 4 expressions with local error:

16.4b
(cbrt (/ 2 (fma (/ k t) (/ k t) 2)))
16.4b
(cbrt (/ 2 (fma (/ k t) (/ k t) 2)))
16.4b
(cbrt (/ 2 (fma (/ k t) (/ k t) 2)))
5.3b
(/ (/ (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) t) (/ (sin k) (/ l t)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
998×times-frac
395×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
97×add-exp-log
81×div-inv
73×add-cbrt-cube
51×cbrt-undiv div-exp
44×associate-/r*
39×cbrt-prod
24×prod-exp cbrt-unprod
9×associate-/r/
7×associate-/l*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div pow1/3
1×clear-num frac-2neg associate-/l/
Counts
4 → 485
Calls
4 calls:
Slowest
61.0ms
(/ (/ (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) t) (/ (sin k) (/ l t)))
1.0ms
(cbrt (/ 2 (fma (/ k t) (/ k t) 2)))
1.0ms
(cbrt (/ 2 (fma (/ k t) (/ k t) 2)))
1.0ms
(cbrt (/ 2 (fma (/ k t) (/ k t) 2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
936.0ms
(/ (/ (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) t) (/ (sin k) (/ l t)))
306.0ms
(cbrt (/ 2 (fma (/ k t) (/ k t) 2)))
252.0ms
(cbrt (/ 2 (fma (/ k t) (/ k t) 2)))
241.0ms
(cbrt (/ 2 (fma (/ k t) (/ k t) 2)))

simplify3.7m

Counts
757 → 497
Calls
757 calls:
Slowest
2.8s
(/ (/ (* (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* t t) t)) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t))))
2.7s
(/ (/ (* (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* t t) t)) (/ (* (* (sin k) (sin k)) (sin k)) (* (* (/ l t) (/ l t)) (/ l t))))
2.7s
(/ (/ (* (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* t t) t)) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t))))
2.4s
(/ (/ (* (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* t t) t)) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t))))
2.2s
(/ (/ (* (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* t t) t)) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t))))

prune9.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.9b

localize96.0ms

Local error

Found 4 expressions with local error:

11.3b
(sqrt (fma (/ k t) (/ k t) 2))
11.3b
(sqrt (fma (/ k t) (/ k t) 2))
6.6b
(* (/ t (cbrt (cos k))) (sqrt (fma (/ k t) (/ k t) 2)))
4.8b
(/ (/ 2 (sqrt (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cbrt (cos k))))

rewrite669.0ms

Algorithm
rewrite-expression-head
Rules
25940×times-frac
10413×add-sqr-sqrt
10395×*-un-lft-identity add-cube-cbrt
3047×cbrt-prod
2433×sqrt-prod
846×div-inv
268×associate-/r*
139×associate-/r/
41×add-exp-log
34×add-cbrt-cube
25×cbrt-undiv div-exp
22×associate-*l* associate-/l*
8×pow1
6×associate-*r* unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 prod-exp cbrt-unprod
1×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 6300
Calls
4 calls:
Slowest
29.0ms
(/ (/ 2 (sqrt (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cbrt (cos k))))
21.0ms
(* (/ t (cbrt (cos k))) (sqrt (fma (/ k t) (/ k t) 2)))
1.0ms
(sqrt (fma (/ k t) (/ k t) 2))
1.0ms
(sqrt (fma (/ k t) (/ k t) 2))

series894.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
477.0ms
(/ (/ 2 (sqrt (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cbrt (cos k))))
294.0ms
(* (/ t (cbrt (cos k))) (sqrt (fma (/ k t) (/ k t) 2)))
64.0ms
(sqrt (fma (/ k t) (/ k t) 2))
59.0ms
(sqrt (fma (/ k t) (/ k t) 2))