Details

Time bar (total: 3.3m)

sample317.0ms

Algorithm
intervals
Results
126.0ms77×body1280valid
82.0ms79×body640valid
48.0ms261×body80valid
25.0ms43×body320valid
7.0ms19×body160valid

simplify143.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
143.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×*-un-lft-identity add-cube-cbrt
44×associate-*l* sqrt-prod
32×add-cbrt-cube add-exp-log
14×pow1
12×associate-/r* prod-exp cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r* associate-*l/ *-commutative
Counts
4 → 172
Calls
4 calls:
Slowest
42.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
24.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
22.0ms
(/ (cos th) (sqrt 2))
16.0ms
(/ (cos th) (sqrt 2))

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
130.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
96.0ms
(/ (cos th) (sqrt 2))
71.0ms
(/ (cos th) (sqrt 2))

simplify8.4s

Counts
180 → 184
Calls
180 calls:
Slowest
658.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
652.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
592.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
547.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
302.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.5b
(/ (sqrt 2) a1)
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.2b
(/ (* (cos th) a1) (/ (sqrt 2) a1))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
78×add-sqr-sqrt
73×*-un-lft-identity add-cube-cbrt
52×sqrt-prod
32×add-cbrt-cube add-exp-log
31×associate-/r*
22×associate-*l*
10×cbrt-undiv div-exp associate-/l*
9×pow1
8×prod-exp cbrt-unprod
6×div-inv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ associate-/r/ *-commutative
Counts
4 → 191
Calls
4 calls:
Slowest
41.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
29.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
16.0ms
(/ (cos th) (sqrt 2))
9.0ms
(/ (sqrt 2) a1)

series822.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
425.0ms
(/ (sqrt 2) a1)
150.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
147.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
100.0ms
(/ (cos th) (sqrt 2))

simplify8.8s

Counts
216 → 203
Calls
216 calls:
Slowest
660.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
581.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
317.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
307.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
279.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (* (* (/ (sqrt 2) a1) (/ (sqrt 2) a1)) (/ (sqrt 2) a1)))

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) a1))
0.2b
(/ (cbrt (sqrt 2)) a1)

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
1108×times-frac
402×add-sqr-sqrt
397×*-un-lft-identity add-cube-cbrt
258×cbrt-prod
151×sqrt-prod
121×add-exp-log
81×div-inv
73×div-exp
69×add-cbrt-cube
45×cbrt-undiv
40×associate-/r*
33×associate-/r/
24×prod-exp associate-/l*
22×associate-*l*
16×cbrt-unprod
9×pow1
8×1-exp
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 602
Calls
4 calls:
Slowest
42.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
34.0ms
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) a1))
16.0ms
(/ (cos th) (sqrt 2))
10.0ms
(/ (cbrt (sqrt 2)) a1)

series875.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
512.0ms
(/ (cbrt (sqrt 2)) a1)
154.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
141.0ms
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) a1))
67.0ms
(/ (cos th) (sqrt 2))

simplify2.7m

Counts
985 → 614
Calls
985 calls:
Slowest
959.0ms
(/ (/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1))) (* (* (/ (cbrt (sqrt 2)) a1) (/ (cbrt (sqrt 2)) a1)) (/ (cbrt (sqrt 2)) a1)))
858.0ms
(/ (/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (* (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1))) (* (* (/ (cbrt (sqrt 2)) a1) (/ (cbrt (sqrt 2)) a1)) (/ (cbrt (sqrt 2)) a1)))
811.0ms
(/ (/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1))) (/ (sqrt 2) (* (* a1 a1) a1)))
781.0ms
(/ (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (cbrt (sqrt 2))) (sqrt a1)))
757.0ms
(/ (/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (/ (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* 1 1) 1))) (* (* (/ (cbrt (sqrt 2)) a1) (/ (cbrt (sqrt 2)) a1)) (/ (cbrt (sqrt 2)) a1)))

prune9.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.4b
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) 1))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.2b
(/ (/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) 1)) (/ (cbrt (cbrt (sqrt 2))) a1))

rewrite884.0ms

Algorithm
rewrite-expression-head
Rules
14831×times-frac
4223×add-sqr-sqrt
4218×*-un-lft-identity add-cube-cbrt
4050×cbrt-prod
1230×div-inv
995×add-exp-log
832×sqrt-prod
738×div-exp
338×associate-/r/
310×add-cbrt-cube
264×cbrt-undiv
207×prod-exp
126×1-exp
104×associate-/l*
72×cbrt-unprod
53×associate-/r*
22×associate-*l*
9×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
2×associate-/l/
1×associate-*r* associate-*l/ *-commutative
Counts
4 → 4136
Calls
4 calls:
Slowest
44.0ms
(/ (/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) 1)) (/ (cbrt (cbrt (sqrt 2))) a1))
36.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
27.0ms
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) 1))
17.0ms
(/ (cos th) (sqrt 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
639.0ms
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) 1))
159.0ms
(/ (/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) 1)) (/ (cbrt (cbrt (sqrt 2))) a1))
140.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
114.0ms
(/ (cos th) (sqrt 2))