Details

Time bar (total: 3.3m)

sample217.0ms

Algorithm
intervals
Results
85.0ms77×body1280valid
56.0ms79×body640valid
34.0ms261×body80valid
18.0ms43×body320valid
6.0ms19×body160valid

simplify110.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
109.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

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))

rewrite108.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg associate-*r* associate-*l/ *-commutative
Counts
4 → 180
Calls
4 calls:
Slowest
43.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
25.0ms
(/ (cos th) (sqrt 2))
21.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
11.0ms
(/ (cos th) (sqrt 2))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
174.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
123.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
68.0ms
(/ (cos th) (sqrt 2))
61.0ms
(/ (cos th) (sqrt 2))

simplify8.6s

Counts
180 → 192
Calls
180 calls:
Slowest
655.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
651.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
591.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
569.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
440.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize48.0ms

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))

rewrite95.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ associate-/r/ *-commutative
Counts
4 → 199
Calls
4 calls:
Slowest
45.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
19.0ms
(/ (cos th) (sqrt 2))
18.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
10.0ms
(/ (sqrt 2) a1)

series412.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
133.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
80.0ms
(/ (cos th) (sqrt 2))
65.0ms
(/ (sqrt 2) a1)

simplify8.8s

Counts
216 → 211
Calls
216 calls:
Slowest
695.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
654.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
370.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
334.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
312.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize35.0ms

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)

rewrite110.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 610
Calls
4 calls:
Slowest
42.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) a1))
9.0ms
(/ (cos th) (sqrt 2))
5.0ms
(/ (cbrt (sqrt 2)) a1)

series760.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
430.0ms
(/ (cbrt (sqrt 2)) a1)
141.0ms
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) a1))
129.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
60.0ms
(/ (cos th) (sqrt 2))

simplify2.7m

Counts
985 → 622
Calls
985 calls:
Slowest
949.0ms
(/ (/ (* (* (* (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)))
878.0ms
(/ (/ (cos th) (/ (cbrt (sqrt 2)) (* (cbrt 1) (cbrt 1)))) (/ (cbrt (sqrt (sqrt 2))) (* (cbrt a1) (cbrt a1))))
838.0ms
(/ (/ (* (* (* (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)))
827.0ms
(/ (/ (* (* (* (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)))
743.0ms
(/ (/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) 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)))

prune9.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize72.0ms

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))

rewrite445.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
2×associate-/l/
1×associate-*r* associate-*l/ *-commutative
Counts
4 → 4144
Calls
4 calls:
Slowest
61.0ms
(/ (/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) 1)) (/ (cbrt (cbrt (sqrt 2))) a1))
44.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
20.0ms
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) 1))
9.0ms
(/ (cos th) (sqrt 2))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
719.0ms
(/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) 1))
589.0ms
(/ (/ (/ (* (cos th) a1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) 1)) (/ (cbrt (cbrt (sqrt 2))) a1))
168.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
116.0ms
(/ (cos th) (sqrt 2))