Details

Time bar (total: 37.2s)

sample251.0ms

Algorithm
intervals
Results
75.0ms74×body1280valid
69.0ms236×body80valid
57.0ms72×body640valid
21.0ms39×body320valid
9.0ms24×body160valid

simplify133.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
133.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))
0.3b
(/ (cos th) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))
0.0b
(+ (* a1 a1) (* a2 a2))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
95×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×sqrt-prod
27×associate-/r*
11×associate-/r/
10×add-cbrt-cube add-exp-log
9×associate-/l*
6×flip3-+ flip-+ div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 insert-posit16
2×clear-num frac-2neg
1×+-commutative sum-log
Counts
3 → 169
Calls
3 calls:
Slowest
32.0ms
(/ (cos th) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))
19.0ms
(/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))
14.0ms
(+ (* a1 a1) (* a2 a2))

series511.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
332.0ms
(/ (cos th) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))
131.0ms
(/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))
48.0ms
(+ (* a1 a1) (* a2 a2))

simplify22.0s

Counts
271 → 178
Calls
271 calls:
Slowest
811.0ms
(* (* (/ (cos th) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (cos th) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))) (/ (cos th) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))))
693.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))))
601.0ms
(/ (* (cbrt (cos th)) (cbrt (cos th))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (+ (* a1 a1) (* a2 a2))) (cbrt (+ (* a1 a1) (* a2 a2))))))
498.0ms
(/ (cos th) (- (* a1 a1) (* a2 a2)))
435.0ms
(* (* (+ (* a1 a1) (* a2 a2)) (+ (* a1 a1) (* a2 a2))) (+ (* a1 a1) (* a2 a2)))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (+ (* a2 a2) (* a1 a1)) (sqrt 2))
0.2b
(* (cos th) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)))
0.0b
(+ (* a2 a2) (* a1 a1))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×*-un-lft-identity add-cube-cbrt
22×associate-*r* sqrt-prod
10×add-cbrt-cube add-exp-log
6×associate-/r*
5×pow1 add-log-exp
3×associate-*l* insert-posit16 associate-/l* unswap-sqr
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv associate-/l/
1×+-commutative clear-num sum-log frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 97
Calls
3 calls:
Slowest
44.0ms
(/ (+ (* a2 a2) (* a1 a1)) (sqrt 2))
32.0ms
(* (cos th) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)))
7.0ms
(+ (* a2 a2) (* a1 a1))

series416.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
272.0ms
(* (cos th) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)))
110.0ms
(/ (+ (* a2 a2) (* a1 a1)) (sqrt 2))
34.0ms
(+ (* a2 a2) (* a1 a1))

simplify9.0s

Counts
128 → 106
Calls
128 calls:
Slowest
667.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2))) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2))))
548.0ms
(* (* (+ (* a2 a2) (* a1 a1)) (+ (* a2 a2) (* a1 a1))) (+ (* a2 a2) (* a1 a1)))
533.0ms
(* (* (* (cos th) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2))) (* (cos th) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)))) (* (cos th) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2))))
454.0ms
(* (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2))) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)))
324.0ms
(+ (pow (* a2 a2) 3) (pow (* a1 a1) 3))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (+ (* a1 a1) (* a2 a2)))
4.0b
(sqrt (+ (* a1 a1) (* a2 a2)))
0.3b
(/ (cos th) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (+ (* a1 a1) (* a2 a2)))))
0.3b
(/ (/ (cos th) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (+ (* a1 a1) (* a2 a2))))) (/ (cbrt (sqrt 2)) (sqrt (+ (* a1 a1) (* a2 a2)))))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
8082×times-frac
2929×add-sqr-sqrt
2927×*-un-lft-identity add-cube-cbrt
2457×sqrt-prod
1512×cbrt-prod
521×associate-/r/
462×sqrt-div
292×div-inv
231×flip3-+ flip-+
72×associate-/r*
45×add-exp-log
44×associate-/l*
35×add-cbrt-cube
27×cbrt-undiv div-exp
6×pow1
4×insert-posit16 add-log-exp
3×prod-exp cbrt-unprod
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 2691
Calls
4 calls:
Slowest
62.0ms
(/ (/ (cos th) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (+ (* a1 a1) (* a2 a2))))) (/ (cbrt (sqrt 2)) (sqrt (+ (* a1 a1) (* a2 a2)))))
26.0ms
(/ (cos th) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (+ (* a1 a1) (* a2 a2)))))
12.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
767.0ms
(/ (cos th) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (+ (* a1 a1) (* a2 a2)))))
255.0ms
(/ (/ (cos th) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (+ (* a1 a1) (* a2 a2))))) (/ (cbrt (sqrt 2)) (sqrt (+ (* a1 a1) (* a2 a2)))))
62.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
57.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))