Details

Time bar (total: 1.3m)

sample223.0ms

Algorithm
intervals
Results
76.0ms80×body1280valid
74.0ms61×body640valid
41.0ms246×body80valid
13.0ms26×body320valid
3.0ms11×body160valid

simplify159.0ms

Calls
1 calls:
Slowest
159.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

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))

rewrite78.0ms

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
Calls
4 calls:
Slowest
38.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
21.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
9.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series471.0ms

Calls
4 calls:
Slowest
170.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
132.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
91.0ms
(/ (cos th) (sqrt 2))
78.0ms
(/ (cos th) (sqrt 2))

simplify8.6s

Calls
180 calls:
Slowest
701.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
699.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
621.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
619.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
312.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.3b
(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.1b
(* (cos th) (* a2 a2))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
44×times-frac
43×add-sqr-sqrt
37×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
28×sqrt-prod
25×associate-*l*
14×pow1
12×associate-/r* prod-exp cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down
4×insert-posit16 associate-/l* add-log-exp unswap-sqr
3×div-inv
2×clear-num frac-2neg associate-*r* *-commutative
1×associate-*l/
Calls
4 calls:
Slowest
38.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
32.0ms
(* (cos th) (* a2 a2))
20.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
17.0ms
(/ (cos th) (sqrt 2))

series788.0ms

Calls
4 calls:
Slowest
503.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
139.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
98.0ms
(/ (cos th) (sqrt 2))
47.0ms
(* (cos th) (* a2 a2))

simplify6.7s

Calls
131 calls:
Slowest
725.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
624.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
408.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
265.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) (* a2 a2)) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
254.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
0.3b
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
0.3b
(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.1b
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
201×times-frac
107×add-sqr-sqrt
94×cbrt-prod *-un-lft-identity add-cube-cbrt
67×associate-*l*
59×add-exp-log
53×sqrt-prod
42×add-cbrt-cube
23×div-inv
20×cbrt-undiv div-exp
19×prod-exp cbrt-unprod
16×associate-/r*
11×associate-/l*
9×pow1
7×unswap-sqr
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
48.0ms
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
39.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
39.0ms
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
12.0ms
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

series784.0ms

Calls
4 calls:
Slowest
424.0ms
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
153.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
142.0ms
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
65.0ms
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

simplify18.1s

Calls
297 calls:
Slowest
425.0ms
(+ (- (log (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (log (cbrt (sqrt 2)))) (+ (log a1) (log a1)))
379.0ms
(* (/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt 2)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
376.0ms
(+ (- (log (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (log (cbrt (sqrt 2)))) (log (* a1 a1)))
367.0ms
(+ (log (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))) (+ (log a1) (log a1)))
353.0ms
(/ (* (* (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt 2))

prune3.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
0.3b
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
0.3b
(/ (* a2 a2) (sqrt 2))
0.1b
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
201×times-frac
107×add-sqr-sqrt
94×cbrt-prod *-un-lft-identity add-cube-cbrt
67×associate-*l*
55×add-exp-log
53×sqrt-prod
38×add-cbrt-cube
23×div-inv
19×cbrt-undiv div-exp
17×prod-exp cbrt-unprod
16×associate-/r*
11×associate-/l*
9×pow1
7×unswap-sqr
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
87.0ms
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
21.0ms
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
19.0ms
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
9.0ms
(/ (* a2 a2) (sqrt 2))

series820.0ms

Calls
4 calls:
Slowest
471.0ms
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
161.0ms
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
96.0ms
(/ (* a2 a2) (sqrt 2))
92.0ms
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

simplify17.6s

Calls
294 calls:
Slowest
591.0ms
(+ (- (- (log (cos th)) (+ (log (cbrt (sqrt 2))) (log (cbrt (sqrt 2))))) (log (cbrt (sqrt 2)))) (log (* a1 a1)))
432.0ms
(+ (- (log (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (log (cbrt (sqrt 2)))) (+ (log a1) (log a1)))
400.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
395.0ms
(- (+ (* 1/24 (* (pow (/ 1 (pow (sqrt 2) 2)) 1/3) (pow th 4))) (pow (/ 1 (pow (sqrt 2) 2)) 1/3)) (* 1/2 (* (pow (/ 1 (pow (sqrt 2) 2)) 1/3) (pow th 2))))
379.0ms
(* (/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt 2)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))

prune3.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes475.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch7.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.1s2509×body1280valid
2.3s2129×body640valid
1.6s7901×body80valid
669.0ms1059×body320valid
232.0ms563×body160valid