Details

Time bar (total: 1.3m)

sample176.0ms

Algorithm
intervals
Results
87.0ms80×body1280valid
33.0ms61×body640valid
30.0ms246×body80valid
10.0ms26×body320valid
3.0ms11×body160valid

simplify173.0ms

Calls
1 calls:
Slowest
173.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

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))

rewrite91.0ms

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
Calls
4 calls:
Slowest
31.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
24.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
16.0ms
(/ (cos th) (sqrt 2))
15.0ms
(/ (cos th) (sqrt 2))

series492.0ms

Calls
4 calls:
Slowest
161.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
151.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
100.0ms
(/ (cos th) (sqrt 2))
78.0ms
(/ (cos th) (sqrt 2))

simplify9.0s

Calls
180 calls:
Slowest
675.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
673.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
616.0ms
(* (* (* (/ (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)))
365.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize24.0ms

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))

rewrite109.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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
39.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
32.0ms
(* (cos th) (* a2 a2))
20.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
14.0ms
(/ (cos th) (sqrt 2))

series402.0ms

Calls
4 calls:
Slowest
135.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
129.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
88.0ms
(/ (cos th) (sqrt 2))
49.0ms
(* (cos th) (* a2 a2))

simplify7.0s

Calls
131 calls:
Slowest
641.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
601.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
370.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
340.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
305.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize42.0ms

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)))

rewrite151.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
59.0ms
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
33.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
28.0ms
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
22.0ms
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

series867.0ms

Calls
4 calls:
Slowest
434.0ms
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
171.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
163.0ms
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
98.0ms
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

simplify19.8s

Calls
297 calls:
Slowest
607.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) a2) (* (* a2 a2) a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
468.0ms
(+ (- (log (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (log (cbrt (sqrt 2)))) (log (* a1 a1)))
457.0ms
(/ (* (* (/ (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))
438.0ms
(- (+ (* 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))))
425.0ms
(+ (- (log (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (log (cbrt (sqrt 2)))) (+ (log a1) (log a1)))

prune3.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize56.0ms

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)))

rewrite135.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
83.0ms
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
20.0ms
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
16.0ms
(/ (* a2 a2) (sqrt 2))
12.0ms
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

series793.0ms

Calls
4 calls:
Slowest
452.0ms
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
140.0ms
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
106.0ms
(/ (* a2 a2) (sqrt 2))
94.0ms
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

simplify18.0s

Calls
294 calls:
Slowest
481.0ms
(+ (- (log (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (log (cbrt (sqrt 2)))) (log (* a1 a1)))
408.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
392.0ms
(- (+ (* 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))))
357.0ms
(+ (- (log (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (log (cbrt (sqrt 2)))) (+ (log a1) (log a1)))
338.0ms
(* (/ (/ (* (* (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)))

prune3.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes497.0ms

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.2s2509×body1280valid
2.3s2129×body640valid
1.9s7901×body80valid
616.0ms1059×body320valid
191.0ms563×body160valid