Details

Time bar (total: 5.8m)

sample232.0ms

Algorithm
intervals
Results
80.0ms84×body1280valid
62.0ms225×body80valid
49.0ms66×body640valid
16.0ms30×body320valid
5.0ms15×body160valid

simplify180.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
180.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize44.0ms

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))
0.2b
(* (/ (cos th) (sqrt 2)) (* a1 a1))

rewrite96.0ms

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
31.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
29.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
17.0ms
(/ (cos th) (sqrt 2))
16.0ms
(/ (cos th) (sqrt 2))

series433.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
131.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
88.0ms
(/ (cos th) (sqrt 2))
83.0ms
(/ (cos th) (sqrt 2))

simplify12.9s

Counts
226 → 184
Calls
226 calls:
Slowest
676.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
640.0ms
(* (* (* (/ (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)))
578.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
369.0ms
(- (+ (/ 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: 0.0b

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))

rewrite78.0ms

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
28.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
24.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
11.0ms
(/ (cos th) (sqrt 2))
9.0ms
(/ (sqrt 2) a1)

series461.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
151.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
81.0ms
(/ (cos th) (sqrt 2))
62.0ms
(/ (sqrt 2) a1)

simplify16.4s

Counts
266 → 203
Calls
266 calls:
Slowest
707.0ms
(* (* (/ (* (cos th) a1) (/ (sqrt 2) a1)) (/ (* (cos th) a1) (/ (sqrt 2) a1))) (/ (* (cos th) a1) (/ (sqrt 2) a1)))
659.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
602.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
540.0ms
(/ (* (cos th) a1) (/ 1 (* (cbrt a1) (cbrt a1))))
533.0ms
(+ (- (log (cos th)) (log (sqrt 2))) (+ (log a2) (log a2)))

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.5b
(/ (sqrt 2) a1)
0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
1149×sqrt-prod
1137×times-frac
626×add-sqr-sqrt
592×*-un-lft-identity add-cube-cbrt
283×associate-*l*
40×associate-/l*
34×add-cbrt-cube add-exp-log
23×div-inv
21×associate-/r*
13×unswap-sqr
11×cbrt-undiv div-exp
9×pow1 prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 748
Calls
4 calls:
Slowest
67.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
19.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
13.0ms
(/ (cos th) (sqrt (sqrt 2)))
9.0ms
(/ (sqrt 2) a1)

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
140.0ms
(/ (cos th) (sqrt (sqrt 2)))
82.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
68.0ms
(/ (sqrt 2) a1)

simplify1.6m

Counts
1099 → 760
Calls
1099 calls:
Slowest
835.0ms
(log (* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2)))
627.0ms
(* (/ (/ (sqrt (cos th)) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (* a2 a2))
506.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (log (* a2 a2)))
505.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
495.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (+ (log a2) (log a2)))

prune11.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.5b
(/ (sqrt 2) a1)
0.3b
(* (/ (/ 1 (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))) (* (* a2 a2) (/ (cos th) (sqrt (sqrt 2)))))
0.2b
(* (* a2 a2) (/ (cos th) (sqrt (sqrt 2))))

rewrite603.0ms

Algorithm
rewrite-expression-head
Rules
1446×sqrt-prod
987×times-frac
528×add-sqr-sqrt
521×*-un-lft-identity add-cube-cbrt
485×associate-*l*
135×add-exp-log
89×add-cbrt-cube
61×prod-exp
44×div-exp
39×cbrt-unprod
32×associate-*r*
25×cbrt-undiv
18×pow1
16×div-inv
12×associate-/r*
9×pow-prod-down associate-/l*
5×rec-exp 1-exp
4×associate-*r/ insert-posit16 add-log-exp unswap-sqr
2×clear-num frac-2neg *-commutative
1×frac-times associate-*l/
Counts
4 → 688
Calls
4 calls:
Slowest
503.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))) (* (* a2 a2) (/ (cos th) (sqrt (sqrt 2)))))
42.0ms
(* (* a2 a2) (/ (cos th) (sqrt (sqrt 2))))
11.0ms
(/ (sqrt 2) a1)
9.0ms
(/ (cos th) (sqrt (sqrt 2)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
204.0ms
(* (* a2 a2) (/ (cos th) (sqrt (sqrt 2))))
159.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))) (* (* a2 a2) (/ (cos th) (sqrt (sqrt 2)))))
127.0ms
(/ (cos th) (sqrt (sqrt 2)))
80.0ms
(/ (sqrt 2) a1)

simplify3.1m

Counts
750 → 700
Calls
750 calls:
Slowest
842.0ms
(* (/ (* (* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt (sqrt 2))))) (/ 1 (sqrt (sqrt (sqrt 2))))) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))) (* (* (* (* a2 a2) a2) (* (* a2 a2) a2)) (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))))
768.0ms
(* (/ (/ (sqrt 1) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (cbrt (sqrt 2))))) (* (* a2 a2) (/ (cos th) (sqrt (sqrt 2)))))
750.0ms
(* (/ (/ (cbrt 1) (sqrt (sqrt (sqrt (sqrt 2))))) (sqrt (sqrt (sqrt 2)))) (* (* a2 a2) (/ (cos th) (sqrt (sqrt 2)))))
748.0ms
(* (/ (/ 1 (sqrt (sqrt (cbrt (sqrt 2))))) (sqrt (sqrt (sqrt (cbrt 2))))) (* (* a2 a2) (/ (cos th) (sqrt (sqrt 2)))))
748.0ms
(* (/ (* (* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt (sqrt 2))))) (/ 1 (sqrt (sqrt (sqrt 2))))) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))) (* (* (* (* a2 a2) (* a2 a2)) (* a2 a2)) (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))))

prune12.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes542.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch8.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.7s2589×body1280valid
1.7s2071×body640valid
1.4s7921×body80valid
667.0ms1025×body320valid
247.0ms530×body160valid