Details

Time bar (total: 5.7m)

sample208.0ms

Algorithm
intervals
Results
87.0ms81×body1280valid
43.0ms67×body640valid
36.0ms247×body80valid
19.0ms39×body320valid
5.0ms17×body160valid

simplify140.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
140.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

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

rewrite81.0ms

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
29.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
29.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
9.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series497.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
123.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
104.0ms
(/ (cos th) (sqrt 2))
104.0ms
(/ (cos th) (sqrt 2))

simplify9.2s

Counts
180 → 192
Calls
180 calls:
Slowest
719.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
640.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
572.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
560.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
514.0ms
(- (/ (pow a1 2) (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
616×sqrt-prod
614×times-frac
345×add-sqr-sqrt
340×*-un-lft-identity add-cube-cbrt
37×associate-/l*
25×add-cbrt-cube add-exp-log
24×associate-/r*
22×associate-*l*
14×div-inv
9×pow1
7×cbrt-undiv div-exp
6×prod-exp cbrt-unprod
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 → 481
Calls
4 calls:
Slowest
34.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
22.0ms
(/ (cos th) (sqrt (sqrt 2)))
17.0ms
(/ (cos th) (sqrt 2))
14.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(/ (cos th) (sqrt (sqrt 2)))
159.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
100.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
97.0ms
(/ (cos th) (sqrt 2))

simplify30.2s

Counts
765 → 493
Calls
765 calls:
Slowest
773.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
700.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
460.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
421.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
400.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))

prune7.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt (sqrt 2)))
0.7b
(* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
1522×sqrt-prod
1185×times-frac
1063×add-sqr-sqrt
500×*-un-lft-identity
432×add-cube-cbrt
377×associate-*r*
156×unswap-sqr
62×associate-*l*
59×add-exp-log
41×add-cbrt-cube
22×div-exp
18×prod-exp
17×div-inv
15×associate-/r*
13×cbrt-undiv
12×cbrt-unprod
11×pow1
6×associate-/l*
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp
2×clear-num frac-2neg associate-*l/ *-commutative
1×frac-times associate-*r/
Counts
4 → 746
Calls
4 calls:
Slowest
59.0ms
(* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
40.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
18.0ms
(/ (cos th) (sqrt (sqrt 2)))
17.0ms
(/ (cos th) (sqrt 2))

series472.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
141.0ms
(/ (cos th) (sqrt (sqrt 2)))
86.0ms
(/ (cos th) (sqrt 2))
82.0ms
(* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))

simplify1.9m

Counts
906 → 758
Calls
906 calls:
Slowest
848.0ms
(* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt 2))))) (/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))))
697.0ms
(* (/ 1 (sqrt (sqrt (sqrt (sqrt 2))))) (/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))))
679.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
563.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
543.0ms
(+ (- (log 1) (log (sqrt (sqrt (sqrt 2))))) (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt (sqrt 2))))))

prune13.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt (sqrt 2)))
0.7b
(/ (cos th) (sqrt (sqrt 2)))
0.7b
(* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
2094×sqrt-prod
1723×times-frac
1338×add-sqr-sqrt
780×*-un-lft-identity
712×add-cube-cbrt
376×associate-*r*
153×unswap-sqr
52×add-exp-log
40×associate-*l*
37×associate-/l*
34×add-cbrt-cube
27×associate-/r* div-inv
23×div-exp
14×cbrt-undiv
12×prod-exp
6×pow1 cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg 1-exp
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 1047
Calls
4 calls:
Slowest
66.0ms
(* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
28.0ms
(/ (cos th) (sqrt (sqrt 2)))
24.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
19.0ms
(/ (cos th) (sqrt (sqrt 2)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(/ (cos th) (sqrt (sqrt 2)))
132.0ms
(/ (cos th) (sqrt (sqrt 2)))
83.0ms
(* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
75.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify2.3m

Counts
1491 → 1059
Calls
1491 calls:
Slowest
890.0ms
(* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt 2))))) (/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))))
863.0ms
(+ (log (/ 1 (sqrt (sqrt (sqrt 2))))) (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt (sqrt 2))))))
774.0ms
(* (/ 1 (sqrt (sqrt (sqrt (sqrt 2))))) (/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))))
515.0ms
(+ (- (log 1) (log (sqrt (sqrt (sqrt 2))))) (log (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2))))))
514.0ms
(* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt 2))))) (/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))))

prune19.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes437.0ms

Accuracy

0% (0.4b remaining)

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

bsearch8.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
2.9s2562×body1280valid
2.2s2140×body640valid
2.0s7923×body80valid
881.0ms1033×body320valid
175.0ms526×body160valid