Details

Time bar (total: 5.4m)

sample224.0ms

Algorithm
intervals
Results
74.0ms81×body1280valid
72.0ms67×body640valid
37.0ms247×body80valid
20.0ms39×body320valid
5.0ms17×body160valid

simplify124.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
124.0ms
(+ (* (/ (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: 0.3b

localize42.0ms

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))

rewrite124.0ms

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
46.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
40.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
16.0ms
(/ (cos th) (sqrt 2))
16.0ms
(/ (cos th) (sqrt 2))

series453.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
152.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
78.0ms
(/ (cos th) (sqrt 2))
63.0ms
(/ (cos th) (sqrt 2))

simplify7.8s

Counts
180 → 184
Calls
180 calls:
Slowest
618.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
609.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
555.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
524.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
300.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.1s

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))

rewrite127.0ms

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×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 473
Calls
4 calls:
Slowest
40.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
28.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
26.0ms
(/ (cos th) (sqrt (sqrt 2)))
11.0ms
(/ (cos th) (sqrt 2))

series460.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
161.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
123.0ms
(/ (cos th) (sqrt (sqrt 2)))
105.0ms
(/ (cos th) (sqrt 2))
71.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify28.0s

Counts
765 → 485
Calls
765 calls:
Slowest
1.1s
(* (* (* (/ (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)))
395.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
381.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
326.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune6.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize79.0ms

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))

rewrite164.0ms

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×pow-prod-down insert-posit16 add-log-exp
3×rec-exp 1-exp
2×clear-num frac-2neg associate-*l/ *-commutative
1×frac-times associate-*r/
Counts
4 → 738
Calls
4 calls:
Slowest
62.0ms
(* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
23.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
18.0ms
(/ (cos th) (sqrt (sqrt 2)))
17.0ms
(/ (cos th) (sqrt 2))

series475.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
130.0ms
(/ (cos th) (sqrt (sqrt 2)))
101.0ms
(/ (cos th) (sqrt 2))
76.0ms
(* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))

simplify1.8m

Counts
906 → 750
Calls
906 calls:
Slowest
812.0ms
(* (/ (sqrt 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)))
668.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
570.0ms
(* (/ 1 (sqrt (sqrt (sqrt (sqrt 2))))) (/ (sqrt (/ (cos th) (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))))
508.0ms
(* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt 2))))) (/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))))

prune13.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize57.0ms

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)))

rewrite177.0ms

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×insert-posit16 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 → 1039
Calls
4 calls:
Slowest
59.0ms
(* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
18.0ms
(/ (cos th) (sqrt (sqrt 2)))
18.0ms
(/ (cos th) (sqrt (sqrt 2)))
14.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(/ (cos th) (sqrt (sqrt 2)))
126.0ms
(/ (cos th) (sqrt (sqrt 2)))
83.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
77.0ms
(* (/ 1 (sqrt (sqrt (sqrt 2)))) (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))

simplify2.1m

Counts
1491 → 1051
Calls
1491 calls:
Slowest
849.0ms
(* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt 2))))) (/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))))
803.0ms
(* (/ 1 (sqrt (sqrt (sqrt (sqrt 2))))) (/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))))
576.0ms
(+ (- (log 1) (log (sqrt (sqrt (sqrt 2))))) (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt (sqrt 2))))))
513.0ms
(* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt 2))))) (/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))))
498.0ms
(* (/ (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

regimes480.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
2.9s2562×body1280valid
2.6s2140×body640valid
1.4s7923×body80valid
613.0ms1033×body320valid
199.0ms526×body160valid