Details

Time bar (total: 5.9m)

sample261.0ms

Algorithm
intervals
Results
92.0ms84×body1280valid
58.0ms66×body640valid
43.0ms30×body320valid
39.0ms225×body80valid
6.0ms15×body160valid

simplify144.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
144.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize45.0ms

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))

rewrite100.0ms

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
41.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
21.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
17.0ms
(/ (cos th) (sqrt 2))
17.0ms
(/ (cos th) (sqrt 2))

series468.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
139.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
84.0ms
(/ (cos th) (sqrt 2))
84.0ms
(/ (cos th) (sqrt 2))

simplify13.0s

Counts
234 → 192
Calls
234 calls:
Slowest
584.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
563.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
561.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
507.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
432.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

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))

rewrite92.0ms

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×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/ associate-/r/ *-commutative
Counts
4 → 199
Calls
4 calls:
Slowest
42.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
19.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
17.0ms
(/ (cos th) (sqrt 2))
9.0ms
(/ (sqrt 2) a1)

series461.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
154.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
77.0ms
(/ (cos th) (sqrt 2))
66.0ms
(/ (sqrt 2) a1)

simplify16.8s

Counts
274 → 211
Calls
274 calls:
Slowest
672.0ms
(* (* (/ (* (cos th) a1) (/ (sqrt 2) a1)) (/ (* (cos th) a1) (/ (sqrt 2) a1))) (/ (* (cos th) a1) (/ (sqrt 2) a1)))
643.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
633.0ms
(/ (* (cos th) a1) (/ 1 (* (cbrt a1) (cbrt a1))))
621.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
559.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize53.0ms

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))

rewrite124.0ms

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×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/
Counts
4 → 756
Calls
4 calls:
Slowest
46.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
29.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
19.0ms
(/ (cos th) (sqrt (sqrt 2)))
5.0ms
(/ (sqrt 2) a1)

series480.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
149.0ms
(/ (cos th) (sqrt (sqrt 2)))
92.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
70.0ms
(/ (sqrt 2) a1)

simplify1.6m

Counts
1107 → 768
Calls
1107 calls:
Slowest
659.0ms
(* (/ (* (* (/ (cos th) (sqrt (sqrt 2))) (/ (cos th) (sqrt (sqrt 2)))) (/ (cos th) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
649.0ms
(* (/ (/ (cos th) (cbrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))) (* a2 a2))
504.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (log (* a2 a2)))
466.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
466.0ms
(+ (- (log (/ (cos th) (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (+ (log a2) (log a2)))

prune11.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize80.0ms

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))))

rewrite255.0ms

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×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×clear-num frac-2neg *-commutative
1×frac-times associate-*l/
Counts
4 → 696
Calls
4 calls:
Slowest
139.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))) (* (* a2 a2) (/ (cos th) (sqrt (sqrt 2)))))
46.0ms
(* (* a2 a2) (/ (cos th) (sqrt (sqrt 2))))
19.0ms
(/ (cos th) (sqrt (sqrt 2)))
9.0ms
(/ (sqrt 2) a1)

series569.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
203.0ms
(* (* a2 a2) (/ (cos th) (sqrt (sqrt 2))))
166.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))) (* (* a2 a2) (/ (cos th) (sqrt (sqrt 2)))))
132.0ms
(/ (cos th) (sqrt (sqrt 2)))
67.0ms
(/ (sqrt 2) a1)

simplify3.1m

Counts
758 → 708
Calls
758 calls:
Slowest
915.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
807.0ms
(* (/ (/ (* (* 1 1) 1) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (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))))))
753.0ms
(* (/ (* (* (/ 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) (sqrt (sqrt 2))) (/ (cos th) (sqrt (sqrt 2)))) (/ (cos th) (sqrt (sqrt 2))))))
741.0ms
(* (sqrt (/ (/ 1 (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))) (* (* a2 a2) (/ (cos th) (sqrt (sqrt 2)))))
738.0ms
(* (/ (/ (* (* 1 1) 1) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (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))))))

prune13.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes480.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
3.2s2589×body1280valid
2.1s2071×body640valid
1.5s7921×body80valid
611.0ms1025×body320valid
232.0ms530×body160valid