Details

Time bar (total: 1.1m)

sample215.0ms

Algorithm
intervals
Results
91.0ms71×body1280valid
44.0ms66×body640valid
43.0ms261×body80valid
15.0ms30×body320valid
7.0ms20×body160valid

simplify154.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
154.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune24.0ms

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))

rewrite111.0ms

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
48.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
28.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms
(/ (cos th) (sqrt 2))
15.0ms
(/ (cos th) (sqrt 2))

series400.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
119.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
97.0ms
(/ (cos th) (sqrt 2))
61.0ms
(/ (cos th) (sqrt 2))

simplify9.0s

Counts
180 → 192
Calls
180 calls:
Slowest
714.0ms
(* (* (* (/ (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))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
655.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
637.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
390.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize51.0ms

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))

rewrite146.0ms

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/
Counts
4 → 144
Calls
4 calls:
Slowest
52.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
38.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
33.0ms
(* (cos th) (* a2 a2))
20.0ms
(/ (cos th) (sqrt 2))

series413.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
128.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
74.0ms
(/ (cos th) (sqrt 2))
55.0ms
(* (cos th) (* a2 a2))

simplify6.6s

Counts
131 → 156
Calls
131 calls:
Slowest
672.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
603.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
332.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
285.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
285.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.3b
(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.1b
(* (cos th) (* a2 a2))
0.1b
(* (cos th) (* a1 a1))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
16×add-sqr-sqrt
14×pow1 *-un-lft-identity add-cube-cbrt
12×associate-/r* times-frac prod-exp sqrt-prod cbrt-unprod
6×cbrt-undiv div-exp associate-*l* pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg associate-*r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 108
Calls
4 calls:
Slowest
35.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
25.0ms
(* (cos th) (* a2 a2))
24.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
16.0ms
(* (cos th) (* a1 a1))

series397.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
184.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
115.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
52.0ms
(* (cos th) (* a2 a2))
47.0ms
(* (cos th) (* a1 a1))

simplify4.6s

Counts
82 → 120
Calls
82 calls:
Slowest
280.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
271.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
266.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
265.0ms
(/ (* (* (* (cos th) (* a1 a1)) (* (cos th) (* a1 a1))) (* (cos th) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
241.0ms
(- (pow a1 2) (* 1/2 (* (pow a1 2) (pow th 2))))

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.2b
(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.2b
(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2)))
0.1b
(* (cos th) (* a2 a2))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
240×sqrt-prod
222×times-frac
98×add-sqr-sqrt
97×*-un-lft-identity add-cube-cbrt
41×add-cbrt-cube add-exp-log
24×associate-/r*
15×associate-/l*
13×cbrt-undiv div-exp div-inv
12×prod-exp cbrt-unprod
9×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l* pow-prod-down
1×associate-*r* *-commutative unswap-sqr associate-/l/
Counts
4 → 253
Calls
4 calls:
Slowest
45.0ms
(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2)))
38.0ms
(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
20.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
18.0ms
(* (cos th) (* a2 a2))

series548.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
216.0ms
(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2)))
148.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
137.0ms
(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
47.0ms
(* (cos th) (* a2 a2))

simplify23.4s

Counts
345 → 265
Calls
345 calls:
Slowest
622.0ms
(/ (/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
493.0ms
(/ (/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) (* a2 a2)) (* a2 a2))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
463.0ms
(/ (/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) a2) (* (* a2 a2) a2))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
370.0ms
(- (- (+ (log (cos th)) (+ (log a2) (log a2))) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2))))
360.0ms
(- (- (+ (log (cos th)) (log (* a2 a2))) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2))))

prune3.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes455.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.4s2537×body1280valid
2.2s2042×body640valid
1.4s7989×body80valid
522.0ms1052×body320valid
223.0ms494×body160valid