Details

Time bar (total: 1.0m)

sample202.0ms

Algorithm
intervals
Results
78.0ms71×body1280valid
47.0ms66×body640valid
37.0ms261×body80valid
14.0ms30×body320valid
7.0ms20×body160valid

simplify167.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
167.0ms
(+ (* (/ (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

localize30.0ms

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))

rewrite88.0ms

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
33.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
21.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
15.0ms
(/ (cos th) (sqrt 2))
14.0ms
(/ (cos th) (sqrt 2))

series471.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
139.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
102.0ms
(/ (cos th) (sqrt 2))
63.0ms
(/ (cos th) (sqrt 2))

simplify8.5s

Counts
180 → 184
Calls
180 calls:
Slowest
731.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
681.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
622.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
617.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
285.0ms
(- (+ (/ 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

localize28.0ms

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))

rewrite83.0ms

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×insert-posit16 associate-/l* add-log-exp unswap-sqr
3×div-inv
2×clear-num frac-2neg associate-*r* *-commutative
1×associate-*l/
Counts
4 → 136
Calls
4 calls:
Slowest
34.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
20.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
15.0ms
(* (cos th) (* a2 a2))
13.0ms
(/ (cos th) (sqrt 2))

series499.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
153.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
107.0ms
(/ (cos th) (sqrt 2))
75.0ms
(* (cos th) (* a2 a2))

simplify6.6s

Counts
131 → 148
Calls
131 calls:
Slowest
666.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
650.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
461.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
297.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
286.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize28.0ms

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))

rewrite94.0ms

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×insert-posit16 add-log-exp
2×clear-num frac-2neg associate-*r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 100
Calls
4 calls:
Slowest
35.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
23.0ms
(* (cos th) (* a2 a2))
18.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
16.0ms
(* (cos th) (* a1 a1))

series416.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
141.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
65.0ms
(* (cos th) (* a1 a1))
61.0ms
(* (cos th) (* a2 a2))

simplify5.2s

Counts
82 → 112
Calls
82 calls:
Slowest
529.0ms
(- (/ (pow a1 2) (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))))
463.0ms
(- (pow a1 2) (* 1/2 (* (pow a1 2) (pow th 2))))
318.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
304.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
233.0ms
(/ (* (* (* (cos th) (* a1 a1)) (* (cos th) (* a1 a1))) (* (cos th) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize58.0ms

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))

rewrite94.0ms

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×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*l* pow-prod-down
1×associate-*r* *-commutative unswap-sqr associate-/l/
Counts
4 → 245
Calls
4 calls:
Slowest
28.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
24.0ms
(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
19.0ms
(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2)))
16.0ms
(* (cos th) (* a2 a2))

series617.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
238.0ms
(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2)))
162.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
155.0ms
(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
62.0ms
(* (cos th) (* a2 a2))

simplify22.7s

Counts
345 → 257
Calls
345 calls:
Slowest
581.0ms
(/ (/ (* (* (* (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))))
500.0ms
(/ (/ (* (* (* (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))))
449.0ms
(/ (/ (* (* (* (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))))
427.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
388.0ms
(- (- (+ (log (cos th)) (log (* a2 a2))) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2))))

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes409.0ms

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
2.8s2537×body1280valid
2.3s2042×body640valid
1.9s7989×body80valid
560.0ms1052×body320valid
157.0ms494×body160valid