Details

Time bar (total: 2.7m)

sample1.2s

Algorithm
intervals
Results
923.0ms82×body1280valid
69.0ms59×body640valid
58.0ms266×body80valid
28.0ms34×body320valid
15.0ms15×body160valid

simplify251.0ms

Calls
1 calls:
Slowest
231.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize69.0ms

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))
0.2b
(* (/ (cos th) (sqrt 2)) (* a2 a2))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×associate-*l*
18×add-cbrt-cube add-exp-log
8×pow1
6×associate-/r* associate-/l*
4×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r* pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
15.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
14.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
9.0ms
(/ (cos th) (sqrt 2))
9.0ms
(/ (cos th) (sqrt 2))

series330.0ms

Calls
4 calls:
Slowest
121.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
100.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
55.0ms
(/ (cos th) (sqrt 2))
53.0ms
(/ (cos th) (sqrt 2))

simplify10.0s

Calls
98 calls:
Slowest
2.1s
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
1.4s
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
722.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
563.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
524.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))

prune3.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
294×times-frac
171×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
144×sqrt-prod
28×associate-/l*
18×add-cbrt-cube add-exp-log
15×associate-/r*
13×associate-*l*
11×div-inv
6×pow1 cbrt-undiv div-exp
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
2×prod-exp cbrt-unprod
1×associate-*r* pow-prod-down associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
18.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
14.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
14.0ms
(/ (cos th) (sqrt (sqrt 2)))
8.0ms
(/ (cos th) (sqrt 2))

series284.0ms

Calls
4 calls:
Slowest
100.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
85.0ms
(/ (cos th) (sqrt (sqrt 2)))
50.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
50.0ms
(/ (cos th) (sqrt 2))

simplify21.9s

Calls
397 calls:
Slowest
1.7s
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
515.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
495.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
475.0ms
(/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (sqrt (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
473.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))

prune10.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
552×times-frac
308×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
288×sqrt-prod
50×associate-/l*
24×associate-/r*
18×add-cbrt-cube add-exp-log div-inv
8×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×associate-/l/
Calls
4 calls:
Slowest
100.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
18.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms
(/ (cos th) (sqrt (sqrt 2)))
9.0ms
(/ (cos th) (sqrt (sqrt 2)))

series523.0ms

Calls
4 calls:
Slowest
204.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
126.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
103.0ms
(/ (cos th) (sqrt (sqrt 2)))
87.0ms
(/ (cos th) (sqrt (sqrt 2)))

simplify47.1s

Calls
696 calls:
Slowest
1.6s
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
1.1s
(/ (* (* (/ (cos th) (sqrt (sqrt 2))) (/ (cos th) (sqrt (sqrt 2)))) (/ (cos th) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
492.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
440.0ms
(/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (sqrt (sqrt (sqrt 2))))
438.0ms
(/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2)))))

prune12.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (/ (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 2) a1))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
166×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
144×sqrt-prod
31×associate-/l*
16×associate-/r*
15×div-inv
13×add-cbrt-cube add-exp-log
5×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×associate-/r/ associate-/l/
Calls
4 calls:
Slowest
18.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
10.0ms
(/ (cos th) (/ (sqrt 2) a1))
9.0ms
(/ (cos th) (sqrt (sqrt 2)))
6.0ms
(/ (sqrt 2) a1)

series283.0ms

Calls
4 calls:
Slowest
101.0ms
(/ (cos th) (/ (sqrt 2) a1))
79.0ms
(/ (cos th) (sqrt (sqrt 2)))
62.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
40.0ms
(/ (sqrt 2) a1)

simplify22.4s

Calls
388 calls:
Slowest
657.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
638.0ms
(- (/ a1 (sqrt 2)) (* 1/2 (/ (* a1 (pow th 2)) (sqrt 2))))
553.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
455.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (/ (sqrt 2) a1) (/ (sqrt 2) a1)) (/ (sqrt 2) a1)))
410.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))

prune9.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes1.2s

Accuracy

0% (0.4b remaining)

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

bsearch22.0ms

end14.0ms

sample18.3s

Algorithm
intervals
Results
6.6s2462×body1280valid
4.7s2073×body640valid
4.0s7959×body80valid
2.4s1026×body320valid
236.0ms514×body160valid