Details

Time bar (total: 54.8s)

sample244.0ms

Algorithm
intervals
Results
98.0ms69×body1280valid
53.0ms72×body640valid
47.0ms265×body80valid
19.0ms30×body320valid
9.0ms24×body160valid

simplify133.0ms

Calls
1 calls:
Slowest
133.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))
0.5b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))

rewrite48.0ms

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×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u 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)) (* a1 a1))
14.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
9.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series475.0ms

Calls
4 calls:
Slowest
182.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
151.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
76.0ms
(/ (cos th) (sqrt 2))
66.0ms
(/ (cos th) (sqrt 2))

simplify4.4s

Calls
98 calls:
Slowest
622.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
517.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
286.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
267.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
213.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))
0.4b
(* (/ (cos th) (sqrt 2)) a2)
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×associate-*l*
13×add-cbrt-cube add-exp-log
6×pow1 associate-/r* associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv div-exp
2×clear-num frac-2neg associate-*l/ prod-exp *-commutative cbrt-unprod
1×associate-*r* pow-prod-down
Calls
4 calls:
Slowest
7.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
7.0ms
(/ (cos th) (sqrt 2))
5.0ms
(* (/ (cos th) (sqrt 2)) a2)
4.0ms
(/ (cos th) (sqrt 2))

series446.0ms

Calls
4 calls:
Slowest
157.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
143.0ms
(* (/ (cos th) (sqrt 2)) a2)
80.0ms
(/ (cos th) (sqrt 2))
65.0ms
(/ (cos th) (sqrt 2))

simplify3.7s

Calls
93 calls:
Slowest
610.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
301.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
274.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
238.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
205.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.4b
(/ (* (cos th) a2) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.2b
(* (/ (* (cos th) a2) (sqrt 2)) a2)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×associate-*l*
13×add-cbrt-cube add-exp-log
6×pow1 associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
3×cbrt-undiv div-exp
2×clear-num frac-2neg associate-*l/ prod-exp *-commutative cbrt-unprod
1×associate-*r* pow-prod-down
Calls
4 calls:
Slowest
10.0ms
(* (/ (* (cos th) a2) (sqrt 2)) a2)
10.0ms
(/ (* (cos th) a2) (sqrt 2))
8.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
4.0ms
(/ (cos th) (sqrt 2))

series512.0ms

Calls
4 calls:
Slowest
152.0ms
(/ (* (cos th) a2) (sqrt 2))
142.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
140.0ms
(* (/ (* (cos th) a2) (sqrt 2)) a2)
78.0ms
(/ (cos th) (sqrt 2))

simplify3.6s

Calls
74 calls:
Slowest
667.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
284.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
271.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
184.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
174.0ms
(- (/ (pow a1 2) (sqrt 2)) (* 1/2 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.4b
(/ (* (cos th) a2) (sqrt 2))
0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
519×times-frac
281×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
264×sqrt-prod
136×associate-*l*
26×associate-/l*
22×add-cbrt-cube add-exp-log
17×div-inv
15×associate-/r*
8×cbrt-undiv div-exp
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg prod-exp cbrt-unprod
1×associate-*r* pow-prod-down associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
22.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
9.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
6.0ms
(/ (* (cos th) a2) (sqrt 2))
4.0ms
(/ (cos th) (sqrt (sqrt 2)))

series554.0ms

Calls
4 calls:
Slowest
184.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
168.0ms
(/ (* (cos th) a2) (sqrt 2))
125.0ms
(/ (cos th) (sqrt (sqrt 2)))
78.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify21.0s

Calls
509 calls:
Slowest
408.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (log (* a1 a1)))
376.0ms
(+ (- (log (/ (cos th) (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (log (* a1 a1)))
349.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
332.0ms
(* (/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
294.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))

prune5.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes439.0ms

Accuracy

0% (0.4b remaining)

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

bsearch6.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
2.7s2507×body1280valid
2.1s2065×body640valid
2.0s8082×body80valid
794.0ms1066×body320valid
206.0ms540×body160valid