Details

Time bar (total: 1.3m)

sample895.0ms

Algorithm
intervals
Results
495.0ms51×body80nan
174.0ms53×body1280valid
68.0ms47×body640valid
53.0ms144×body80valid
20.0ms18×body320valid
9.0ms11×body160valid

simplify438.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
437.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize50.0ms

Local error

Found 4 expressions with local error:

17.6b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(/ x (tan B))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×add-exp-log
19×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube
12×times-frac
7×unpow-prod-down associate-*l*
6×associate-/r* prod-exp
5×pow1 div-exp
4×insert-posit16 associate-/l* add-log-exp
3×pow-to-exp cbrt-undiv pow-unpow associate-*r* pow-exp unswap-sqr sqr-pow
2×clear-num frac-2neg cbrt-unprod div-inv
1×pow-pow tan-quot associate-/r/ *-commutative
Counts
4 → 97
Calls
4 calls:
Slowest
70.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
40.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
33.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.0ms
(/ x (tan B))

series541.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
223.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
119.0ms
(/ x (tan B))
109.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
89.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify10.4s

Counts
79 → 109
Calls
79 calls:
Slowest
570.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
547.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
507.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
496.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
444.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

17.6b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(/ (* x (cos B)) (sin B))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
18×add-sqr-sqrt
16×add-cbrt-cube
13×*-un-lft-identity add-cube-cbrt
7×unpow-prod-down associate-*l* prod-exp
6×associate-/r* times-frac div-exp
5×pow1
4×cbrt-undiv insert-posit16 add-log-exp
3×pow-to-exp pow-unpow associate-*r* pow-exp cbrt-unprod unswap-sqr sqr-pow
2×clear-num frac-2neg div-inv associate-/l*
1×pow-pow *-commutative
Counts
4 → 90
Calls
4 calls:
Slowest
71.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
32.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
20.0ms
(/ (* x (cos B)) (sin B))
18.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

series574.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
229.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
133.0ms
(/ (* x (cos B)) (sin B))
108.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
104.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify9.9s

Counts
66 → 102
Calls
66 calls:
Slowest
525.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
518.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
515.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
502.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
484.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

18.0b
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
18.0b
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))
0.2b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))

rewrite385.0ms

Algorithm
rewrite-expression-head
Rules
72×add-exp-log
42×prod-exp
26×pow-unpow
24×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×times-frac
18×add-cbrt-cube
16×pow-to-exp pow-exp
13×div-exp
9×unpow-prod-down
7×associate-*l*
6×pow1 cbrt-unprod
4×insert-posit16 add-log-exp
3×cbrt-undiv associate-/r* div-inv sqr-pow
2×pow-pow
1×clear-num frac-2neg associate-*r* *-commutative associate-/l*
Counts
4 → 121
Calls
4 calls:
Slowest
171.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
146.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))
38.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
28.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))

series562.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
229.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
122.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
110.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
100.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))

simplify15.6s

Counts
94 → 133
Calls
94 calls:
Slowest
840.0ms
(/ (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (* (* (sin B) (sin B)) (sin B)))
645.0ms
(/ (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (* (* F F) F))) (* (* (sin B) (sin B)) (sin B)))
593.0ms
(- (+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (log (sin B)))
589.0ms
(/ (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (* (* (sin B) (sin B)) (sin B)))
449.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (log F)))

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

18.0b
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
18.0b
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log
30×add-sqr-sqrt
26×pow-unpow
25×*-un-lft-identity add-cube-cbrt
24×prod-exp
18×times-frac
14×associate-*l*
13×unpow-prod-down
11×add-cbrt-cube
10×pow-to-exp pow-exp
6×pow1
5×sqr-pow
4×associate-*r* cbrt-unprod insert-posit16 add-log-exp
3×unswap-sqr
2×pow-pow *-commutative div-inv
Counts
4 → 113
Calls
4 calls:
Slowest
168.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))
104.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)
23.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
23.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))

series548.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)
148.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
127.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))
118.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))

simplify12.7s

Counts
86 → 125
Calls
86 calls:
Slowest
621.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) (/ -1/2 2)) (sqrt F))
590.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) (/ -1/2 2)) (sqrt F))
454.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (log F)))
433.0ms
(- (pow 2 -1/4) (+ (* 1/4 (* (pow F 2) (pow 1/32 1/4))) (* 1/4 (* x (pow 1/2 1/4)))))
420.0ms
(* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (* (* F F) F))

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes332.0ms

Accuracy

98.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.2b

bsearch566.0ms

end0.0ms

sample14.0s

Algorithm
intervals
Results
5.3s1740×body1280valid
3.0s1415×body640valid
2.0s4741×body80valid
1.5s649×body320valid
1.2s1655×body80nan
733.0ms327×body160valid