Details

Time bar (total: 1.7m)

sample488.0ms

Algorithm
intervals
Results
156.0ms45×body1280valid
81.0ms40×body640valid
77.0ms169×body80valid
26.0ms20×body320valid
20.0ms50×body80nan
7.0ms8×body160valid

simplify411.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
410.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

localize60.0ms

Local error

Found 4 expressions with local error:

18.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(/ x (tan B))

rewrite170.0ms

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
88.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
41.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
26.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms
(/ x (tan B))

series568.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
200.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
132.0ms
(/ x (tan B))
119.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
115.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.5s

Counts
79 → 109
Calls
79 calls:
Slowest
646.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
607.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
578.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
560.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
455.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

18.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(* (/ x (sin B)) (cos B))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×add-exp-log
20×associate-*l*
19×*-un-lft-identity add-cube-cbrt
16×add-cbrt-cube
13×times-frac
8×prod-exp
7×pow1 unpow-prod-down
6×associate-*r*
5×div-exp unswap-sqr
4×cbrt-unprod insert-posit16 add-log-exp
3×pow-to-exp cbrt-undiv pow-unpow associate-/r* pow-exp sqr-pow
2×*-commutative div-inv
1×clear-num pow-pow frac-2neg pow-prod-down associate-*l/ associate-/l*
Counts
4 → 101
Calls
4 calls:
Slowest
109.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
41.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
24.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
20.0ms
(* (/ x (sin B)) (cos B))

series600.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
244.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
126.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
117.0ms
(* (/ x (sin B)) (cos B))
113.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify11.0s

Counts
77 → 113
Calls
77 calls:
Slowest
627.0ms
(pow (* (cbrt (+ (+ 2 (* F F)) (* 2 x))) (cbrt (+ (+ 2 (* F F)) (* 2 x)))) -1/2)
616.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
554.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
547.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
470.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

18.8b
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
18.8b
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
0.4b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))

rewrite428.0ms

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
221.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))
149.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
36.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
18.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))

series581.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
197.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
141.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
136.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
107.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))

simplify15.8s

Counts
94 → 133
Calls
94 calls:
Slowest
857.0ms
(/ (* (* (* (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)))
593.0ms
(/ (* (* (* (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)))
566.0ms
(/ (* (* (* (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)))
439.0ms
(- (pow 2 -1/4) (+ (* 1/4 (* (pow F 2) (pow 1/32 1/4))) (* 1/4 (* x (pow 1/2 1/4)))))
437.0ms
(- (pow 2 -1/4) (+ (* 1/4 (* (pow F 2) (pow 1/32 1/4))) (* 1/4 (* x (pow 1/2 1/4)))))

prune2.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

18.8b
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
18.8b
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
3.6b
(* (/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) 1) (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F) (sin B)))
0.4b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F) (sin B))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
133×add-exp-log
62×div-exp
59×prod-exp
53×add-sqr-sqrt
51×times-frac
41×*-un-lft-identity
38×add-cube-cbrt
30×add-cbrt-cube
26×pow-unpow
25×associate-*l*
20×pow-to-exp pow-exp
17×unpow-prod-down
15×1-exp
9×cbrt-undiv cbrt-unprod
8×pow1
7×associate-*r* unswap-sqr sqr-pow
5×div-inv
4×insert-posit16 add-log-exp
3×associate-/r*
2×pow-pow
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l*
Counts
4 → 173
Calls
4 calls:
Slowest
171.0ms
(* (/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) 1) (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F) (sin B)))
59.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F) (sin B))
35.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
24.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))

series664.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F) (sin B))
199.0ms
(* (/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) 1) (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F) (sin B)))
126.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
124.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))

simplify36.3s

Counts
155 → 185
Calls
155 calls:
Slowest
746.0ms
(* (* (* (/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) 1) (/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) 1)) (/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) 1)) (/ (* (* (* (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))))
724.0ms
(+ (- (* (log (+ (+ 2 (* F F)) (* 2 x))) (/ -1/2 2)) 0) (- (+ (* (log (+ (+ 2 (* F F)) (* 2 x))) (/ -1/2 2)) (log F)) (log (sin B))))
654.0ms
(* (/ (* (* (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))) (* (* 1 1) 1)) (/ (* (* (* (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))))
628.0ms
(* (* (* (/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) 1) (/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) 1)) (/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) 1)) (/ (* (* (* (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))))
625.0ms
(- (/ (* F (sqrt (/ -1 F))) (sin B)) (* 1/2 (/ (sqrt (/ -1 F)) (* F (sin B)))))

prune2.8s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes392.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.8b

bsearch653.0ms

end0.0ms

sample13.4s

Algorithm
intervals
Results
4.6s1633×body1280valid
3.5s1366×body640valid
2.3s4840×body80valid
1.3s1625×body80nan
1.2s709×body320valid
361.0ms349×body160valid