Details

Time bar (total: 2.7m)

sample542.0ms

Algorithm
intervals
Results
136.0ms48×body1280valid
114.0ms173×body80valid
89.0ms42×body640valid
21.0ms12×body320valid
21.0ms51×body80nan
15.0ms17×body160valid

simplify417.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
416.0ms
(+ (- (* 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

localize66.0ms

Local error

Found 4 expressions with local error:

17.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.5b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b
(/ x (tan B))

rewrite201.0ms

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
107.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
59.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
20.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms
(/ x (tan B))

series637.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
228.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
149.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
146.0ms
(/ x (tan B))
113.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify27.5s

Counts
129 → 109
Calls
129 calls:
Slowest
969.0ms
(* (* (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B)) (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))) (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B)))
765.0ms
(real->posit16 (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
715.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) 1)
647.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
641.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (* (cbrt (sin B)) (cbrt (sin B))))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

17.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b
(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
0.3b
(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
36×times-frac
32×add-sqr-sqrt
27×*-un-lft-identity add-cube-cbrt
26×div-exp
20×add-cbrt-cube
15×prod-exp
8×associate-/r*
7×cbrt-undiv unpow-prod-down associate-*l*
6×pow-to-exp pow1 pow-exp div-inv associate-/l*
5×rec-exp 1-exp
4×insert-posit16 add-log-exp
3×pow-unpow associate-*r* cbrt-unprod unswap-sqr sqr-pow
2×clear-num frac-2neg
1×pow-pow associate-/r/ *-commutative pow-flip inv-pow
Counts
4 → 131
Calls
4 calls:
Slowest
114.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
67.0ms
(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
53.0ms
(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
42.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

series704.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
246.0ms
(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
224.0ms
(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
139.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
95.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify48.8s

Counts
174 → 143
Calls
174 calls:
Slowest
1.2s
(* (* (/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))) (/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))) (/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))))
814.0ms
(/ 1 (/ (* (cbrt (sin B)) (cbrt (sin B))) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
746.0ms
(real->posit16 (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
686.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
671.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

prune2.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

17.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.5b
(/ (* (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))

rewrite181.0ms

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
69.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
56.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
38.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
15.0ms
(* (/ x (sin B)) (cos B))

series585.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
237.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
133.0ms
(* (/ x (sin B)) (cos B))
114.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
101.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify28.4s

Counts
124 → 113
Calls
124 calls:
Slowest
976.0ms
(* (* (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B)) (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))) (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B)))
720.0ms
(sqrt (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B)))
666.0ms
(real->posit16 (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
661.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
654.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (* (cbrt (sin B)) (cbrt (sin B))))

prune1.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

17.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.5b
(/ (* (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 (cos B)) (sin B))

rewrite179.0ms

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
94.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
38.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
34.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
12.0ms
(/ (* x (cos B)) (sin B))

series583.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
236.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
120.0ms
(/ (* x (cos B)) (sin B))
120.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
107.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify27.8s

Counts
116 → 102
Calls
116 calls:
Slowest
1.2s
(* (* (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B)) (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))) (/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B)))
635.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (* (cbrt (sin B)) (cbrt (sin B))))
624.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
598.0ms
(real->posit16 (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
595.0ms
(* (pow (cbrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) F)

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes379.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.4b

bsearch650.0ms

end0.0ms

sample14.2s

Algorithm
intervals
Results
5.2s1692×body1280valid
3.1s1404×body640valid
2.7s4795×body80valid
1.5s1670×body80nan
1.0s652×body320valid
374.0ms367×body160valid