Details

Time bar (total: 2.7m)

sample444.0ms

Algorithm
intervals
Results
139.0ms56×body1280valid
57.0ms43×body640valid
46.0ms153×body80valid
19.0ms20×body320valid
18.0ms59×body80nan
5.0ms9×body160valid

simplify466.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
465.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.3b

localize52.0ms

Local error

Found 4 expressions with local error:

17.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.9b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(/ x (tan B))

rewrite230.0ms

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
133.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
45.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
37.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
11.0ms
(/ x (tan B))

series617.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
197.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
162.0ms
(/ x (tan B))
148.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
109.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify28.7s

Counts
129 → 109
Calls
129 calls:
Slowest
1.1s
(* (* (/ (* (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)))
715.0ms
(- (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (sin B)))
692.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) F)
688.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
679.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (* (cbrt (sin B)) (cbrt (sin B))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

17.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.9b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(/ 1 (/ (tan B) x))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
58×add-sqr-sqrt
53×*-un-lft-identity add-cube-cbrt
31×add-exp-log
16×associate-/r* add-cbrt-cube
11×div-exp
7×unpow-prod-down associate-*l*
6×pow1 prod-exp div-inv
5×cbrt-undiv
4×insert-posit16 associate-/l* add-log-exp
3×pow-to-exp pow-unpow associate-*r* pow-exp unswap-sqr sqr-pow
2×rec-exp clear-num frac-2neg 1-exp cbrt-unprod
1×pow-pow associate-/r/ *-commutative pow-flip inv-pow
Counts
4 → 145
Calls
4 calls:
Slowest
90.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
39.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
33.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
11.0ms
(/ 1 (/ (tan B) x))

series474.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
218.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
87.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
86.0ms
(/ 1 (/ (tan B) x))
83.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify33.6s

Counts
206 → 157
Calls
206 calls:
Slowest
1.5s
(* (* (/ (* (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)))
719.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (* (cbrt (sin B)) (cbrt (sin B))))
661.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
641.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
635.0ms
(real->posit16 (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 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)
0.9b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(/ x (sin B))

rewrite197.0ms

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 *-commutative
Counts
4 → 96
Calls
4 calls:
Slowest
83.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
61.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
40.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms
(/ x (sin B))

series519.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
129.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
107.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
77.0ms
(/ x (sin B))

simplify28.4s

Counts
128 → 108
Calls
128 calls:
Slowest
1.3s
(* (* (/ (* (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)))
691.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
683.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
646.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (* (cbrt (sin B)) (cbrt (sin B))))
644.0ms
(real->posit16 (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

17.3b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
17.3b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
0.9b
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
0.6b
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))

rewrite386.0ms

Algorithm
rewrite-expression-head
Rules
51×add-exp-log
50×add-sqr-sqrt
44×unpow-prod-down
28×prod-exp sqrt-prod
20×*-un-lft-identity add-cube-cbrt
16×unswap-sqr
15×add-cbrt-cube
12×pow-to-exp swap-sqr pow-exp sqr-pow
11×div-exp
10×associate-*r* associate-*l*
6×pow1
4×sqrt-div cbrt-unprod insert-posit16 add-log-exp
3×cbrt-undiv associate-/r* times-frac
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×pow2 clear-num frac-2neg pow-prod-down pow-sqr *-commutative pow-prod-up div-inv associate-/l*
Counts
4 → 135
Calls
4 calls:
Slowest
176.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
153.0ms
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
28.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
27.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
209.0ms
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
82.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
79.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
55.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

simplify47.3s

Counts
183 → 147
Calls
183 calls:
Slowest
1.4s
(* (pow (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
1.0s
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (* (cbrt (+ (+ 2 (* F F)) (* 2 x))) (cbrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2))
982.0ms
(* (pow (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
933.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) -1/2))
927.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (* (cbrt (sqrt (+ (+ 2 (* F F)) (* 2 x)))) (cbrt (sqrt (+ (+ 2 (* F F)) (* 2 x))))) -1/2))

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes331.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.4b

bsearch610.0ms

end0.0ms

sample13.8s

Algorithm
intervals
Results
5.0s1650×body1280valid
2.9s1356×body640valid
2.2s4779×body80valid
1.7s715×body320valid
905.0ms354×body160valid
677.0ms1629×body80nan