Details

Time bar (total: 4.0m)

sample520.0ms

Algorithm
intervals
Results
148.0ms54×body1280valid
117.0ms49×body640valid
76.0ms161×body80valid
68.0ms53×body80nan
23.0ms17×body320valid
10.0ms11×body160valid

simplify365.0ms

Calls
1 calls:
Slowest
365.0ms
(+ (- (* 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: 10.2b

localize46.0ms

Local error

Found 4 expressions with local error:

17.1b
(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))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
154×*-un-lft-identity
95×associate-*l*
83×add-sqr-sqrt
81×times-frac
60×distribute-lft-out
59×unpow-prod-down
58×add-cube-cbrt
27×associate-/l*
22×add-exp-log
15×associate-*r* unswap-sqr
13×add-cbrt-cube
11×sqr-pow
7×pow1
6×associate-/r* prod-exp
5×div-exp *-commutative
4×insert-posit16 add-log-exp
3×pow-to-exp cbrt-undiv pow-unpow pow-exp
2×clear-num frac-2neg cbrt-unprod div-inv
1×pow-pow pow-prod-down tan-quot associate-/r/
Calls
4 calls:
Slowest
795.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
377.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
93.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.0ms
(/ x (tan B))

series578.0ms

Calls
4 calls:
Slowest
225.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
134.0ms
(/ x (tan B))
111.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
107.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify49.2s

Calls
250 calls:
Slowest
903.0ms
(/ (cbrt (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (sqrt (sin B)))
763.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (* (cbrt F) (cbrt F))) 1)
686.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sqrt F)) (* (cbrt (sin B)) (cbrt (sin B))))
680.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt (sin B)))
614.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))

prune2.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

17.1b
(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 (cos B)) (sin B))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
171×*-un-lft-identity
108×add-sqr-sqrt times-frac
107×associate-*l*
75×add-cube-cbrt
60×distribute-lft-out
59×unpow-prod-down
36×associate-/l*
27×associate-*r*
25×add-exp-log
19×unswap-sqr
16×add-cbrt-cube
11×sqr-pow
9×*-commutative
7×pow1 prod-exp
6×associate-/r* div-exp
4×cbrt-undiv insert-posit16 add-log-exp
3×pow-to-exp pow-unpow pow-exp cbrt-unprod
2×clear-num frac-2neg div-inv
1×pow-pow pow-prod-down
Calls
4 calls:
Slowest
929.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
362.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
93.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
15.0ms
(/ (* x (cos B)) (sin B))

series578.0ms

Calls
4 calls:
Slowest
218.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
131.0ms
(/ (* x (cos B)) (sin B))
118.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
111.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify51.3s

Calls
312 calls:
Slowest
737.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (* (cbrt F) (cbrt F))) 1)
679.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sqrt F)) (* (cbrt (sin B)) (cbrt (sin B))))
674.0ms
(/ (* (sqrt (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (sqrt F)) (* (cbrt (sin B)) (cbrt (sin B))))
635.0ms
(* (cbrt (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (cbrt (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
589.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))

prune3.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

17.1b
(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)
0.3b
(* (cos B) (/ x (sin B)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
157×*-un-lft-identity
98×associate-*l*
90×add-sqr-sqrt
82×times-frac
60×add-cube-cbrt distribute-lft-out
59×unpow-prod-down
28×associate-*r* associate-/l*
25×add-exp-log
17×unswap-sqr
16×add-cbrt-cube
11×sqr-pow
9×pow1 associate-*r/
8×prod-exp
6×associate-/r* *-commutative
5×div-exp
4×cbrt-unprod insert-posit16 add-log-exp
3×pow-to-exp cbrt-undiv pow-unpow clear-num pow-exp
2×frac-2neg pow-prod-down un-div-inv div-inv
1×pow-pow
Calls
4 calls:
Slowest
914.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
346.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
95.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
15.0ms
(* (cos B) (/ x (sin B)))

series504.0ms

Calls
4 calls:
Slowest
204.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
107.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
98.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
95.0ms
(* (cos B) (/ x (sin B)))

simplify48.8s

Calls
259 calls:
Slowest
1.1s
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (* (cbrt F) (cbrt F))) 1)
659.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sqrt F)) (* (cbrt (sin B)) (cbrt (sin B))))
650.0ms
(/ (* (cbrt (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (cbrt (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))) (sqrt (sin B)))
623.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
619.0ms
(/ (sqrt (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (sqrt (sin B)))

prune3.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

17.1b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sin B))
0.2b
(* F (/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sin B)))
0.2b
(/ (* x (cos B)) (sin B))

rewrite976.0ms

Algorithm
rewrite-expression-head
Rules
222×*-un-lft-identity
117×times-frac
95×add-sqr-sqrt
90×distribute-lft-out
82×unpow-prod-down
77×add-cube-cbrt
60×associate-*l*
55×associate-*r*
39×associate-/l*
25×add-exp-log
19×associate-*r/
16×add-cbrt-cube
10×sqr-pow
9×associate-/r*
8×div-exp unswap-sqr
7×pow1
5×prod-exp *-commutative
4×cbrt-undiv clear-num insert-posit16 add-log-exp
3×pow-to-exp pow-unpow frac-2neg pow-exp cbrt-unprod div-inv
2×un-div-inv
1×pow-pow pow-prod-down
Calls
4 calls:
Slowest
530.0ms
(* F (/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sin B)))
292.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sin B))
131.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
14.0ms
(/ (* x (cos B)) (sin B))

series1.0s

Calls
4 calls:
Slowest
547.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sin B))
203.0ms
(* F (/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sin B)))
128.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
123.0ms
(/ (* x (cos B)) (sin B))

simplify52.5s

Calls
291 calls:
Slowest
964.0ms
(* (* (* F F) F) (* (* (/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sin B)) (/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sin B))) (/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sin B))))
761.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sqrt (sin B)))
719.0ms
(/ (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (* (* (sin B) (sin B)) (sin B)))
529.0ms
(/ (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) 1)
475.0ms
(* (sqrt F) (sqrt (/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (sin B))))

prune3.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes437.0ms

Accuracy

97.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.6b

bsearch502.0ms

end0.0ms

sample14.2s

Algorithm
intervals
Results
5.7s1664×body1280valid
2.8s4738×body80valid
2.7s1397×body640valid
1.5s692×body320valid
685.0ms1710×body80nan
467.0ms375×body160valid