Details

Time bar (total: 1.5m)

sample609.0ms

Algorithm
intervals
Results
226.0ms45×body640valid
142.0ms44×body1280valid
69.0ms155×body80valid
28.0ms20×body320valid
15.0ms45×body80nan
13.0ms15×body160valid

simplify435.0ms

Calls
1 calls:
Slowest
434.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.7b

localize39.0ms

Local error

Found 4 expressions with local error:

19.1b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.5b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b
(/ x (tan B))

rewrite185.0ms

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
Calls
4 calls:
Slowest
95.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
41.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
36.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms
(/ x (tan B))

series570.0ms

Calls
4 calls:
Slowest
183.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
170.0ms
(/ x (tan B))
110.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
107.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.8s

Calls
79 calls:
Slowest
645.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
624.0ms
(* (sqrt (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (sqrt F))
577.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
558.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
541.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

19.1b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b
(/ 1 (sin B))

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
31×prod-exp
29×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube
18×times-frac
16×associate-*r*
10×div-exp
8×pow1 associate-*l*
7×unpow-prod-down cbrt-unprod
6×pow-to-exp pow-exp
5×rec-exp 1-exp
4×insert-posit16 add-log-exp
3×cbrt-undiv pow-unpow associate-/r* associate-/l* unswap-sqr sqr-pow
2×*-commutative div-inv
1×clear-num pow-pow frac-2neg pow-prod-down associate-*r/ un-div-inv pow-flip inv-pow
Calls
4 calls:
Slowest
127.0ms
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
106.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
27.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms
(/ 1 (sin B))

series531.0ms

Calls
4 calls:
Slowest
260.0ms
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
127.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
124.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
20.0ms
(/ 1 (sin B))

simplify14.3s

Calls
101 calls:
Slowest
620.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
578.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
570.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
493.0ms
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
478.0ms
(+ (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (- 0 (log (sin B))))

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

19.1b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.5b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b
(* x (cos B))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
20×add-sqr-sqrt
13×*-un-lft-identity add-cbrt-cube add-cube-cbrt
10×associate-*l*
7×pow1 unpow-prod-down prod-exp
6×associate-*r*
4×div-exp insert-posit16 add-log-exp unswap-sqr
3×pow-to-exp pow-unpow associate-/r* times-frac pow-exp cbrt-unprod sqr-pow
2×cbrt-undiv *-commutative
1×clear-num pow-pow frac-2neg pow-prod-down div-inv associate-/l*
Calls
4 calls:
Slowest
98.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
63.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
37.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
8.0ms
(* x (cos B))

series507.0ms

Calls
4 calls:
Slowest
208.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
122.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
119.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
58.0ms
(* x (cos B))

simplify10.2s

Calls
63 calls:
Slowest
990.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
538.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
514.0ms
(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
508.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
490.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

19.0b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
19.0b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
0.6b
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
0.5b
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))

rewrite437.0ms

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*
Calls
4 calls:
Slowest
249.0ms
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
153.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
19.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
15.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

series461.0ms

Calls
4 calls:
Slowest
232.0ms
(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
96.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
80.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
54.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

simplify29.4s

Calls
140 calls:
Slowest
598.0ms
(/ (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) 1)
580.0ms
(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F)) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F)) (* (* (sin B) (sin B)) (sin B)))
562.0ms
(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (* F F) F)) (* (* (sin B) (sin B)) (sin B)))
543.0ms
(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (* F F) F)) (* (* (sin B) (sin B)) (sin B)))
477.0ms
(* (* (cbrt (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (cbrt (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (cbrt (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (cbrt (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))))

prune2.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes289.0ms

Accuracy

98.5% (0.2b remaining)

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

bsearch782.0ms

end0.0ms

sample13.8s

Algorithm
intervals
Results
5.6s1630×body1280valid
3.3s1425×body640valid
2.6s4750×body80valid
924.0ms694×body320valid
726.0ms1625×body80nan
356.0ms354×body160valid