Details

Time bar (total: 3.8m)

sample597.0ms

Algorithm
intervals
Results
181.0ms54×body1280valid
150.0ms49×body640valid
89.0ms161×body80valid
62.0ms17×body320valid
24.0ms53×body80nan
11.0ms11×body160valid

simplify394.0ms

Calls
1 calls:
Slowest
393.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.0b

localize42.0ms

Local error

Found 4 expressions with local error:

17.1b
(pow (fma 2 x (fma F F 2)) -1/2)
5.2b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.2b
(/ (sin B) F)
0.2b
(/ x (tan B))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
181×times-frac
108×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
45×unpow-prod-down
22×associate-/r* add-exp-log
16×associate-/l*
15×sqr-pow
13×add-cbrt-cube
11×div-exp div-inv
10×associate-/r/
5×pow1 cbrt-undiv
4×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow pow-exp
1×pow-pow tan-quot
Calls
4 calls:
Slowest
19.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
14.0ms
(/ (sin B) F)
9.0ms
(/ x (tan B))
6.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series765.0ms

Calls
4 calls:
Slowest
355.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
217.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
159.0ms
(/ x (tan B))
34.0ms
(/ (sin B) F)

simplify53.7s

Calls
285 calls:
Slowest
845.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) 1))
841.0ms
(/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (/ (* (cbrt (sin B)) (cbrt (sin B))) (* (cbrt F) (cbrt F))))
796.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
602.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
586.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))

prune3.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.7b

localize61.0ms

Local error

Found 4 expressions with local error:

17.1b
(pow (fma x 2 (fma F F 2)) -1/2)
0.4b
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
0.3b
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.2b
(/ x (tan B))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt
56×add-exp-log
34×*-un-lft-identity
31×prod-exp
30×add-cube-cbrt
27×associate-*l* unswap-sqr
26×times-frac
24×associate-*r*
20×add-cbrt-cube
14×unpow-prod-down
12×pow1
9×div-exp associate-*l/
8×sqr-pow
7×cbrt-unprod
6×pow-to-exp associate-/r* pow-exp associate-/l*
4×expm1-log1p-u rec-exp 1-exp pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow *-commutative
2×clear-num frac-2neg div-inv
1×pow-pow tan-quot associate-/r/
Calls
4 calls:
Slowest
99.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
21.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
9.0ms
(/ x (tan B))
4.0ms
(pow (fma x 2 (fma F F 2)) -1/2)

series726.0ms

Calls
4 calls:
Slowest
291.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
158.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
151.0ms
(/ x (tan B))
127.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify30.7s

Calls
146 calls:
Slowest
804.0ms
(+ (- (log 1) (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
614.0ms
(* (sqrt 1) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
573.0ms
(* (/ 1 (sqrt (sin B))) (* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (sqrt F)))
553.0ms
(* (/ 1 (sqrt (sin B))) (* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F)))
552.0ms
(* (/ (sqrt 1) (sqrt (sin B))) (sqrt (* (pow (fma x 2 (fma F F 2)) -1/2) F)))

prune3.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.7b

localize70.0ms

Local error

Found 4 expressions with local error:

17.1b
(sqrt (fma 2 x (fma F F 2)))
17.1b
(sqrt (fma 2 x (fma F F 2)))
0.4b
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F))
0.3b
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
259×times-frac
152×add-sqr-sqrt
150×*-un-lft-identity add-cube-cbrt
108×unpow-prod-down
60×sqrt-prod
32×add-exp-log
23×associate-/l*
21×div-exp
19×associate-/r*
18×sqr-pow
13×div-inv
11×add-cbrt-cube
9×associate-/r/
6×pow1
5×pow-to-exp pow-exp
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg 1-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
11.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F))
9.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B))
1.0ms
(sqrt (fma 2 x (fma F F 2)))
1.0ms
(sqrt (fma 2 x (fma F F 2)))

series1.2s

Calls
4 calls:
Slowest
504.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B))
403.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F))
165.0ms
(sqrt (fma 2 x (fma F F 2)))
130.0ms
(sqrt (fma 2 x (fma F F 2)))

simplify1.7m

Calls
401 calls:
Slowest
768.0ms
(/ (pow (sqrt (sqrt (fma 2 x (fma F F 2)))) -1/2) (cbrt (sin B)))
731.0ms
(/ (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (* (* (sin B) (sin B)) (sin B)))
694.0ms
(/ (pow (sqrt (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2))))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
660.0ms
(/ (pow (* (cbrt (sqrt (fma 2 x (fma F F 2)))) (cbrt (sqrt (fma 2 x (fma F F 2))))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
650.0ms
(/ (sqrt (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (/ (cbrt 1) (cbrt F)))

prune5.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.7b

localize87.0ms

Local error

Found 4 expressions with local error:

17.1b
(sqrt (fma 2 x (fma F F 2)))
17.1b
(sqrt (fma 2 x (fma F F 2)))
17.1b
(sqrt (fma 2 x (fma F F 2)))
0.7b
(* (sqrt (sqrt (fma 2 x (fma F F 2)))) (sqrt (sqrt (fma 2 x (fma F F 2)))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
52×add-sqr-sqrt
35×sqrt-pow1
30×pow1
19×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
20.0ms
(* (sqrt (sqrt (fma 2 x (fma F F 2)))) (sqrt (sqrt (fma 2 x (fma F F 2)))))
1.0ms
(sqrt (fma 2 x (fma F F 2)))
1.0ms
(sqrt (fma 2 x (fma F F 2)))
1.0ms
(sqrt (fma 2 x (fma F F 2)))

series570.0ms

Calls
4 calls:
Slowest
163.0ms
(sqrt (fma 2 x (fma F F 2)))
146.0ms
(sqrt (fma 2 x (fma F F 2)))
142.0ms
(sqrt (fma 2 x (fma F F 2)))
118.0ms
(* (sqrt (sqrt (fma 2 x (fma F F 2)))) (sqrt (sqrt (fma 2 x (fma F F 2)))))

simplify6.0s

Calls
133 calls:
Slowest
323.0ms
(- (+ (sqrt 2) (* x (sqrt 1/2))) (* 1/2 (* (pow x 2) (sqrt 1/8))))
304.0ms
(- (+ (sqrt 2) (* x (sqrt 1/2))) (* 1/2 (* (pow x 2) (sqrt 1/8))))
294.0ms
(- (+ (sqrt 2) (* x (sqrt 1/2))) (* 1/2 (* (pow x 2) (sqrt 1/8))))
289.0ms
(- (+ (sqrt 2) (* x (sqrt 1/2))) (* 1/2 (* (pow x 2) (sqrt 1/8))))
230.0ms
(* (* (* (sqrt (sqrt (fma 2 x (fma F F 2)))) (sqrt (sqrt (fma 2 x (fma F F 2))))) (sqrt (sqrt (fma 2 x (fma F F 2))))) (* (* (sqrt (sqrt (fma 2 x (fma F F 2)))) (sqrt (sqrt (fma 2 x (fma F F 2))))) (sqrt (sqrt (fma 2 x (fma F F 2))))))

prune2.5s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 9.7b

regimes506.0ms

Accuracy

0% (0.7b remaining)

Error of 10.6b against oracle of 9.9b and baseline of 10.6b

bsearch4.0ms

end0.0ms

sample14.1s

Algorithm
intervals
Results
5.7s1664×body1280valid
2.9s1397×body640valid
2.6s4738×body80valid
1.5s692×body320valid
721.0ms1710×body80nan
378.0ms375×body160valid