Details

Time bar (total: 2.1m)

sample1.0s

Algorithm
intervals
Results
168.0ms45×body640valid
142.0ms44×body1280valid
62.0ms155×body80valid
54.0ms20×body320valid
43.0ms15×body160valid
16.0ms45×body80nan

simplify423.0ms

Calls
1 calls:
Slowest
422.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune47.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize43.0ms

Local error

Found 4 expressions with local error:

19.1b
(pow (fma 2 x (fma F F 2)) -1/2)
7.4b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.1b
(/ (sin B) F)
0.1b
(/ x (tan B))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
181×times-frac
106×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
45×unpow-prod-down
22×add-exp-log
19×associate-/r*
15×sqr-pow
13×add-cbrt-cube associate-/l*
11×div-exp div-inv
5×pow1 cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow clear-num frac-2neg pow-exp
2×associate-/r/
1×pow-pow tan-quot
Calls
4 calls:
Slowest
17.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
12.0ms
(/ (sin B) F)
10.0ms
(/ x (tan B))
7.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series715.0ms

Calls
4 calls:
Slowest
276.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
230.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
154.0ms
(/ x (tan B))
55.0ms
(/ (sin B) F)

simplify52.2s

Calls
278 calls:
Slowest
890.0ms
(/ (* (cbrt (pow (fma 2 x (fma F F 2)) -1/2)) (cbrt (pow (fma 2 x (fma F F 2)) -1/2))) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
623.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
591.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
560.0ms
(/ (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (/ 1 (* (cbrt F) (cbrt F))))
552.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))

prune3.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.4b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

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 associate-*l*
18×times-frac
10×div-exp
8×pow1
7×unpow-prod-down cbrt-unprod
6×pow-to-exp pow-exp
5×rec-exp 1-exp
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u 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-*l/ pow-flip inv-pow
Calls
4 calls:
Slowest
50.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
8.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
5.0ms
(/ 1 (sin B))
4.0ms
(pow (fma x 2 (fma F F 2)) -1/2)

series626.0ms

Calls
4 calls:
Slowest
298.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
157.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
146.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
25.0ms
(/ 1 (sin B))

simplify12.6s

Calls
97 calls:
Slowest
733.0ms
(+ (- (log 1) (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
580.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
512.0ms
(+ (- (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
507.0ms
(+ (- (log 1) (log (sin B))) (log (* (pow (fma x 2 (fma F F 2)) -1/2) F)))
502.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.4b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
69×add-exp-log
42×add-sqr-sqrt
37×prod-exp
27×*-un-lft-identity
24×times-frac add-cube-cbrt
20×add-cbrt-cube
14×div-exp associate-*l*
10×associate-*r*
9×pow-to-exp unpow-prod-down pow-exp unswap-sqr
8×pow1
7×rec-exp 1-exp cbrt-unprod
5×sqr-pow
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow associate-/r* associate-*l/ associate-/l*
2×*-commutative div-inv
1×clear-num pow-pow frac-2neg pow-prod-down pow-flip inv-pow
Calls
4 calls:
Slowest
45.0ms
(* (* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2)) F)
27.0ms
(* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2))
9.0ms
(/ 1 (sin B))
2.0ms
(pow (fma x 2 (fma F F 2)) -1/2)

series532.0ms

Calls
4 calls:
Slowest
240.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
144.0ms
(* (* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2)) F)
134.0ms
(* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2))
14.0ms
(/ 1 (sin B))

simplify17.2s

Calls
118 calls:
Slowest
689.0ms
(* (sqrt (/ 1 (sin B))) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
576.0ms
(* (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))) (* (* (pow (fma x 2 (fma F F 2)) -1/2) (pow (fma x 2 (fma F F 2)) -1/2)) (pow (fma x 2 (fma F F 2)) -1/2)))
565.0ms
(* (sqrt (/ 1 (sin B))) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
538.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
524.0ms
(* (sqrt (/ 1 (sin B))) (pow (fma x 2 (fma F F 2)) (/ -1/2 2)))

prune2.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.4b

localize67.0ms

Local error

Found 4 expressions with local error:

19.1b
(pow (fma x 2 (fma F F 2)) -1/2)
1.8b
(log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))
0.4b
(* (/ 1 (sin B)) (expm1 (log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
0.2b
(* (pow (fma x 2 (fma F F 2)) -1/2) F)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
20×associate-*l*
19×add-exp-log
18×*-un-lft-identity
17×add-cube-cbrt
11×times-frac add-cbrt-cube
7×pow1 unpow-prod-down prod-exp
6×associate-*r* unswap-sqr
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow cbrt-unprod sqr-pow
2×pow-to-exp div-exp pow-exp *-commutative
1×cbrt-undiv rec-exp log1p-udef pow-pow 1-exp pow-prod-down associate-*l/ log1p-expm1 div-inv
Calls
4 calls:
Slowest
14.0ms
(* (/ 1 (sin B)) (expm1 (log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
8.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
2.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
0.0ms
(log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))

series996.0ms

Calls
4 calls:
Slowest
349.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
327.0ms
(* (/ 1 (sin B)) (expm1 (log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
193.0ms
(log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))
127.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify12.8s

Calls
66 calls:
Slowest
725.0ms
(+ (- 0 (log (sin B))) (log (expm1 (log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))
555.0ms
(* (sqrt (/ 1 (sin B))) (sqrt (expm1 (log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))
555.0ms
(* (/ (sqrt 1) (sqrt (sin B))) (sqrt (expm1 (log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))
529.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
525.0ms
(cbrt (expm1 (log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))))

prune1.9s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.5b

regimes472.0ms

Accuracy

84.6% (0.8b remaining)

Error of 5.6b against oracle of 4.8b and baseline of 10.2b

bsearch217.0ms

end0.0ms

sample14.0s

Algorithm
intervals
Results
5.3s1630×body1280valid
3.4s1425×body640valid
2.9s4750×body80valid
1.1s694×body320valid
697.0ms1625×body80nan
326.0ms354×body160valid