Details

Time bar (total: 1.9m)

sample630.0ms

Algorithm
intervals
Results
181.0ms48×body1280valid
111.0ms50×body640valid
78.0ms154×body80valid
34.0ms22×body320valid
17.0ms39×body80nan
13.0ms13×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)))))

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize59.0ms

Local error

Found 4 expressions with local error:

15.7b
(pow (fma 2 x (fma F F 2)) -1/2)
6.7b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.2b
(/ x (tan B))
0.1b
(/ (sin B) F)

rewrite30.0ms

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
Counts
4 → 214
Calls
4 calls:
Slowest
9.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
8.0ms
(/ (sin B) F)
5.0ms
(/ x (tan B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series771.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
346.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
244.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
130.0ms
(/ x (tan B))
51.0ms
(/ (sin B) F)

simplify53.2s

Counts
278 → 226
Calls
278 calls:
Slowest
1.0s
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
751.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sqrt (/ (sin B) F)))
633.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
584.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
575.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ (sqrt (sin B)) 1))

prune3.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.6b

localize62.0ms

Local error

Found 4 expressions with local error:

15.7b
(pow (fma x 2 (fma F F 2)) -1/2)
0.3b
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.2b
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
0.2b
(/ x (tan B))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
56×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
9×div-exp
7×pow1 unpow-prod-down cbrt-unprod
6×pow-to-exp pow-exp
4×expm1-log1p-u rec-exp 1-exp 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/ tan-quot associate-/r/
Counts
4 → 126
Calls
4 calls:
Slowest
33.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
10.0ms
(/ x (tan B))
9.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
2.0ms
(pow (fma x 2 (fma F F 2)) -1/2)

series718.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
287.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
173.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
141.0ms
(/ x (tan B))
116.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify13.0s

Counts
96 → 138
Calls
96 calls:
Slowest
598.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
581.0ms
(* (* (* (/ 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)) (* (* F F) F)))
545.0ms
(+ (- (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
541.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))
509.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))

prune2.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.6b

localize78.0ms

Local error

Found 4 expressions with local error:

15.7b
(pow (fma x 2 (fma F F 2)) -1/2)
0.3b
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.2b
(* (/ x (sin B)) (cos B))
0.2b
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
34×add-sqr-sqrt
33×associate-*l* prod-exp
24×*-un-lft-identity add-cube-cbrt
23×add-cbrt-cube
19×times-frac
9×pow1 div-exp cbrt-unprod
7×unpow-prod-down associate-*r*
6×pow-to-exp pow-exp
5×unswap-sqr
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow *-commutative sqr-pow
2×pow-prod-down associate-*l/ div-inv
1×pow-pow
Counts
4 → 130
Calls
4 calls:
Slowest
57.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
30.0ms
(* (/ x (sin B)) (cos B))
17.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
4.0ms
(pow (fma x 2 (fma F F 2)) -1/2)

series720.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
259.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
190.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
155.0ms
(* (/ x (sin B)) (cos B))
115.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify12.7s

Counts
94 → 142
Calls
94 calls:
Slowest
556.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
544.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
536.0ms
(+ (- (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
476.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))
466.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))

prune2.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.6b

localize55.0ms

Local error

Found 4 expressions with local error:

15.7b
(pow (fma 2 x (fma F F 2)) -1/2)
0.3b
(* F (pow (fma 2 x (fma F F 2)) -1/2))
0.2b
(* (/ x (sin B)) (cos B))
0.2b
(/ (* F (pow (fma 2 x (fma F F 2)) -1/2)) (sin B))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×add-exp-log
19×*-un-lft-identity add-cube-cbrt
16×add-cbrt-cube associate-*l*
13×times-frac
10×associate-*r*
8×prod-exp
7×pow1 unpow-prod-down
5×div-exp unswap-sqr
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp cbrt-undiv pow-unpow associate-/r* pow-exp sqr-pow
2×*-commutative div-inv
1×clear-num pow-pow frac-2neg pow-prod-down associate-*l/ associate-/l*
Counts
4 → 109
Calls
4 calls:
Slowest
29.0ms
(* (/ x (sin B)) (cos B))
22.0ms
(/ (* F (pow (fma 2 x (fma F F 2)) -1/2)) (sin B))
17.0ms
(* F (pow (fma 2 x (fma F F 2)) -1/2))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series792.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
339.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
198.0ms
(/ (* F (pow (fma 2 x (fma F F 2)) -1/2)) (sin B))
135.0ms
(* (/ x (sin B)) (cos B))
120.0ms
(* F (pow (fma 2 x (fma F F 2)) -1/2))

simplify7.9s

Counts
77 → 121
Calls
77 calls:
Slowest
656.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
497.0ms
(- (+ (log F) (log (pow (fma 2 x (fma F F 2)) -1/2))) (log (sin B)))
447.0ms
(* (sqrt F) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
433.0ms
(* (sqrt F) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
425.0ms
(* (* (* F F) F) (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)))

prune1.9s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes372.0ms

Accuracy

94.8% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 10.8b

bsearch452.0ms

end0.0ms

sample14.0s

Algorithm
intervals
Results
5.6s1658×body1280valid
2.9s1380×body640valid
2.7s4823×body80valid
1.2s1607×body80nan
1.1s711×body320valid
303.0ms364×body160valid