Details

Time bar (total: 2.5m)

sample486.0ms

Algorithm
intervals
Results
93.0ms42×body1280valid
92.0ms54×body640valid
90.0ms164×body80valid
71.0ms66×body80nan
37.0ms29×body320valid
5.0ms7×body160valid

simplify385.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
385.0ms
(+ (- (* 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

localize44.0ms

Local error

Found 4 expressions with local error:

15.7b
(pow (fma 2 x (fma F F 2)) -1/2)
7.5b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.1b
(/ (sin B) F)
0.1b
(/ x (tan B))

rewrite38.0ms

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
13.0ms
(/ x (tan B))
9.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
8.0ms
(/ (sin B) F)
3.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series684.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
281.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
247.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
123.0ms
(/ x (tan B))
32.0ms
(/ (sin B) F)

simplify53.8s

Counts
278 → 226
Calls
278 calls:
Slowest
663.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
652.0ms
(/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (/ (sqrt (sin B)) (* (cbrt F) (cbrt F))))
600.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) 1)
599.0ms
(/ (pow (cbrt (fma 2 x (fma F F 2))) -1/2) (/ (sqrt (sin B)) (sqrt F)))
591.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))

prune3.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.4b

localize46.0ms

Local error

Found 4 expressions with local error:

15.7b
(pow (fma x 2 (fma F F 2)) -1/2)
0.3b
(* (/ 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))

rewrite67.0ms

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
Counts
4 → 129
Calls
4 calls:
Slowest
33.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
16.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
11.0ms
(/ 1 (sin B))
4.0ms
(pow (fma x 2 (fma F F 2)) -1/2)

series535.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
145.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
129.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
26.0ms
(/ 1 (sin B))

simplify13.3s

Counts
97 → 141
Calls
97 calls:
Slowest
862.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))
613.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
521.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))
483.0ms
(+ (- (log 1) (log (sin B))) (log (* (pow (fma x 2 (fma F F 2)) -1/2) F)))
467.0ms
(+ (- (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))

prune2.3s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.4b

localize46.0ms

Local error

Found 4 expressions with local error:

15.7b
(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))
0.3b
(* (* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2)) F)
0.1b
(/ 1 (sin B))

rewrite101.0ms

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
Counts
4 → 142
Calls
4 calls:
Slowest
57.0ms
(* (* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2)) F)
34.0ms
(* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2))
5.0ms
(/ 1 (sin B))
2.0ms
(pow (fma x 2 (fma F F 2)) -1/2)

series559.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
278.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
154.0ms
(* (* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2)) F)
101.0ms
(* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2))
26.0ms
(/ 1 (sin B))

simplify17.7s

Counts
118 → 154
Calls
118 calls:
Slowest
674.0ms
(* (sqrt (/ 1 (sin B))) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
605.0ms
(* (* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2)) F)
597.0ms
(* (sqrt (/ 1 (sin B))) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
581.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
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)))

prune2.5s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.4b

localize78.0ms

Local error

Found 4 expressions with local error:

15.7b
(sqrt (fma x 2 (fma F F 2)))
15.7b
(sqrt (fma x 2 (fma F F 2)))
0.7b
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
0.4b
(* (/ 1 (sin B)) (* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
118×add-exp-log
85×prod-exp
59×add-sqr-sqrt
44×unpow-prod-down
30×pow-to-exp pow-exp
28×sqrt-prod
26×*-un-lft-identity
25×add-cube-cbrt
23×associate-*l*
20×div-exp
19×unswap-sqr
18×add-cbrt-cube
12×swap-sqr sqr-pow
11×times-frac associate-*r*
10×rec-exp 1-exp
8×pow1
7×cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down *-commutative
1×pow2 associate-*l/ pow-sqr pow-prod-up div-inv
Counts
4 → 179
Calls
4 calls:
Slowest
47.0ms
(* (/ 1 (sin B)) (* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2)))
38.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
2.0ms
(sqrt (fma x 2 (fma F F 2)))
2.0ms
(sqrt (fma x 2 (fma F F 2)))

series499.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(sqrt (fma x 2 (fma F F 2)))
132.0ms
(sqrt (fma x 2 (fma F F 2)))
123.0ms
(* (/ 1 (sin B)) (* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2)))
80.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))

simplify37.7s

Counts
176 → 191
Calls
176 calls:
Slowest
832.0ms
(+ (- (log 1) (log (sin B))) (+ (* (log (sqrt (fma x 2 (fma F F 2)))) -1/2) (* (log (sqrt (fma x 2 (fma F F 2)))) -1/2)))
722.0ms
(+ (- (log 1) (log (sin B))) (+ (* (log (sqrt (fma x 2 (fma F F 2)))) -1/2) (* (log (sqrt (fma x 2 (fma F F 2)))) -1/2)))
679.0ms
(+ (- (log 1) (log (sin B))) (+ (* (log (sqrt (fma x 2 (fma F F 2)))) -1/2) (* (log (sqrt (fma x 2 (fma F F 2)))) -1/2)))
678.0ms
(+ (- (log 1) (log (sin B))) (+ (* (log (sqrt (fma x 2 (fma F F 2)))) -1/2) (* (log (sqrt (fma x 2 (fma F F 2)))) -1/2)))
646.0ms
(+ (- 0 (log (sin B))) (+ (* (log (sqrt (fma x 2 (fma F F 2)))) -1/2) (* (log (sqrt (fma x 2 (fma F F 2)))) -1/2)))

prune3.6s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 9.4b

regimes579.0ms

Accuracy

0% (0.6b remaining)

Error of 10.8b against oracle of 10.2b and baseline of 10.8b

bsearch5.0ms

end0.0ms

sample13.8s

Algorithm
intervals
Results
5.2s1665×body1280valid
2.9s1423×body640valid
2.8s4812×body80valid
1.4s664×body320valid
659.0ms1624×body80nan
336.0ms320×body160valid