Details

Time bar (total: 2.4m)

sample477.0ms

Algorithm
intervals
Results
119.0ms47×body1280valid
116.0ms49×body640valid
73.0ms34×body320valid
61.0ms144×body80valid
20.0ms57×body80nan
8.0ms9×body160valid

simplify441.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
440.0ms
(+ (- (* 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: 11.0b

localize69.0ms

Local error

Found 4 expressions with local error:

13.8b
(pow (fma 2 x (fma F F 2)) -1/2)
5.8b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.1b
(/ (sin B) F)
0.1b
(/ x (tan B))

rewrite70.0ms

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
27.0ms
(/ (sin B) F)
17.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
11.0ms
(/ x (tan B))
7.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series707.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
272.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
218.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
166.0ms
(/ x (tan B))
50.0ms
(/ (sin B) F)

simplify51.9s

Counts
278 → 226
Calls
278 calls:
Slowest
730.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
669.0ms
(/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
620.0ms
(/ (pow (cbrt (fma 2 x (fma F F 2))) -1/2) (/ (cbrt (sin B)) (sqrt F)))
599.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
574.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))

prune3.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.7b

localize71.0ms

Local error

Found 4 expressions with local error:

13.8b
(pow (fma 2 x (fma F F 2)) -1/2)
0.4b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
0.3b
(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
0.1b
(/ x (tan B))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
54×times-frac
45×*-un-lft-identity add-cube-cbrt
25×unpow-prod-down associate-*l*
22×add-exp-log
13×add-cbrt-cube
10×associate-/l*
9×sqr-pow
7×pow1 div-exp
6×associate-/r*
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-to-exp cbrt-undiv pow-unpow associate-*r* pow-exp div-inv
2×clear-num frac-2neg cbrt-unprod
1×pow-pow pow-prod-down associate-*l/ tan-quot associate-/r/ *-commutative
Counts
4 → 150
Calls
4 calls:
Slowest
14.0ms
(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
14.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
5.0ms
(/ x (tan B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series792.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
197.0ms
(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
169.0ms
(/ x (tan B))
158.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))

simplify23.9s

Counts
142 → 162
Calls
142 calls:
Slowest
850.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) 1)
841.0ms
(* (* (* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))) (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))) (* (* F F) F))
782.0ms
(/ (* (* (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)) (* (* (sin B) (sin B)) (sin B)))
531.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
448.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) 1)

prune2.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.7b

localize52.0ms

Local error

Found 4 expressions with local error:

13.8b
(pow (fma 2 x (fma F F 2)) -1/2)
0.4b
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
0.3b
(* (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) F)
0.1b
(/ x (tan B))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
42×add-sqr-sqrt
37×prod-exp
27×*-un-lft-identity
24×times-frac add-cube-cbrt
20×add-cbrt-cube
16×associate-*r*
13×div-exp
9×pow-to-exp unpow-prod-down pow-exp unswap-sqr
8×associate-*l*
7×pow1 cbrt-unprod
6×rec-exp 1-exp
5×sqr-pow
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow associate-/r* associate-/l*
2×associate-*l/ associate-*r/ un-div-inv *-commutative div-inv
1×clear-num pow-pow frac-2neg pow-prod-down tan-quot associate-/r/
Counts
4 → 141
Calls
4 calls:
Slowest
28.0ms
(* (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) F)
16.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
9.0ms
(/ x (tan B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series815.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
276.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
229.0ms
(* (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) F)
176.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
134.0ms
(/ x (tan B))

simplify17.8s

Counts
120 → 153
Calls
120 calls:
Slowest
610.0ms
(+ (+ (* (log (fma 2 x (fma F F 2))) -1/2) (- 0 (log (sin B)))) (log F))
580.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
576.0ms
(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sqrt (/ 1 (sin B))))
566.0ms
(* (* (* (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)) (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))))
525.0ms
(* (* (pow (fma 2 x (fma F F 2)) -1/2) 1) F)

prune2.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.7b

localize75.0ms

Local error

Found 4 expressions with local error:

13.8b
(pow (fma 2 x (fma F F 2)) -1/2)
0.4b
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
0.3b
(* (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) F)
0.2b
(* x (/ 1 (tan B)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
74×add-exp-log
49×add-sqr-sqrt
41×prod-exp
30×associate-*r*
28×*-un-lft-identity
26×times-frac
24×add-cube-cbrt
23×add-cbrt-cube
14×div-exp
12×unswap-sqr
11×associate-*l*
9×pow-to-exp pow1 unpow-prod-down pow-exp cbrt-unprod
7×rec-exp 1-exp
5×sqr-pow
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow associate-*r/ un-div-inv *-commutative
2×pow-prod-down associate-*l/ div-inv
1×pow-pow tan-quot associate-/r/
Counts
4 → 150
Calls
4 calls:
Slowest
62.0ms
(* (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) F)
29.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
27.0ms
(* x (/ 1 (tan B)))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series842.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
282.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
247.0ms
(* (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) F)
165.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
148.0ms
(* x (/ 1 (tan B)))

simplify18.3s

Counts
125 → 162
Calls
125 calls:
Slowest
578.0ms
(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sqrt (/ 1 (sin B))))
531.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
522.0ms
(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sqrt (/ 1 (sin B))))
504.0ms
(* (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) F)
492.0ms
(* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (sqrt (/ 1 (sin B))))

prune3.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.6b

regimes515.0ms

Accuracy

0% (0.7b remaining)

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

bsearch3.0ms

end0.0ms

sample13.9s

Algorithm
intervals
Results
4.9s1700×body1280valid
3.8s1310×body640valid
2.6s4860×body80valid
1.2s701×body320valid
758.0ms1702×body80nan
312.0ms325×body160valid