Details

Time bar (total: 4.8m)

sample804.0ms

Algorithm
intervals
Results
218.0ms45×body1280valid
127.0ms20×body320valid
125.0ms40×body640valid
90.0ms169×body80valid
41.0ms8×body160valid
24.0ms50×body80nan

simplify573.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
573.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize62.0ms

Local error

Found 4 expressions with local error:

18.3b
(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)

rewrite57.0ms

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
17.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
15.0ms
(/ (sin B) F)
10.0ms
(/ x (tan B))
6.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series736.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
275.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
257.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
168.0ms
(/ x (tan B))
36.0ms
(/ (sin B) F)

simplify53.6s

Counts
278 → 226
Calls
278 calls:
Slowest
706.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (cbrt (/ (sin B) F)))
664.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
644.0ms
(/ (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (/ (sin B) F))
641.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
633.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))

prune3.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.4b

localize89.0ms

Local error

Found 4 expressions with local error:

18.3b
(sqrt (fma 2 x (fma F F 2)))
18.3b
(sqrt (fma 2 x (fma F F 2)))
0.4b
(* (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B)) (/ (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) (/ 1 F))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
631×times-frac
491×add-sqr-sqrt
275×*-un-lft-identity
255×add-cube-cbrt
236×unpow-prod-down
201×add-exp-log
135×associate-*r*
129×div-exp
124×sqrt-prod
65×unswap-sqr
58×sqr-pow
52×prod-exp
34×associate-*l*
33×pow-to-exp pow-exp
30×add-cbrt-cube
24×div-inv
15×rec-exp 1-exp
13×associate-/r*
12×cbrt-undiv
10×associate-/l*
8×pow1
6×cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 520
Calls
4 calls:
Slowest
51.0ms
(* (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B)) (/ (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) (/ 1 F))
3.0ms
(sqrt (fma 2 x (fma F F 2)))
2.0ms
(sqrt (fma 2 x (fma F F 2)))

series888.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
374.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F))
213.0ms
(* (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B)) (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F)))
153.0ms
(sqrt (fma 2 x (fma F F 2)))
147.0ms
(sqrt (fma 2 x (fma F F 2)))

simplify3.1m

Counts
678 → 532
Calls
678 calls:
Slowest
683.0ms
(/ (pow (* (cbrt (sqrt (fma 2 x (fma F F 2)))) (cbrt (sqrt (fma 2 x (fma F F 2))))) -1/2) (/ (* (cbrt 1) (cbrt 1)) 1))
658.0ms
(* (sqrt (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B))) (/ (pow (sqrt (sqrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (sqrt F))))
657.0ms
(* (/ (sqrt (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (sqrt (sin B))) (/ (sqrt (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (/ (sqrt 1) (sqrt F))))
656.0ms
(/ (pow (sqrt (sqrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
648.0ms
(* (/ (* (* (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))) (/ (* (* (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)) (* (* (/ 1 F) (/ 1 F)) (/ 1 F))))

prune9.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.4b

localize43.0ms

Local error

Found 4 expressions with local error:

18.3b
(sqrt (fma x 2 (fma F F 2)))
0.4b
(/ (/ (* 1 F) (sqrt (fma x 2 (fma F F 2)))) (sin B))
0.2b
(/ (* 1 F) (sqrt (fma x 2 (fma F F 2))))
0.2b
(/ x (tan B))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
69×times-frac
41×add-sqr-sqrt
40×*-un-lft-identity add-cube-cbrt
25×add-exp-log
21×sqrt-prod
20×add-cbrt-cube
14×associate-/l*
12×associate-/r*
11×div-exp
8×cbrt-undiv
7×div-inv
5×pow1
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×1-exp cbrt-unprod
1×rem-sqrt-square sqrt-pow1 pow1/2 tan-quot associate-/r/ associate-/l/
Counts
4 → 142
Calls
4 calls:
Slowest
22.0ms
(/ (/ (* 1 F) (sqrt (fma x 2 (fma F F 2)))) (sin B))
11.0ms
(/ (* 1 F) (sqrt (fma x 2 (fma F F 2))))
5.0ms
(/ x (tan B))
1.0ms
(sqrt (fma x 2 (fma F F 2)))

series661.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
210.0ms
(/ (/ (* 1 F) (sqrt (fma x 2 (fma F F 2)))) (sin B))
172.0ms
(sqrt (fma x 2 (fma F F 2)))
146.0ms
(/ x (tan B))
133.0ms
(/ (* 1 F) (sqrt (fma x 2 (fma F F 2))))

simplify10.0s

Counts
146 → 154
Calls
146 calls:
Slowest
584.0ms
(/ (* (* (* 1 1) 1) (* (* F F) F)) (* (* (sqrt (fma x 2 (fma F F 2))) (sqrt (fma x 2 (fma F F 2)))) (sqrt (fma x 2 (fma F F 2)))))
419.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
400.0ms
(/ (* (* (/ (* 1 F) (sqrt (fma x 2 (fma F F 2)))) (/ (* 1 F) (sqrt (fma x 2 (fma F F 2))))) (/ (* 1 F) (sqrt (fma x 2 (fma F F 2))))) (* (* (sin B) (sin B)) (sin B)))
278.0ms
(- (+ (sqrt 2) (* x (sqrt 1/2))) (* 1/2 (* (pow x 2) (sqrt 1/8))))
274.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

18.3b
(sqrt (fma x 2 (fma F F 2)))
0.3b
(/ F (* (sin B) (sqrt (fma x 2 (fma F F 2)))))
0.2b
(* (sin B) (sqrt (fma x 2 (fma F F 2))))
0.2b
(/ x (tan B))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube add-exp-log
12×times-frac
7×pow1 sqrt-prod
6×associate-*r* associate-/l*
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*l*
2×clear-num frac-2neg prod-exp cbrt-unprod div-inv unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down tan-quot associate-/r/ *-commutative
Counts
4 → 96
Calls
4 calls:
Slowest
20.0ms
(* (sin B) (sqrt (fma x 2 (fma F F 2))))
11.0ms
(/ F (* (sin B) (sqrt (fma x 2 (fma F F 2)))))
5.0ms
(/ x (tan B))
1.0ms
(sqrt (fma x 2 (fma F F 2)))

series852.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
304.0ms
(* (sin B) (sqrt (fma x 2 (fma F F 2))))
263.0ms
(/ F (* (sin B) (sqrt (fma x 2 (fma F F 2)))))
146.0ms
(/ x (tan B))
139.0ms
(sqrt (fma x 2 (fma F F 2)))

simplify4.3s

Counts
71 → 108
Calls
71 calls:
Slowest
876.0ms
(* (* (* (sin B) (sin B)) (sin B)) (* (* (sqrt (fma x 2 (fma F F 2))) (sqrt (fma x 2 (fma F F 2)))) (sqrt (fma x 2 (fma F F 2)))))
407.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
352.0ms
(- (+ (sqrt 2) (* x (sqrt 1/2))) (* 1/2 (* (pow x 2) (sqrt 1/8))))
303.0ms
(- (+ (* (sqrt 2) B) (* x (* B (sqrt 1/2)))) (* 1/6 (* (sqrt 2) (pow B 3))))
228.0ms
(/ (* (* F F) F) (* (* (* (sin B) (sqrt (fma x 2 (fma F F 2)))) (* (sin B) (sqrt (fma x 2 (fma F F 2))))) (* (sin B) (sqrt (fma x 2 (fma F F 2))))))

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes347.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.8b

bsearch534.0ms

end0.0ms

sample13.5s

Algorithm
intervals
Results
5.3s1633×body1280valid
2.8s1366×body640valid
2.5s4840×body80valid
982.0ms709×body320valid
810.0ms1625×body80nan
781.0ms349×body160valid