Details

Time bar (total: 2.0m)

sample598.0ms

Algorithm
intervals
Results
220.0ms47×body640valid
95.0ms159×body80valid
90.0ms42×body1280valid
70.0ms29×body320valid
19.0ms57×body80nan
5.0ms7×body160valid

simplify431.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
430.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune46.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.7b

localize49.0ms

Local error

Found 4 expressions with local error:

21.2b
(pow (fma 2 x (fma F F 2)) -1/2)
7.7b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.1b
(/ x (tan B))
0.1b
(/ (sin B) F)

rewrite49.0ms

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
16.0ms
(/ (sin B) F)
16.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
7.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
5.0ms
(/ x (tan B))

series780.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
315.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
260.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
160.0ms
(/ x (tan B))
45.0ms
(/ (sin B) F)

simplify54.2s

Counts
278 → 226
Calls
278 calls:
Slowest
687.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
681.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ (sqrt (sin B)) (sqrt F)))
643.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
632.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (cbrt (sin B)) (cbrt F)))
627.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))

prune3.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.3b

localize43.0ms

Local error

Found 4 expressions with local error:

21.2b
(pow (fma x 2 (fma F F 2)) -1/2)
0.6b
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
0.3b
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.1b
(/ x (tan B))

rewrite65.0ms

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
47.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
9.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
5.0ms
(/ x (tan B))
2.0ms
(pow (fma x 2 (fma F F 2)) -1/2)

series815.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
312.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
185.0ms
(/ x (tan B))
163.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
154.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify13.2s

Counts
96 → 138
Calls
96 calls:
Slowest
632.0ms
(* (cbrt (pow (fma x 2 (fma F F 2)) -1/2)) (cbrt (pow (fma x 2 (fma F F 2)) -1/2)))
609.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
529.0ms
(+ (- (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
511.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
487.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.3b

localize66.0ms

Local error

Found 4 expressions with local error:

21.2b
(pow (fma x 2 (fma F F 2)) -1/2)
0.6b
(* (/ 1 (sin B)) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
0.3b
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.3b
(expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))

rewrite56.0ms

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×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×pow-unpow cbrt-unprod sqr-pow
2×pow-to-exp div-exp pow-exp *-commutative
1×cbrt-undiv rec-exp expm1-log1p pow-pow 1-exp pow-prod-down associate-*l/ div-inv expm1-udef
Counts
4 → 98
Calls
4 calls:
Slowest
32.0ms
(* (/ 1 (sin B)) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
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)
1.0ms
(expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))

series939.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
313.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
312.0ms
(* (/ 1 (sin B)) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
185.0ms
(expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))
129.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify12.6s

Counts
66 → 110
Calls
66 calls:
Slowest
643.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
555.0ms
(* (/ 1 (sin B)) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
537.0ms
(* (sqrt (/ 1 (sin B))) (sqrt (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))
536.0ms
(* (/ 1 (sqrt (sin B))) (sqrt (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))
529.0ms
(* (/ (sqrt 1) (sqrt (sin B))) (sqrt (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.3b

localize66.0ms

Local error

Found 4 expressions with local error:

21.2b
(pow (fma x 2 (fma F F 2)) -1/2)
0.6b
(* (/ 1 (sin B)) (log1p (log1p (expm1 (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))))
0.3b
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.3b
(expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))

rewrite39.0ms

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×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×pow-unpow cbrt-unprod sqr-pow
2×pow-to-exp div-exp pow-exp *-commutative
1×cbrt-undiv rec-exp expm1-log1p pow-pow 1-exp pow-prod-down associate-*l/ div-inv expm1-udef
Counts
4 → 98
Calls
4 calls:
Slowest
20.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
13.0ms
(* (/ 1 (sin B)) (log1p (log1p (expm1 (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))))
2.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
1.0ms
(expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
404.0ms
(* (/ 1 (sin B)) (log1p (log1p (expm1 (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))))
310.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
162.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
146.0ms
(expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))

simplify12.6s

Counts
66 → 110
Calls
66 calls:
Slowest
754.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))
596.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
592.0ms
(* (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))) (* (* (log1p (log1p (expm1 (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))) (log1p (log1p (expm1 (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))) (log1p (log1p (expm1 (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))))
526.0ms
(log1p (log1p (expm1 (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))
516.0ms
(* (sqrt (/ 1 (sin B))) (sqrt (log1p (log1p (expm1 (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))))

prune2.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.3b

regimes694.0ms

Accuracy

0% (0.6b remaining)

Error of 10.7b against oracle of 10.1b and baseline of 10.7b

bsearch8.0ms

end0.0ms

sample13.5s

Algorithm
intervals
Results
5.4s1686×body1280valid
3.3s1414×body640valid
2.1s4670×body80valid
1.3s714×body320valid
604.0ms1611×body80nan
355.0ms349×body160valid