Details

Time bar (total: 6.6m)

sample114.0ms

Algorithm
intervals
Results
54.0ms233×body80nan
40.0ms256×body80valid

simplify211.0ms

Calls
1 calls:
Slowest
211.0ms
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3 (* v v))
0.0b
(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))
0.0b
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
0.0b
(sqrt (- 1 (* 3 (* v v))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
319×add-sqr-sqrt
178×*-un-lft-identity
172×frac-times
139×add-cube-cbrt
125×associate-*l*
120×sqrt-prod
106×sqrt-div
92×flip3-- flip--
91×associate-*r*
90×prod-diff
86×associate-*l/
76×unswap-sqr
72×associate-/l*
48×times-frac
47×distribute-rgt-in distribute-lft-in
46×difference-of-squares
36×associate-/r*
30×swap-sqr
23×add-cbrt-cube add-exp-log
20×*-commutative
17×pow1
12×clear-num frac-2neg
10×prod-exp associate-*r/ cbrt-unprod
8×distribute-lft-out--
7×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv sub-neg div-exp div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
722.0ms
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
169.0ms
(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))
115.0ms
(sqrt (- 1 (* 3 (* v v))))
42.0ms
(* 3 (* v v))

series663.0ms

Calls
4 calls:
Slowest
339.0ms
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
214.0ms
(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))
73.0ms
(sqrt (- 1 (* 3 (* v v))))
37.0ms
(* 3 (* v v))

simplify1.8m

Calls
557 calls:
Slowest
862.0ms
(* (* (sqrt (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (- (pow 1 3) (pow (* v v) 3)))
860.0ms
(* (fma (- (* (cbrt v) v)) (* (cbrt v) (cbrt v)) (* (* (cbrt v) v) (* (cbrt v) (cbrt v)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))))
835.0ms
(* (* (* (/ (sqrt 2) 4) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* 3 (* v v))))))
826.0ms
(* (* (- 4) (sqrt (+ 1 (* 3 (* v v))))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))))
797.0ms
(* (* (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* 4 4) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* 3 (* v v)))))) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v))))

prune6.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4 (sqrt 2))
1.0b
(/ (* (- 1 (* v v)) (sqrt (fma (* v v) -3 1))) (/ 4 (sqrt 2)))
0.0b
(sqrt (fma (* v v) -3 1))
0.0b
(* (- 1 (* v v)) (sqrt (fma (* v v) -3 1)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
1156×times-frac
952×add-sqr-sqrt
711×*-un-lft-identity
495×add-cube-cbrt
384×associate-*l*
375×sqrt-prod
240×difference-of-squares
144×associate-*r*
96×unswap-sqr
72×*-commutative
48×swap-sqr distribute-lft-out--
34×associate-/r* associate-/l*
31×div-inv
20×add-cbrt-cube add-exp-log
12×associate-/r/
7×pow1 cbrt-undiv div-exp
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg prod-exp cbrt-unprod
2×flip3-- flip-- associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down
Calls
4 calls:
Slowest
111.0ms
(/ (* (- 1 (* v v)) (sqrt (fma (* v v) -3 1))) (/ 4 (sqrt 2)))
44.0ms
(* (- 1 (* v v)) (sqrt (fma (* v v) -3 1)))
8.0ms
(/ 4 (sqrt 2))
2.0ms
(sqrt (fma (* v v) -3 1))

series616.0ms

Calls
4 calls:
Slowest
342.0ms
(/ (* (- 1 (* v v)) (sqrt (fma (* v v) -3 1))) (/ 4 (sqrt 2)))
186.0ms
(* (- 1 (* v v)) (sqrt (fma (* v v) -3 1)))
87.0ms
(sqrt (fma (* v v) -3 1))
0.0ms
(/ 4 (sqrt 2))

simplify3.9m

Calls
1388 calls:
Slowest
870.0ms
(/ (* (- 1 (* v v)) (sqrt (fma (* v v) -3 1))) (/ (cbrt 4) (sqrt (cbrt 2))))
830.0ms
(/ (* (- 1 (* v v)) (sqrt (fma (* v v) -3 1))) (/ (sqrt 4) (sqrt (cbrt 2))))
790.0ms
(/ (* (- 1 (* v v)) (sqrt (* (cbrt (fma (* v v) -3 1)) (cbrt (fma (* v v) -3 1))))) (/ 1 (sqrt 1)))
789.0ms
(/ (* (- (sqrt 1) v) (sqrt (fma (* v v) -3 1))) (/ 4 (sqrt (sqrt 2))))
664.0ms
(/ (sqrt (* (- 1 (* v v)) (sqrt (fma (* v v) -3 1)))) (cbrt (/ 4 (sqrt 2))))

prune8.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (* (* 1/4 (sqrt (fma -3 (* v v) 1))) (* (- 1 v) (sqrt (sqrt 2)))))
0.0b
(* (- 1 v) (sqrt (sqrt 2)))
0.0b
(sqrt (fma -3 (* v v) 1))
0.0b
(fma (sqrt (sqrt 2)) v (sqrt (sqrt 2)))

rewrite430.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
103×associate-*r*
79×unswap-sqr
57×sqrt-prod
34×associate-*l*
26×*-un-lft-identity
25×pow1
24×add-cbrt-cube add-exp-log
20×add-cube-cbrt
14×pow-prod-down prod-exp cbrt-unprod
5×*-commutative
4×expm1-log1p-u associate-*l/ associate-*r/ insert-posit16 log1p-expm1-u add-log-exp difference-of-squares
2×flip3-- flip-- distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Calls
4 calls:
Slowest
384.0ms
(* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (* (* 1/4 (sqrt (fma -3 (* v v) 1))) (* (- 1 v) (sqrt (sqrt 2)))))
37.0ms
(* (- 1 v) (sqrt (sqrt 2)))
2.0ms
(sqrt (fma -3 (* v v) 1))
0.0ms
(fma (sqrt (sqrt 2)) v (sqrt (sqrt 2)))

series1.0s

Calls
4 calls:
Slowest
627.0ms
(* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (* (* 1/4 (sqrt (fma -3 (* v v) 1))) (* (- 1 v) (sqrt (sqrt 2)))))
163.0ms
(fma (sqrt (sqrt 2)) v (sqrt (sqrt 2)))
123.0ms
(* (- 1 v) (sqrt (sqrt 2)))
90.0ms
(sqrt (fma -3 (* v v) 1))

simplify29.0s

Calls
142 calls:
Slowest
963.0ms
(+ (log (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2)))) (+ (+ (log 1/4) (log (sqrt (fma -3 (* v v) 1)))) (+ (log (- 1 v)) (log (sqrt (sqrt 2))))))
686.0ms
(* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (* (* 1/4 (sqrt (fma -3 (* v v) 1))) (* (- 1 v) (sqrt (sqrt 2)))))
683.0ms
(* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (* (* 1/4 (sqrt (fma -3 (* v v) 1))) (* (- 1 v) (sqrt (sqrt 2)))))
635.0ms
(* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (* (* 1/4 (sqrt (fma -3 (* v v) 1))) (* (- 1 v) (sqrt (sqrt 2)))))
634.0ms
(* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (* (* 1/4 (sqrt (fma -3 (* v v) 1))) (* (- 1 v) (sqrt (sqrt 2)))))

prune2.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes52.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.8s8259×body80nan
1.3s8000×body80valid