Details

Time bar (total: 1.9m)

sample111.0ms

Algorithm
intervals
Results
50.0ms256×body80valid
43.0ms259×body80nan

simplify204.0ms

Calls
1 calls:
Slowest
204.0ms
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 3 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
474×times-frac
294×add-sqr-sqrt
262×*-un-lft-identity
219×add-cube-cbrt
141×sqrt-prod
131×associate-*l*
86×difference-of-squares
30×associate-/r/
26×associate-/r*
19×add-cbrt-cube add-exp-log
16×div-inv
14×flip3-- flip--
10×unswap-sqr
9×associate-/l*
7×cbrt-undiv div-exp
6×associate-*r*
5×pow1
3×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×pow-prod-down associate-*l/ *-commutative
Calls
3 calls:
Slowest
25.0ms
(* (/ (sqrt 2) (/ 4 (- 1 (* v v)))) (sqrt (fma (* v v) -3 1)))
21.0ms
(/ (sqrt 2) (/ 4 (- 1 (* v v))))
7.0ms
(/ 4 (- 1 (* v v)))

series603.0ms

Calls
3 calls:
Slowest
330.0ms
(* (/ (sqrt 2) (/ 4 (- 1 (* v v)))) (sqrt (fma (* v v) -3 1)))
218.0ms
(/ (sqrt 2) (/ 4 (- 1 (* v v))))
54.0ms
(/ 4 (- 1 (* v v)))

simplify59.0s

Calls
497 calls:
Slowest
584.0ms
(+ (log (/ (sqrt 2) (/ 4 (- 1 (* v v))))) (log (sqrt (fma (* v v) -3 1))))
564.0ms
(/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (/ (* (* 4 4) 4) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))))
458.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (* (cbrt 4) (cbrt 4)) (+ 1 v)))
431.0ms
(* (/ (sqrt 2) (/ 4 (- 1 (* v v)))) (sqrt (fma (* v v) -3 1)))
431.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (* (cbrt 4) (cbrt 4)) (+ (sqrt 1) v)))

prune4.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* v v) (* v v))
0.1b
(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))
0.0b
(* (* (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))) (/ (cbrt (sqrt 2)) (+ 1 (* v v)))) (sqrt (fma (* v v) -3 1)))
0.0b
(/ (cbrt (sqrt 2)) (+ 1 (* v v)))

rewrite574.0ms

Algorithm
rewrite-expression-head
Rules
138×pow1
96×add-exp-log
84×add-cbrt-cube
57×prod-exp cbrt-unprod
39×pow-prod-down
36×pow-prod-up
32×add-sqr-sqrt
31×times-frac
30×*-un-lft-identity add-cube-cbrt
24×cbrt-prod
22×pow-sqr
18×pow-plus associate-*l/
15×sqrt-prod
13×pow2
12×cbrt-undiv div-exp
9×associate-*l* associate-/l*
8×associate-*r*
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* *-commutative unswap-sqr
2×flip3-- associate-/r/ frac-sub div-inv flip-- sub-div
1×clear-num frac-2neg flip3-+ swap-sqr associate-*r/ flip-+
Calls
4 calls:
Slowest
430.0ms
(* (* (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))) (/ (cbrt (sqrt 2)) (+ 1 (* v v)))) (sqrt (fma (* v v) -3 1)))
94.0ms
(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))
36.0ms
(* (* v v) (* v v))
8.0ms
(/ (cbrt (sqrt 2)) (+ 1 (* v v)))

series1.9s

Calls
4 calls:
Slowest
1.1s
(* (* (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))) (/ (cbrt (sqrt 2)) (+ 1 (* v v)))) (sqrt (fma (* v v) -3 1)))
534.0ms
(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))
217.0ms
(/ (cbrt (sqrt 2)) (+ 1 (* v v)))
46.0ms
(* (* v v) (* v v))

simplify25.8s

Calls
219 calls:
Slowest
1.0s
(* (/ (* (sqrt 2) (sqrt 2)) (* (* 4 4) 4)) (* (* (* (* v v) v) (* (* v v) v)) (* (* (* v v) v) (* (* v v) v))))
793.0ms
(* (* (* (* (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))) (/ (cbrt (sqrt 2)) (+ 1 (* v v)))) (* (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))) (/ (cbrt (sqrt 2)) (+ 1 (* v v))))) (* (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))) (/ (cbrt (sqrt 2)) (+ 1 (* v v))))) (* (* (sqrt (fma (* v v) -3 1)) (sqrt (fma (* v v) -3 1))) (sqrt (fma (* v v) -3 1))))
700.0ms
(* (* (* (* (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))) (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v))))) (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v))))) (/ (sqrt 2) (* (* (+ 1 (* v v)) (+ 1 (* v v))) (+ 1 (* v v))))) (* (* (sqrt (fma (* v v) -3 1)) (sqrt (fma (* v v) -3 1))) (sqrt (fma (* v v) -3 1))))
615.0ms
(* (* (* (* (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))) (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v))))) (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v))))) (* (* (/ (cbrt (sqrt 2)) (+ 1 (* v v))) (/ (cbrt (sqrt 2)) (+ 1 (* v v)))) (/ (cbrt (sqrt 2)) (+ 1 (* v v))))) (* (* (sqrt (fma (* v v) -3 1)) (sqrt (fma (* v v) -3 1))) (sqrt (fma (* v v) -3 1))))
546.0ms
(* (* (- (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 4) (* (* v v) (* v v)))) (cbrt (sqrt 2))) (sqrt (fma (* v v) -3 1)))

prune3.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4))
0.2b
(* v (sqrt (sqrt 2)))
0.0b
(- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2))))
0.0b
(* (* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4)) (sqrt (fma (* v v) -3 1)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
39×*-un-lft-identity
38×add-sqr-sqrt
37×associate-*r*
27×add-cube-cbrt
20×add-cbrt-cube add-exp-log
19×times-frac
13×pow1
12×distribute-rgt-out--
9×fma-neg prod-diff
8×prod-exp cbrt-unprod
7×associate-*l*
6×add-log-exp
5×pow-prod-down unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×*-commutative
2×cbrt-undiv div-exp associate-*r/
1×sub-neg flip3-- diff-log associate-*l/ div-inv flip--
Calls
4 calls:
Slowest
47.0ms
(* (* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4)) (sqrt (fma (* v v) -3 1)))
23.0ms
(- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2))))
22.0ms
(* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4))
9.0ms
(* v (sqrt (sqrt 2)))

series1.4s

Calls
4 calls:
Slowest
576.0ms
(* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4))
552.0ms
(* (* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4)) (sqrt (fma (* v v) -3 1)))
168.0ms
(- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2))))
115.0ms
(* v (sqrt (sqrt 2)))

simplify9.8s

Calls
114 calls:
Slowest
445.0ms
(* (* (* (* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4)) (* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4))) (* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4))) (* (* (sqrt (fma (* v v) -3 1)) (sqrt (fma (* v v) -3 1))) (sqrt (fma (* v v) -3 1))))
417.0ms
(- (+ (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))) (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3))))) (+ (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3)))))))
414.0ms
(* (* (* (* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2)))) (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2)))) (/ (* (* (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2))))) (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2))))) (* (* 4 4) 4))) (* (* (sqrt (fma (* v v) -3 1)) (sqrt (fma (* v v) -3 1))) (sqrt (fma (* v v) -3 1))))
391.0ms
(- (+ (* 1/4 (sqrt 2)) (* 3/32 (* (sqrt 2) (pow v 4)))) (* 5/8 (* (sqrt 2) (pow v 2))))
365.0ms
(* (* (* (* (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2))) (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2)))) (fma (sqrt (sqrt 2)) v (sqrt (sqrt 2)))) (* (* (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4)) (/ (- (sqrt (sqrt 2)) (* v (sqrt (sqrt 2)))) 4))) (* (* (sqrt (fma (* v v) -3 1)) (sqrt (fma (* v v) -3 1))) (sqrt (fma (* v v) -3 1))))

prune2.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes84.0ms

Accuracy

0% (0.0b remaining)

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

bsearch7.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.7s8000×body80valid
1.1s8122×body80nan