Details

Time bar (total: 2.1m)

sample103.0ms

Algorithm
intervals
Results
52.0ms240×body80nan
34.0ms256×body80valid

simplify189.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
189.0ms
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
459×times-frac
282×add-sqr-sqrt
249×*-un-lft-identity
210×add-cube-cbrt
144×sqrt-prod
131×associate-*l*
78×difference-of-squares
28×associate-/r/
21×associate-/r*
17×add-cbrt-cube add-exp-log
15×div-inv
13×flip3-- flip--
10×unswap-sqr
6×pow1 cbrt-undiv div-exp associate-*r* associate-/l*
3×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative
Counts
3 → 353
Calls
3 calls:
Slowest
39.0ms
(* (/ (sqrt 2) (/ 4 (- 1 (* v v)))) (sqrt (fma (* v v) -3 1)))
17.0ms
(/ (sqrt 2) (/ 4 (- 1 (* v v))))
1.0ms
(sqrt (fma (* v v) -3 1))

series567.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
337.0ms
(* (/ (sqrt 2) (/ 4 (- 1 (* v v)))) (sqrt (fma (* v v) -3 1)))
159.0ms
(/ (sqrt 2) (/ 4 (- 1 (* v v))))
71.0ms
(sqrt (fma (* v v) -3 1))

simplify57.8s

Counts
461 → 362
Calls
461 calls:
Slowest
742.0ms
(/ (cbrt (sqrt 2)) (/ 4 (- 1 (* v v))))
588.0ms
(/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (/ (* (* 4 4) 4) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))))
450.0ms
(/ (sqrt 1) (/ 4 (- (* 1 1) (* (* v v) (* v v)))))
416.0ms
(/ (sqrt 1) (/ 4 (- (* 1 1) (* (* v v) (* v v)))))
411.0ms
(/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* (/ 4 (- 1 (* v v))) (/ 4 (- 1 (* v v)))) (/ 4 (- 1 (* v v)))))

prune4.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
692×times-frac
416×add-sqr-sqrt
406×sqrt-prod
367×*-un-lft-identity
327×add-cube-cbrt
191×associate-*r*
80×difference-of-squares
34×sqrt-div
32×add-cbrt-cube add-exp-log
30×associate-/r*
28×associate-/r/
17×flip3-- flip--
15×div-inv
14×unswap-sqr
12×pow1
10×prod-exp cbrt-unprod
9×cbrt-undiv div-exp associate-*l* associate-*l/
6×associate-/l*
4×expm1-log1p-u frac-times pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
2×associate-*r/ *-commutative
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
Counts
4 → 513
Calls
4 calls:
Slowest
81.0ms
(* (* (sqrt (- 1 (* v v))) (/ (sqrt 2) (/ 4 (sqrt (- 1 (* v v)))))) (sqrt (fma (* v v) -3 1)))
61.0ms
(* (sqrt (- 1 (* v v))) (/ (sqrt 2) (/ 4 (sqrt (- 1 (* v v))))))
15.0ms
(/ (sqrt 2) (/ 4 (sqrt (- 1 (* v v)))))
1.0ms
(sqrt (fma (* v v) -3 1))

series772.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
329.0ms
(* (* (sqrt (- 1 (* v v))) (/ (sqrt 2) (/ 4 (sqrt (- 1 (* v v)))))) (sqrt (fma (* v v) -3 1)))
201.0ms
(/ (sqrt 2) (/ 4 (sqrt (- 1 (* v v)))))
176.0ms
(* (sqrt (- 1 (* v v))) (/ (sqrt 2) (/ 4 (sqrt (- 1 (* v v))))))
66.0ms
(sqrt (fma (* v v) -3 1))

simplify53.8s

Counts
673 → 525
Calls
673 calls:
Slowest
926.0ms
(+ (+ (log (sqrt (- 1 (* v v)))) (- (log (sqrt 2)) (- (log 4) (log (sqrt (- 1 (* v v))))))) (log (sqrt (fma (* v v) -3 1))))
571.0ms
(* (* (* (* (sqrt (- 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v)))) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* (/ 4 (sqrt (- 1 (* v v)))) (/ 4 (sqrt (- 1 (* v v))))) (/ 4 (sqrt (- 1 (* v v))))))) (* (* (sqrt (fma (* v v) -3 1)) (sqrt (fma (* v v) -3 1))) (sqrt (fma (* v v) -3 1))))
523.0ms
(* (* (* (* (sqrt (- 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v)))) (* (* (/ (sqrt 2) (/ 4 (sqrt (- 1 (* v v))))) (/ (sqrt 2) (/ 4 (sqrt (- 1 (* v v)))))) (/ (sqrt 2) (/ 4 (sqrt (- 1 (* v v))))))) (* (* (sqrt (fma (* v v) -3 1)) (sqrt (fma (* v v) -3 1))) (sqrt (fma (* v v) -3 1))))
467.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ 4 (sqrt (- (pow 1 3) (pow (* v v) 3)))))
462.0ms
(* (* (* (* (sqrt (- 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v)))) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (/ (* (* 4 4) 4) (* (* (sqrt (- 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))))) (* (* (sqrt (fma (* v v) -3 1)) (sqrt (fma (* v v) -3 1))) (sqrt (fma (* v v) -3 1))))

prune6.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes81.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.7s8000×body80valid
1.3s8069×body80nan