Details

simplify20.8m

Calls

6827 calls:

Slowest
2.2s
(cbrt (* (* (- (* (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (- (+ (log x) (log 2)) (/ 3/32 (pow x 4)))) (* (/ (/ -1/4 x) x) (/ (/ -1/4 x) x))) (+ (* (- (* (+ (log x) (log 2)) (+ (log x) (log 2))) (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4)))) x) (* (+ (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ -1/4 x)))) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))))
2.2s
(cbrt (* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (* (- (pow (+ (log x) (log 2)) 3) (pow (/ 3/32 (pow x 4)) 3)) x) (* (+ (* (+ (log x) (log 2)) (+ (log x) (log 2))) (+ (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4))) (* (+ (log x) (log 2)) (/ 3/32 (pow x 4))))) (/ -1/4 x)))) (+ (* (- (pow (+ (log x) (log 2)) 3) (pow (/ 3/32 (pow x 4)) 3)) x) (* (+ (* (+ (log x) (log 2)) (+ (log x) (log 2))) (+ (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4))) (* (+ (log x) (log 2)) (/ 3/32 (pow x 4))))) (/ -1/4 x)))))
1.9s
(cbrt (* (* (+ (pow (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) 3) (pow (/ (/ -1/4 x) x) 3)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))) (+ (* (- (* (+ (log x) (log 2)) (+ (log x) (log 2))) (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4)))) x) (* (+ (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ -1/4 x)))))
1.8s
(cbrt (* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (* (- (* (- (* (log x) (log x)) (* (log 2) (log 2))) (pow x 4)) (* (- (log x) (log 2)) 3/32)) x) (* (* (- (log x) (log 2)) (pow x 4)) (/ -1/4 x)))) (+ (pow (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) 3) (pow (/ (/ -1/4 x) x) 3))))
1.7s
(cbrt (* (* (+ (* (- (* (+ (log x) (log 2)) (+ (log x) (log 2))) (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4)))) x) (* (+ (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ -1/4 x))) (+ (pow (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) 3) (pow (/ (/ -1/4 x) x) 3))) (+ (* (- (* (+ (log x) (log 2)) (+ (log x) (log 2))) (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4)))) x) (* (+ (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ -1/4 x)))))

sample11.2m

Algorithm
72×intervals
Results
8.2m79095×body10240exit
54.6s32888×body1280valid
26.5s198172×body80valid
22.4s24516×body640valid
19.2s152158×body80nan
14.0s25034×body320valid
12.3s35239×body160valid
9.4s153736×pre80true
3.2s3033×body2560valid
1.0s4094×pre10240exit
969.0ms7988×body160nan
345.0ms244×body5120valid

prune2.7m

series42.9s

Calls

449 calls:

Slowest
616.0ms
(* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))))
542.0ms
(* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))))
511.0ms
(cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2))
494.0ms
(cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2))
470.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))

regimes13.9s

Accuracy

Total 38.0b remaining (11.6%)

6.7b23.4%Cubic critical, narrow range
5.6b47.4%Quotient of products
4.3b84.5%Cubic critical
3.2b0%Cubic critical, wide range
3.1b0%Quadratic roots, narrow range

rewrite6.6s

Algorithm
131×rewrite-expression-head
Calls

449 calls:

Slowest
1.2s
(+ (- (log (fma (- 1 (* x x)) (sqrt (- 1 (* x x))) 1)) (log (* (+ (* (* (sqrt (- 1 (* x x))) (sqrt (- (* 1 1) (* (* x x) (* x x))))) (+ (* (* 1 1) (* 1 1)) (+ (* (* (sqrt (- 1 (* x x))) 1) (* (sqrt (- 1 (* x x))) 1)) (* (* 1 1) (* (sqrt (- 1 (* x x))) 1))))) (* (sqrt (+ 1 (* x x))) (- (pow (* 1 1) 3) (pow (* (sqrt (- 1 (* x x))) 1) 3)))) x))) (log (* (sqrt (+ 1 (* x x))) (+ (* (* 1 1) (* 1 1)) (+ (* (* (sqrt (- 1 (* x x))) 1) (* (sqrt (- 1 (* x x))) 1)) (* (* 1 1) (* (sqrt (- 1 (* x x))) 1)))))))
926.0ms
(* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)))
505.0ms
(cbrt (* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))))
390.0ms
(* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)))
193.0ms
(* (- (/ (/ (/ (* m (- (pow 1 3) (pow m 3))) (sqrt (+ (fma m m m) 1))) (sqrt (+ (fma m m m) 1))) v) 1) m)
Rules
1864×frac-times
1674×frac-add
1396×*-un-lft-identity
1284×add-sqr-sqrt
1200×add-exp-log
1190×add-cube-cbrt
1062×flip-+
1061×flip3-+
1048×sqrt-div
1043×associate-*l/
936×flip--
935×flip3--
870×pow1
657×add-cbrt-cube
624×frac-sub
531×add-log-exp
500×log-div
459×times-frac
457×expm1-log1p-u
450×log1p-expm1-u
449×insert-posit16
442×associate--r-
420×associate-*r/
415×prod-exp
402×cbrt-div
380×prod-diff
379×sqrt-prod
285×associate-*l*
270×pow-exp
257×associate-+l+
254×associate-*r*
241×associate-/l*
240×div-inv
210×associate-/r/
200×div-exp
186×pow-to-exp
151×associate-/r*
150×fma-neg
144×cbrt-prod
134×log-prod
116×pow-prod-down
113×log-pow
98×rec-exp
95×cbrt-unprod
88×fma-udef
87×fma-def
86×*-commutative
84×distribute-lft-out frac-2neg clear-num
71×sub-neg
68×pow1/2 pow-prod-up
66×pow1/3
61×distribute-rgt-in distribute-lft-in
56×pow-plus
55×distribute-lft-out--
52×associate-/l/
42×pow2
39×rem-sqrt-square
38×associate--l+
36×cube-mult
35×difference-of-squares unpow3
34×cbrt-undiv unpow-prod-down
31×diff-log
27×+-commutative div-sub
26×pow-pow
25×sum-log
24×tan-quot
23×associate-+r+ exp-prod
22×pow-flip rem-log-exp
20×cube-prod
16×inv-pow log1p-udef
14×exp-sum
12×pow3
11×associate-+r-
log1p-expm1 difference-of-sqr-1 acos-asin
rem-exp-log associate-+l-
distribute-rgt-out--
sin-sum cube-unmult associate--r+ cos-sum rem-cbrt-cube
expm1-udef difference-cubes sqrt-unprod sin-mult rem-square-sqrt
expm1-log1p neg-sub0 exp-diff associate--l- un-div-inv distribute-rgt-out
cos-mult log1p-def distribute-frac-neg log-rec acos-neg cos-diff
distribute-rgt1-in neg-mul-1 hypot-udef unpow1/3 expm1-def
tanh-undef asin-acos sub-div unsub-neg sin-diff

localize3.3s

bsearch994.0ms

end1.0ms