Details

sample10.6m

Algorithm
72×intervals
Results
7.7m81358×body10240exit
50.2s32611×body1280valid
25.4s198182×body80valid
22.1s24831×body640valid
20.5s152356×body80nan
13.0s34966×body160valid
13.0s25145×body320valid
9.7s154082×pre80true
2.6s3101×body2560valid
1.8s7894×body160nan
1.2s4189×pre10240exit
657.0ms255×body5120valid

simplify3.6m

prune3.4m

series46.9s

Calls

397 calls:

Slowest
676.0ms
(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))
603.0ms
(cbrt (/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) a))
590.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
582.0ms
(cbrt (/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a)))
565.0ms
(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))

regimes14.1s

Accuracy

Total 51.6b remaining (23.2%)

Threshold costs 3.5b (1.6%)

8.0b42.9%Quadratic roots, narrow range
7.0b0%Quadratic roots, medium range
6.9b23.7%Cubic critical, narrow range
5.2b50.7%Quotient of products
4.9b81.9%Quadratic roots, full range

rewrite8.8s

Algorithm
126×rewrite-expression-head
Calls

397 calls:

Slowest
528.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
401.0ms
(* (/ (fma (/ (* (* a c) (* a c)) b) 27/8 (* -9/2 (* b (* c a)))) 3) (/ (/ 1 a) (fma b (+ (sqrt (fma b b (* (* a c) -3))) b) (fma b b (* (* a c) -3)))))
275.0ms
(* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))
225.0ms
(* (- (/ (* (* m (+ 1 (sqrt m))) (- 1 (sqrt m))) v) 1) (- 1 m))
180.0ms
(- (- (- (* c_n (log 1/2)) (fma (* c_n (* s s)) 1/8 (* (* 1/2 c_n) s))) (* c_p (log1p (exp (- s))))) (- (* c_n (log1p (/ -1 (+ 1 (exp (- t)))))) (* c_p (+ (* -1/2 t) (fma 1/8 (* t t) (log 2))))))
Rules
9525×*-un-lft-identity
9444×times-frac
8658×add-sqr-sqrt
6143×add-cube-cbrt
3283×prod-diff
2650×add-exp-log
1266×pow1
1261×add-cbrt-cube
1100×difference-of-squares
1001×prod-exp
969×div-exp
877×distribute-lft-out
694×associate-*r*
693×pow-exp
645×sqrt-prod
616×distribute-lft-out--
607×div-inv
592×add-log-exp
505×associate-/r*
486×associate-/l*
459×associate-/r/
420×cbrt-prod
400×expm1-log1p-u
398×log1p-expm1-u
397×insert-posit16
378×associate-*l*
353×fma-neg
346×pow-to-exp
327×associate-+r+
303×cbrt-undiv
273×cbrt-unprod
256×difference-of-sqr-1
230×pow-prod-down
219×flip--
218×flip3--
200×flip-+
199×fma-def flip3-+
180×pow-prod-up
164×distribute-rgt-in distribute-lft-in
152×unswap-sqr
148×1-exp rec-exp
132×tan-quot
127×frac-times
126×associate-*r/ swap-sqr
110×pow-sqr
109×log-prod
98×pow-plus
92×associate-*l/
86×frac-2neg clear-num
85×*-commutative
82×diff-log
80×sub-neg
69×pow2
67×fma-udef
63×associate--l+
61×associate-/l/
57×exp-prod
54×log-pow
50×cbrt-div
48×pow1/3
43×unpow-prod-down
37×sqrt-pow1
33×sin-sum
32×div-sub
31×pow1/2
29×rem-sqrt-square
26×frac-add
25×frac-sub
24×pow-flip cos-sum log-div
22×associate--r+
21×sum-log
20×exp-sum sqrt-div
19×distribute-rgt-neg-in
18×pow-pow
17×+-commutative inv-pow
16×pow3 distribute-lft-neg-in
15×exp-to-pow
14×cube-unmult neg-mul-1
13×rem-log-exp
11×difference-cubes
10×log1p-udef sqr-pow expm1-def
9×pow-unpow associate--r-
8×acos-asin distribute-rgt-out
4×remove-posit16 exp-diff log1p-expm1 distribute-frac-neg rem-exp-log
3×neg-sub0 cube-prod associate--l- hypot-udef
2×expm1-log1p expm1-udef distribute-rgt1-in sub-div associate-+l- log1p-def acos-neg cos-diff
1×associate-+l+ associate-+r- rem-cube-cbrt distribute-rgt-neg-out unpow3 neg-log tanh-def un-div-inv tanh-undef distribute-rgt-out-- asin-acos sin-mult unpow1/3 distribute-neg-frac cube-mult rem-cbrt-cube sin-diff

localize4.6s

bsearch1.7s

end1.0ms