Details

simplify14.4m (42.2%)

sample14.3m (41.8%)

Algorithm
77×intervals
Results
9.9m56513×body10240exit
1.7m42716×body1280valid
40.5s28957×body640valid
28.7s201213×body80valid
21.0s151601×body80nan
19.1s27171×body320valid
13.3s35663×body160valid
13.2s196458×pre80true
3.5s3035×body2560valid
1.3s7845×body160nan
913.0ms4138×pre10240exit
320.0ms205×body5120valid
3.0ms2×body320nan
3.0ms1×body640nan

prune1.9m (5.6%)

rewrite1.6m (4.6%)

Algorithm
143×rewrite-expression-head
Calls

482 calls:

6.7s
(cbrt (* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))))
1.2s
(* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
499.0ms
(* (* (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1))))) (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))))
304.0ms
(* (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))))
221.0ms
(* (- (* (* m (- 1 m)) (/ 1 v)) 1) m)
Rules
2285240×tan-quot
1378486×frac-times
765735×associate-*r/
761892×associate-*l/
524670×frac-sub
238527×cbrt-div
163232×sub-div
11948×flip--
11947×flip3--
11839×*-un-lft-identity
10382×times-frac
9583×add-sqr-sqrt
6698×add-cube-cbrt
4225×prod-diff
2587×add-exp-log
1506×distribute-lft-out
1371×pow1
1341×exp-sum
1292×difference-of-squares
1263×add-cbrt-cube
1175×sqrt-prod
956×prod-exp
868×div-exp
810×log-prod
778×associate-/r/ distribute-lft-out--
694×pow-exp
664×add-log-exp
613×div-inv
594×associate-*r*
515×associate-/r*
508×associate-/l*
484×expm1-log1p-u log1p-expm1-u
482×insert-posit16
446×cbrt-prod
437×associate-*l*
409×difference-of-sqr-1
404×flip-+
403×flip3-+
346×pow-to-exp
301×fma-neg
259×pow-prod-down
250×cbrt-unprod
234×fma-def
233×cbrt-undiv
193×distribute-rgt-in distribute-lft-in
159×pow-prod-up
152×exp-prod
149×unswap-sqr
137×1-exp rec-exp
135×swap-sqr
129×log-pow
128×sqrt-pow1
100×sqrt-div sub-neg
98×*-commutative
97×pow-sqr
96×frac-2neg clear-num
82×fma-udef
80×pow-plus
73×associate-+r+
70×associate-/l/ frac-add
67×pow1/3
63×diff-log
58×cos-sum
53×unpow-prod-down
51×pow2 log-div
48×sin-mult
46×pow1/2
44×div-sub
41×pow3
35×sum-log
27×difference-cubes rem-log-exp
25×cube-unmult
22×sin-sum +-commutative rem-sqrt-square
20×cos-mult associate--l+ associate--r+
18×sin-diff
16×associate--r-
14×pow-flip distribute-rgt-neg-in
11×inv-pow cos-diff
10×rem-exp-log
9×exp-diff sqr-pow acos-asin expm1-def distribute-lft-neg-in
8×sin-cos-mult
6×pow-unpow pow-pow distribute-rgt-out
5×associate--l-
4×neg-sub0 associate-+l- hypot-def log1p-udef
3×expm1-log1p expm1-udef log1p-expm1 distribute-frac-neg neg-log neg-mul-1 acos-neg log1p-def rem-cbrt-cube
2×distribute-rgt1-in hypot-1-def un-div-inv sqr-cos
1×remove-posit16 associate-+r- log-rec sqrt-unprod tanh-def tanh-undef hypot-udef distribute-rgt-out-- asin-acos rem-square-sqrt

series1.5m (4.3%)

Calls

482 calls:

1.9s
(* (fma -3 (* c a) (* b b)) (sqrt (fma -3 (* c a) (* b b))))
1.6s
(* (fma -3 (* c a) (* b b)) (sqrt (fma -3 (* c a) (* b b))))
1.5s
(* (fma c (* -4 a) (* b b)) (sqrt (fma c (* -4 a) (* b b))))
1.4s
(- (* (fma -3 (* c a) (* b b)) (sqrt (fma -3 (* c a) (* b b)))) (* b (* b b)))
1.4s
(- (* (fma -3 (* c a) (* b b)) (sqrt (fma -3 (* c a) (* b b)))) (* b (* b b)))

regimes21.7s (1.1%)

Accuracy

Total 36.2b remaining (10.6%)

Threshold costs 5.6b (1.6%)

5.4b50.2%Quotient of products
4.6b83.5%Quadratic roots, full range
3.3b0%Cubic critical, medium range
3.2b0%Quadratic roots, wide range
3.1b0%Quadratic roots, medium range

localize7.0s (0.3%)

bsearch1.5s (0.1%)

end2.0ms (0.0%)