Details

simplify5.7m (45.1%)

sample4.4m (34.9%)

Algorithm
56×intervals
16×halfpoints
Results
53.5s66914×body1280valid
33.0s17447×body2560valid
19.0s41775×body640valid
10.0s12457×body10240exit
8.7s93556×body80valid
7.0s21350×body320valid
5.6s63645×body80nan
2.3s10578×body160valid
1.3s47375×pre80true
692.0ms692×body1280nan
543.0ms368×body320nan
494.0ms698×body640nan
282.0ms472×body5120valid
40.0ms192×body160nan

prune1.1m (9.0%)

series53.0s (7.0%)

Calls

391 calls:

1.3s
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
656.0ms
(expm1 (log1p (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
624.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
620.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
598.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite18.3s (2.4%)

Algorithm
123×rewrite-expression-head
Calls

391 calls:

579.0ms
(* (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))) (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
487.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
369.0ms
(* (sqrt (/ (cbrt (* (+ (exp (- x)) (exp x)) (+ (exp (- x)) (exp x)))) 1)) (* (sqrt (/ (cbrt (+ (exp (- x)) (exp x))) 2.0)) (* (sqrt (/ (+ (exp (- x)) (exp x)) 2.0)) (cos y))))
307.0ms
(* (sqrt (/ (cbrt (pow (+ (exp (- x)) (exp x)) 3)) 2.0)) (* (sqrt (/ (+ (exp (- x)) (exp x)) 2.0)) (cos y)))
276.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
Rules
18327×times-frac
17474×*-un-lft-identity
15799×add-sqr-sqrt
13419×add-cube-cbrt
10181×prod-diff
7226×sqrt-prod
1389×distribute-lft-out
1354×unpow-prod-down
1126×add-exp-log
1065×div-inv
972×difference-of-squares
887×add-cbrt-cube
769×fma-neg
742×associate-/r/
718×pow1
679×distribute-lft-out--
631×add-log-exp
623×cbrt-prod
525×sqrt-div
517×associate-/l*
509×associate-*l*
474×sqr-pow
461×cube-prod
437×associate-/r*
381×log1p-expm1-u expm1-log1p-u
377×distribute-rgt-neg-in
369×distribute-lft-neg-in
357×associate-*r*
329×flip-+ flip3-+
252×div-exp
247×flip-- associate-+l+ flip3--
230×prod-exp
194×distribute-rgt-in distribute-lft-in
165×cbrt-undiv
144×cbrt-unprod
129×swap-sqr
126×unswap-sqr
124×log-prod
123×neg-mul-1
109×sub-neg
108×diff-log
107×fma-def
106×log-pow
100×unpow3 cube-mult
85×pow-unpow
81×pow-prod-down
72×tan-quot
71×frac-2neg clear-num
69×sqrt-pow1
65×associate-*l/
61×pow1/2
58×associate-/l/
56×pow1/3 frac-times
49×*-commutative
46×associate-*r/
43×exp-prod
42×exp-sum
41×rem-sqrt-square pow-exp
39×1-exp pow-to-exp
33×rec-exp
31×frac-sub
28×pow-prod-up
27×fma-udef
26×log-div div-sub
22×pow-sqr cbrt-div
20×sum-log pow-pow
18×associate--l+
17×+-commutative
16×cube-div
13×frac-add complex-mul-def associate--r+
12×rem-cube-cbrt unpow2
11×pow-flip rem-log-exp
10×pow-plus
9×difference-cubes pow2
8×inv-pow
7×associate--l-
6×neg-sub0 distribute-rgt-out--
5×expm1-log1p expm1-udef sub-div rem-cbrt-cube
4×log1p-udef log1p-expm1 *.c-commutative hypot-def
3×rem-exp-log exp-diff un-div-inv sqrt-unprod pow3 +.c-commutative rem-square-sqrt distribute-frac-neg
2×sin-sum associate--r- exp-neg complex-add-def neg-log cos-sum tan-sum associate-+l- exp-to-pow
1×associate-+l+.c sqrt-pow2 diff-atan sin-cos-mult diff-cos associate-*l*.c sqr-cos sin-mult cos-mult frac-2neg.c diff-sin

regimes4.1s (0.5%)

Accuracy

Total 32.6b remaining (16.2%)

Threshold costs 5.7b (2.8%)

5.0b76.3%expax (section 3.5)
4.6b84.2%quadp (p42, positive)
4.5b84.4%quad2p (problem 3.2.1, positive)
3.9b54.6%expq3 (problem 3.4.2)
3.4b87.7%quadm (p42, negative)

localize3.9s (0.5%)

bsearch3.2s (0.4%)

end1.0ms (0.0%)