Details

simplify5.5m (44.1%)

sample4.4m (35.3%)

Algorithm
56×intervals
16×halfpoints
Results
52.6s66914×body1280valid
31.5s17447×body2560valid
19.0s41775×body640valid
10.7s12457×body10240exit
7.2s93556×body80valid
6.4s21350×body320valid
6.0s63645×body80nan
2.3s10578×body160valid
1.3s47375×pre80true
702.0ms692×body1280nan
460.0ms698×body640nan
296.0ms472×body5120valid
126.0ms368×body320nan
79.0ms192×body160nan

prune1.2m (9.4%)

series54.1s (7.2%)

Calls

396 calls:

1.5s
(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)))
930.0ms
(expm1 (log1p (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
602.0ms
(- (/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1)) (tan x))
558.0ms
(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
548.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite20.1s (2.7%)

Algorithm
123×rewrite-expression-head
Calls

396 calls:

652.0ms
(* (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))) (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
482.0ms
(tan (+ x eps))
482.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
480.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))
459.0ms
(* (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))))
Rules
18035×times-frac
17481×*-un-lft-identity
15787×add-sqr-sqrt
13335×add-cube-cbrt
10140×prod-diff
6949×sqrt-prod
1416×distribute-lft-out
1351×unpow-prod-down
1156×add-exp-log
1037×div-inv
996×difference-of-squares
940×add-cbrt-cube
755×fma-neg
743×associate-/r/
705×pow1
699×distribute-lft-out--
648×add-log-exp
623×associate-*l*
614×cbrt-prod
528×sqrt-div
525×associate-/l*
480×cube-prod
467×sqr-pow
389×associate-/r*
386×log1p-expm1-u
385×expm1-log1p-u
364×associate-*r*
336×flip-+ flip3-+
301×distribute-rgt-neg-in
289×distribute-lft-neg-in
252×prod-exp
251×associate-+l+
248×flip-- flip3--
239×div-exp
220×distribute-rgt-in distribute-lft-in
170×cbrt-undiv
167×cbrt-unprod
137×unswap-sqr
126×fma-def swap-sqr
124×pow-unpow
112×sub-neg
109×diff-log
105×unpow3 cube-mult
104×log-prod
96×neg-mul-1
87×pow-prod-down
83×log-pow
73×associate-*l/ frac-2neg clear-num
72×tan-quot
66×sqrt-pow1
62×associate-/l/
58×frac-times
57×pow1/2
56×*-commutative
53×pow1/3
49×associate-*r/
47×pow-exp
45×pow-to-exp
42×exp-prod
36×rem-sqrt-square
34×fma-udef
31×frac-sub
27×1-exp pow-prod-up
26×div-sub pow-pow
25×rec-exp sum-log
23×log-div
22×cbrt-div
21×pow-sqr +-commutative
17×exp-sum
16×cube-div
14×rem-cube-cbrt unpow2
13×frac-add complex-mul-def associate--l+
11×rem-log-exp
9×difference-cubes pow-flip pow-plus
8×pow2
7×inv-pow neg-sub0
6×associate--r+ distribute-rgt-out--
5×associate-+r+ associate--l- sub-div expm1-udef rem-cbrt-cube
4×distribute-neg-in *.c-commutative expm1-log1p distribute-frac-neg
3×exp-diff log1p-udef sqrt-unprod pow3 log1p-expm1 +.c-commutative rem-square-sqrt hypot-def neg-log associate-+l-
2×rem-exp-log sin-sum exp-neg associate-+r- un-div-inv complex-add-def cos-sum tan-sum distribute-rgt-neg-out exp-to-pow
1×associate-+l+.c sin-cos-mult sqrt-pow2 associate--r- diff-atan diff-cos associate-*l*.c sin-mult frac-2neg.c diff-sin

regimes4.3s (0.6%)

Accuracy

Total 32.5b remaining (15.9%)

Threshold costs 5.7b (2.8%)

5.3b75.2%expax (section 3.5)
4.6b84.2%quadp (p42, positive)
4.5b84.4%quad2p (problem 3.2.1, positive)
3.5b56.3%expq3 (problem 3.4.2)
3.4b87.7%quadm (p42, negative)

localize3.3s (0.4%)

bsearch3.2s (0.4%)

end0.0ms (0.0%)