Details

simplify5.8m (46.5%)

sample4.5m (35.9%)

Algorithm
56×intervals
16×halfpoints
Results
48.4s66599×body1280valid
34.0s17327×body2560valid
19.7s41902×body640valid
10.9s12868×body10240exit
8.3s93800×body80valid
6.8s21104×body320valid
5.6s64266×body80nan
2.4s47408×pre80true
1.8s10710×body160valid
903.0ms654×body1280nan
371.0ms674×body640nan
369.0ms510×body5120valid
167.0ms374×body320nan
39.0ms207×body160nan

prune56.4s (7.6%)

series49.8s (6.7%)

Calls

358 calls:

2.0s
(- (fma (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin eps) 3) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (+ (fma (/ (/ (pow (sin eps) 2) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (pow (cos eps) 2)) (+ (pow (/ (sin x) (cos x)) 3) (/ (sin x) (cos x))) (/ (sin x) (* (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3)) (cos x)))) (/ (/ (sin eps) (cos eps)) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))))) (/ (sin x) (cos x)))
1.4s
(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)))
1.0s
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
686.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
530.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite16.1s (2.2%)

Algorithm
123×rewrite-expression-head
Calls

358 calls:

556.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
533.0ms
(/ (- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (+ 1.0 (exp x)) (fma 1.0 1.0 (exp (* 2 x)))))
422.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
297.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
289.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
Rules
9113×times-frac
8950×*-un-lft-identity
8144×add-sqr-sqrt
6587×add-cube-cbrt
3099×prod-diff
3018×sqrt-prod
1285×add-exp-log
1034×add-cbrt-cube
755×associate-*l*
706×pow1
697×distribute-lft-out
642×unpow-prod-down
627×difference-of-squares
572×add-log-exp
556×associate-/l*
524×distribute-lft-out--
508×div-inv
488×cbrt-prod
443×pow-unpow
437×associate-*r*
401×fma-neg
395×associate-/r*
388×distribute-rgt-neg-in
351×distribute-lft-neg-in
347×log1p-expm1-u
346×expm1-log1p-u
326×associate-/r/
322×div-exp
304×prod-exp
252×associate-+l+
226×cbrt-undiv
215×cbrt-unprod
211×sqr-pow
208×flip-- cube-prod flip3--
154×flip-+ flip3-+
144×log-prod
130×unswap-sqr
117×neg-mul-1
114×fma-def
103×sqrt-div
102×pow-prod-down
99×sub-neg
98×sqrt-pow1
95×diff-log associate-*l/
76×swap-sqr
75×distribute-rgt-in distribute-lft-in
74×log-pow
73×frac-2neg associate-*r/ clear-num
67×associate-/l/ pow1/2
66×tan-quot
61×frac-times
58×exp-sum
52×cbrt-div
51×unpow2
50×*-commutative pow1/3
48×unpow3 cube-mult
42×pow-exp
39×pow-to-exp associate--l+
33×1-exp
31×pow-pow div-sub rec-exp
28×fma-udef log-div
26×rem-sqrt-square
25×pow-prod-up frac-add
23×pow-flip
22×exp-prod
21×sum-log
19×pow-sqr
15×+-commutative
13×complex-mul-def
12×neg-sub0
11×rem-cube-cbrt
10×pow-div rem-log-exp
8×associate--l- inv-pow pow-plus frac-sub associate-+l-
7×associate--r+ neg-log pow2
6×cube-div exp-diff
5×sqrt-unprod
4×associate-+r+ distribute-neg-in distribute-frac-neg *.c-commutative
3×sin-cos-mult +.c-commutative sin-sum
2×rem-exp-log exp-neg complex-add-def rem-square-sqrt cos-sum sin-mult tan-sum rem-cbrt-cube distribute-rgt-neg-out sqrt-undiv exp-to-pow
1×associate-+l+.c difference-cubes sqrt-pow2 log1p-udef associate-+r- diff-atan un-div-inv log1p-expm1 diff-cos expm1-log1p unsub-neg associate-*l*.c expm1-udef frac-2neg.c diff-sin

regimes3.3s (0.4%)

Accuracy

Total 29.9b remaining (21.4%)

Threshold costs 5.8b (4.2%)

5.9b82.7%quad2p (problem 3.2.1, positive)
5.5b77.2%quad2m (problem 3.2.1, negative)
5.5b77.2%quadm (p42, negative)
3.2b0%expq3 (problem 3.4.2)
1.5b93.5%quadp (p42, positive)

localize3.0s (0.4%)

bsearch2.1s (0.3%)

end0.0ms (0.0%)