Details

sample1.9m (47.0%)

Algorithm
56×intervals
16×halfpoints
Results
24.1s66552×body1280valid
17.1s17500×body2560valid
8.4s43236×body640valid
3.8s13173×body10240exit
3.1s93436×body80valid
2.5s20275×body320valid
1.6s63526×body80nan
872.0ms10566×body160valid
550.0ms47387×pre80true
295.0ms682×body1280nan
209.0ms671×body640nan
127.0ms457×body5120valid
67.0ms359×body320nan
20.0ms182×body160nan

prune55.5s (23.0%)

series40.3s (16.7%)

Calls

396 calls:

820.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
687.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
635.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
559.0ms
(cbrt (fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0))))
467.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite14.3s (5.9%)

Algorithm
124×rewrite-expression-head
Calls

396 calls:

777.0ms
(+ (+ (- (* (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x))) 2.0) (fma (- 2.0) 1 2.0)) (exp (- x)))
341.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
340.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
339.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
337.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
15404×*-un-lft-identity
14755×times-frac
13322×add-sqr-sqrt
10214×add-cube-cbrt
6570×prod-diff
3994×sqrt-prod
1813×cbrt-prod
1762×associate-+l+
1401×distribute-lft-out
1377×unpow-prod-down
1307×difference-of-squares
1235×distribute-lft-out--
1218×add-exp-log
918×add-cbrt-cube
783×pow1
744×associate-*l*
724×div-inv
700×add-log-exp
668×associate-/l*
635×associate-/r/
551×distribute-rgt-neg-in
546×fma-neg
536×associate-*r* cube-prod
492×sqr-pow
382×log1p-expm1-u
381×expm1-log1p-u
312×associate-/r*
307×flip-- flip3--
296×prod-exp
285×distribute-lft-neg-in
264×log-prod
256×div-exp
254×unswap-sqr
245×flip-+ flip3-+
174×cbrt-undiv
166×sqrt-div
164×cbrt-unprod
161×fma-def
152×sqrt-pow1
125×diff-log
121×unpow2
119×sub-neg
115×distribute-rgt-in distribute-lft-in
111×pow1/2
108×unpow3 cube-mult
107×log-pow
101×pow-prod-down
99×pow-unpow
97×swap-sqr
95×neg-mul-1
77×pow-exp
75×pow-to-exp associate-+r+
72×tan-quot
71×associate-*r/
70×associate-/l/ exp-prod
61×pow-prod-up associate-*l/
60×frac-2neg clear-num
59×frac-times
55×*-commutative
49×pow1/3
45×cbrt-div
44×sum-log
42×exp-sum
41×rem-sqrt-square frac-add
38×fma-udef
34×log-div
30×1-exp rec-exp
29×pow-sqr
27×+-commutative
25×rem-log-exp
24×complex-mul-def
23×pow-flip
22×neg-sub0
21×pow-pow div-sub
18×associate--l- frac-sub
17×associate-+l-
16×pow-plus neg-log
10×pow-div
9×inv-pow pow2 associate--l+
8×exp-diff sqrt-unprod hypot-def distribute-rgt-out--
7×rem-cube-cbrt
6×*.c-commutative
5×un-div-inv
4×rem-exp-log associate-+r- exp-neg +.c-commutative complex-add-def sin-mult associate--r+ log-rec
3×difference-cubes sub-div difference-of-sqr-1 rem-square-sqrt cos-mult
2×cube-div associate-+l+.c expm1-def associate-*l*.c cos-sum tan-sum rem-cbrt-cube sin-sum
1×sin-cos-mult sqrt-pow2 diff-atan diff-cos expm1-log1p unsub-neg expm1-udef frac-2neg.c diff-sin

simplify11.6s (4.8%)

regimes3.2s (1.3%)

Accuracy

Total 26.2b remaining (11.7%)

Threshold costs 7.2b (3.2%)

4.4b84.4%quad2m (problem 3.2.1, negative)
4.4b84.5%quadm (p42, negative)
3.1b88%quadp (p42, positive)
3.1b0%expq3 (problem 3.4.2)
1.4b94.2%quad2p (problem 3.2.1, positive)

localize2.1s (0.9%)

bsearch1.1s (0.5%)

end1.0ms (0.0%)