Details

sample1.9m (51.7%)

Algorithm
56×intervals
16×halfpoints
Results
23.7s66552×body1280valid
17.1s17500×body2560valid
8.4s43236×body640valid
3.9s13173×body10240exit
2.9s93436×body80valid
2.5s20275×body320valid
1.7s63526×body80nan
840.0ms10566×body160valid
518.0ms47387×pre80true
292.0ms682×body1280nan
207.0ms671×body640nan
138.0ms457×body5120valid
65.0ms359×body320nan
23.0ms182×body160nan

prune38.0s (17.5%)

series37.3s (17.1%)

Calls

405 calls:

829.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
529.0ms
(* (cbrt (/ (/ 1 2.0) (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
485.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
472.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
414.0ms
(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite12.7s (5.8%)

Algorithm
125×rewrite-expression-head
Calls

405 calls:

323.0ms
(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
291.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
232.0ms
(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
207.0ms
(* (sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (/ (sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
191.0ms
(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
Rules
11447×times-frac
10060×*-un-lft-identity
8636×add-sqr-sqrt
5601×add-cube-cbrt
3341×sqrt-prod
2389×cbrt-prod
1439×add-exp-log
1299×distribute-lft-out
1279×difference-of-squares
1072×add-cbrt-cube
1070×distribute-lft-out--
892×unpow-prod-down
793×associate-/l*
740×pow1
725×add-log-exp
668×associate-*r*
614×associate-*l*
469×cube-prod
467×associate-/r*
386×log-prod
362×prod-exp
354×div-inv
333×div-exp
324×sqr-pow
305×associate-/r/
263×unswap-sqr
260×flip-- flip3--
256×distribute-rgt-neg-in
219×cbrt-undiv
205×cbrt-unprod
194×flip-+ flip3-+
162×sqrt-div
139×sub-neg
130×associate-*l/
125×diff-log
122×unpow2
116×log-pow
110×sqrt-pow1
103×pow-unpow
102×pow-prod-down
101×associate-+l+
97×associate-+r+
92×associate-*r/
90×pow-exp
86×pow-to-exp
82×associate-/l/
80×exp-prod
78×pow1/2
76×distribute-rgt-in distribute-lft-in
75×*-commutative
74×clear-num frac-2neg
68×frac-times
59×swap-sqr
57×cbrt-div
52×unpow3 cube-mult
49×sum-log
46×rec-exp 1-exp
39×pow-prod-up
37×rem-sqrt-square
35×log-div pow1/3 +-commutative
32×frac-add
27×pow-pow
25×rem-log-exp
24×complex-mul-def
23×frac-sub
21×tan-quot
19×div-sub
18×associate--l+
15×neg-sub0
14×associate--l- pow-flip associate--r+
13×pow-sqr
12×cube-div inv-pow
11×neg-log
10×rem-cube-cbrt
sin-mult associate-+l-
exp-diff exp-sum
un-div-inv
difference-cubes sqrt-unprod distribute-rgt-out-- cos-mult *.c-commutative
associate-+r- exp-to-pow
pow-div pow2 +.c-commutative complex-add-def pow-plus rem-cbrt-cube log-rec
sub-div
rem-exp-log associate-+l+.c exp-neg difference-of-sqr-1 distribute-rgt-out cos-sum tan-sum associate-*l*.c sin-sum
sin-cos-mult sqrt-pow2 distribute-lft1-in distribute-lft-neg-in diff-atan sqr-sin diff-cos unsub-neg rem-square-sqrt quot-tan neg-mul-1 distribute-rgt-neg-out frac-2neg.c distribute-neg-frac diff-sin

simplify11.0s (5.1%)

regimes3.0s (1.4%)

Accuracy

Total 18.9b remaining (9.1%)

Threshold costs 7.7b (3.7%)

3.1b88%quadp (p42, positive)
3.1b0%expq3 (problem 3.4.2)
1.3b85.3%2nthrt (problem 3.4.6)
1.3b87%2cos (problem 3.3.5)
1.3b94.8%quad2p (problem 3.2.1, positive)

localize2.0s (0.9%)

bsearch1.2s (0.6%)

end1.0ms (0.0%)