Details

sample2.0m (57.1%)

Algorithm
56×intervals
16×halfpoints
Results
26.8s67246×body1280valid
17.6s17146×body2560valid
9.6s42329×body640valid
5.3s94223×body80valid
4.7s12595×body10240exit
3.2s20800×body320valid
3.1s63403×body80nan
1.1s10247×body160valid
731.0ms39136×pre80overflowed
339.0ms661×body1280nan
263.0ms654×body640nan
151.0ms448×body5120valid
101.0ms8256×pre80true
87.0ms358×body320nan
26.0ms174×body160nan

series33.3s (16.1%)

Calls

398 calls:

745.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
500.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
496.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
456.0ms
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
451.0ms
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

prune32.8s (15.9%)

simplify10.4s (5.0%)

Algorithm
194×egg-herbie

rewrite6.3s (3.0%)

Algorithm
122×rewrite-expression-head
Calls

398 calls:

175.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
139.0ms
(* (sqrt (sqrt (/ (+ (exp x) (exp (- x))) 2.0))) (* (sqrt (sqrt (/ (+ (exp x) (exp (- x))) 2.0))) (* (sqrt (/ (+ (exp x) (exp (- x))) 2.0)) (cos y))))
121.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
102.0ms
(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))
92.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
Rules
6014×*-un-lft-identity
5824×times-frac
5574×add-sqr-sqrt
3361×add-cube-cbrt
1864×add-exp-log
1707×sqrt-prod
1114×add-cbrt-cube
1065×associate-*r*
822×unpow-prod-down
789×difference-of-squares distribute-lft-out
729×add-log-exp
717×pow1
609×distribute-lft-out--
569×associate-*l*
564×associate-/l*
547×prod-exp div-exp
425×associate-/r*
393×sqr-pow
333×unswap-sqr
245×flip-- flip3--
241×cube-prod
239×associate-/r/
226×cbrt-undiv
224×cbrt-unprod div-inv
172×unpow2
169×cbrt-prod
165×log-prod
160×flip-+ flip3-+
154×associate-*l/
145×pow-exp
142×pow-to-exp
138×log-pow
125×sub-neg
120×diff-log
118×distribute-rgt-neg-in
116×sqrt-div
115×exp-prod
112×1-exp
108×pow-unpow
102×pow-prod-down
98×associate-*r/
85×*-commutative
82×rec-exp
80×frac-2neg clear-num
75×associate-/l/ frac-times
73×difference-cubes
67×swap-sqr
65×sqrt-pow1
59×pow1/2
55×cbrt-div
49×sum-log
41×rem-sqrt-square
37×unpow3 cube-mult
36×distribute-rgt-in frac-add distribute-lft-in
35×pow1/3
34×log-div
32×tan-quot
30×+-commutative rem-log-exp
26×div-sub exp-to-pow
25×frac-sub associate--l+
24×complex-mul-def
23×pow-pow
22×exp-lft-cube
20×pow-flip neg-sub0
19×associate-+l+ associate--l-
15×pow-prod-up associate--r+ neg-log
12×inv-pow
11×un-div-inv pow-sqr sin-mult
9×exp-diff distribute-lft-neg-in neg-mul-1
8×associate-+r+ exp-sum associate-+l-
7×rem-cube-cbrt cos-mult
6×cube-div *.c-commutative
5×sqrt-unprod pow-plus sub-div pow2
4×+.c-commutative complex-add-def
3×associate-+r- sin-cos-mult
2×cos-sum rem-exp-log associate-+l+.c associate--r- exp-neg distribute-rgt-out-- difference-of-sqr-1 rem-square-sqrt distribute-frac-neg tan-sum frac-2neg.c associate-*l*.c rem-cbrt-cube sin-sum
1×sqrt-pow2 diff-atan sqr-sin diff-cos distribute-rgt-neg-out cube-unmult distribute-neg-frac diff-sin log-rec

regimes2.6s (1.3%)

Accuracy

Total 26.4b remaining (12.9%)

Threshold costs 6.5b (3.2%)

6.7b74.6%quad2p (problem 3.2.1, positive)
3.4b0%expq3 (problem 3.4.2)
3.2b87.9%quadm (p42, negative)
2.7b72.4%2cos (problem 3.3.5)
1.6b81.9%2nthrt (problem 3.4.6)

localize2.0s (1.0%)

bsearch1.4s (0.7%)

end1.0ms (0.0%)