Details

sample4.5m (40.8%)

Algorithm
56×intervals
16×halfpoints
Results
52.8s66906×body1280valid
31.8s17504×body2560valid
18.4s42466×body640valid
10.2s12824×body10240exit
7.7s93701×body80valid
6.4s20408×body320valid
5.9s62864×body80nan
1.7s10800×body160valid
1.7s47484×pre80true
629.0ms719×body1280nan
454.0ms661×body640nan
396.0ms490×body5120valid
188.0ms359×body320nan
36.0ms193×body160nan

simplify4.0m (36.2%)

prune1.1m (10.4%)

series50.9s (7.7%)

Calls

404 calls:

1.1s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* eps (* (* eps eps) (* (* a a) a)))) (+ (* eps a) (* (* (* eps eps) 1/2) (* a a)))) (- (exp (* b eps)) 1.0)))
698.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
689.0ms
(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
667.0ms
(/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0))
609.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite18.7s (2.8%)

Algorithm
124×rewrite-expression-head
Calls

404 calls:

673.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* eps (* (* eps eps) (* (* a a) a)))) (+ (* eps a) (* (* (* eps eps) 1/2) (* a a)))) (- (exp (* b eps)) 1.0)))
634.0ms
(* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) 2.0) (sin y))
621.0ms
(* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y))
570.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
553.0ms
(/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0))
Rules
3747×*-un-lft-identity
3694×add-sqr-sqrt
3251×times-frac
2444×add-cube-cbrt
2071×sqrt-prod
1401×add-exp-log
1237×add-cbrt-cube
986×pow1
712×associate-*l*
668×add-log-exp
498×difference-of-squares
402×prod-exp
372×distribute-lft-out--
368×associate-*r*
363×cbrt-prod
357×associate-/l*
348×cbrt-unprod
317×distribute-lft-out
275×associate-/r*
256×div-exp
243×associate-*l/
235×pow-prod-down
229×flip3-- flip--
214×log-prod
205×cbrt-undiv
203×unpow-prod-down
187×div-inv
169×flip-+ flip3-+
133×unswap-sqr
132×associate-/r/
119×sqr-pow
118×cbrt-div
114×frac-times
112×pow1/3
110×pow-unpow
105×associate-*r/
103×sub-neg
102×diff-log
100×associate-/l/
86×*-commutative
79×log-pow
78×sqrt-pow1
72×swap-sqr
70×frac-2neg clear-num
68×sqrt-div
59×frac-add
57×cube-prod
53×pow1/2 pow-prod-up
45×exp-prod
39×distribute-rgt-neg-in
35×sum-log distribute-rgt-in distribute-lft-in
33×pow-sqr
31×pow-flip rem-sqrt-square
26×1-exp
24×rec-exp +-commutative
23×div-sub
21×log-div
20×associate--r+
19×pow2 pow-plus pow-pow
17×cos-mult
16×rem-log-exp
15×associate--l+
14×frac-sub pow-div complex-mul-def
12×associate-+l+ pow-exp tan-quot pow-to-exp
11×associate--l- sqr-cos
10×neg-sub0 cube-unmult
8×neg-log exp-to-pow
7×associate-+r+
5×distribute-frac-neg difference-cubes inv-pow
4×distribute-rgt-neg-out un-div-inv rem-cbrt-cube distribute-rgt-out--
3×exp-sum *.c-commutative pow3 sqrt-unprod +.c-commutative rem-exp-log associate-+l-
2×exp-diff sin-sum associate-+r- rem-cube-cbrt exp-neg unpow3 sub-div cos-sum tan-sum associate-*l*.c cube-mult complex-add-def distribute-rgt-out
1×quot-tan diff-atan distribute-neg-out sin-mult frac-2neg.c diff-sin associate-+l+.c diff-cos

localize6.1s (0.9%)

regimes6.1s (0.9%)

Accuracy

Total 25.0b remaining (19.8%)

Threshold costs 7.5b (5.9%)

4.2b87.7%quadp (p42, positive)
4.1b87.9%quad2p (problem 3.2.1, positive)
4.1b85.9%quadm (p42, negative)
3.4b0%expq3 (problem 3.4.2)
1.8b78.9%2nthrt (problem 3.4.6)

bsearch1.3s (0.2%)

end1.0ms (0.0%)