Details

sample1.8m (45.0%)

Algorithm
56×intervals
16×halfpoints
Results
23.7s66440×body1280valid
16.8s17084×body2560valid
8.3s42436×body640valid
3.8s12389×body10240exit
2.9s93821×body80valid
2.6s21081×body320valid
1.7s63205×body80nan
850.0ms10554×body160valid
538.0ms47540×pre80true
312.0ms682×body1280nan
218.0ms672×body640nan
136.0ms510×body5120valid
67.0ms356×body320nan
21.0ms187×body160nan

prune58.8s (24.1%)

series40.5s (16.6%)

Calls

416 calls:

2.3s
(log (sqrt (exp (* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))))
496.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
485.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
467.0ms
(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
466.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

rewrite15.8s (6.5%)

Algorithm
125×rewrite-expression-head
Calls

416 calls:

665.0ms
(* (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
605.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
456.0ms
(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
438.0ms
(+ (- (/ 1 (/ (+ x 1.0) 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
332.0ms
(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
Rules
31020×times-frac
19486×*-un-lft-identity
18187×add-sqr-sqrt
12842×add-cube-cbrt
8452×cbrt-prod
3464×sqrt-prod
2448×difference-of-squares
2333×distribute-lft-out--
1578×associate-/l*
1468×add-exp-log
1105×distribute-lft-out
1052×add-cbrt-cube
983×distribute-rgt-neg-in
828×associate-*l*
770×add-log-exp
709×pow1
674×associate-*r*
537×unpow-prod-down
485×log-prod
434×div-inv
406×prod-exp
403×associate-/r*
290×div-exp
273×associate-/r/
255×unswap-sqr
250×sqr-pow
248×flip3-- flip--
207×cbrt-unprod
195×cbrt-undiv
191×flip-+ flip3-+
149×log-pow
139×associate-*l/
133×sqrt-div
131×diff-log
130×exp-prod
128×cbrt-div
126×sub-neg
121×unpow2
112×associate-*r/
110×sqrt-pow1
106×associate-+r+
103×pow-exp
96×pow-to-exp cube-prod
93×pow-prod-down
86×*-commutative
80×associate-/l/
75×pow-unpow
72×frac-2neg clear-num
66×sum-log
62×frac-times
61×log-div
60×swap-sqr
54×pow1/2
51×associate-+l+ frac-add pow1/3 frac-sub
39×distribute-rgt-in distribute-lft-in
37×pow-pow +-commutative
34×rem-sqrt-square rem-log-exp
28×tan-quot
27×1-exp rec-exp
25×div-sub exp-sum associate--l+
24×complex-mul-def neg-sub0
21×exp-diff
19×associate-+l-
15×unpow3 associate--l- cube-mult pow-prod-up
14×distribute-rgt-out--
13×pow-sqr associate--r+
12×neg-log
11×sum-cubes sin-mult
10×pow-flip
9×rem-cube-cbrt cos-mult exp-to-pow
8×inv-pow exp-neg
7×cube-div associate-+r-
6×*.c-commutative
5×rem-exp-log sqrt-unprod pow2 pow-plus
4×sub-div +.c-commutative complex-add-def
3×un-div-inv difference-of-sqr-1
2×cos-sum associate-+l+.c unpow-prod-up pow-sub associate-*l*.c tan-sum rem-cbrt-cube pow-neg sin-sum
1×sin-cos-mult diff-atan diff-cos rem-square-sqrt quot-tan frac-2neg.c +-inverses diff-sin

simplify12.5s (5.1%)

Algorithm
197×egg-herbie

regimes3.0s (1.2%)

Accuracy

Total 20.4b remaining (8.8%)

Threshold costs 5.4b (2.3%)

5.4b41.7%expq3 (problem 3.4.2)
3.2b88.8%quad2m (problem 3.2.1, negative)
1.4b94.1%quad2p (problem 3.2.1, positive)
1.3b85%2nthrt (problem 3.4.6)
1.3b94.7%quadp (p42, positive)

localize2.0s (0.8%)

bsearch1.2s (0.5%)

end1.0ms (0.0%)