Details

sample1.8m (50.8%)

Algorithm
56×intervals
16×halfpoints
Results
24.0s66440×body1280valid
16.6s17084×body2560valid
8.3s42436×body640valid
3.7s12389×body10240exit
2.9s93821×body80valid
2.6s21081×body320valid
1.7s63205×body80nan
851.0ms10554×body160valid
507.0ms47540×pre80true
298.0ms682×body1280nan
212.0ms672×body640nan
133.0ms510×body5120valid
66.0ms356×body320nan
20.0ms187×body160nan

prune40.6s (18.8%)

series39.3s (18.1%)

Calls

389 calls:

1.5s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* b eps) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
580.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
519.0ms
(* (cbrt (/ (/ 1 2.0) (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
477.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
472.0ms
(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify10.6s (4.9%)

Algorithm
196×egg-herbie

rewrite10.2s (4.7%)

Algorithm
124×rewrite-expression-head
Calls

389 calls:

315.0ms
(* (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
313.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
221.0ms
(* (cbrt (/ (/ 1 2.0) (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
218.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
212.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
Rules
10384×*-un-lft-identity
10370×times-frac
9000×add-sqr-sqrt
6820×add-cube-cbrt
3191×prod-diff
2594×sqrt-prod
1308×add-exp-log
1036×distribute-lft-out
1009×unpow-prod-down
948×add-cbrt-cube
842×difference-of-squares
788×distribute-lft-out--
783×pow1
691×associate-/l*
616×add-log-exp
595×associate-*r*
564×associate-*l*
522×log-prod
447×div-inv
420×associate-/r*
403×fma-neg
392×sqr-pow
382×distribute-rgt-neg-in
378×associate-/r/
376×log1p-expm1-u
374×expm1-log1p-u
333×div-exp
296×prod-exp
275×cbrt-prod
266×unswap-sqr
247×associate-+l+
240×exp-sum
194×flip-- flip3--
192×cbrt-undiv
187×sqrt-pow1
180×distribute-lft-neg-in
168×flip-+ flip3-+
164×cbrt-unprod
149×unpow2
142×pow-prod-down sqrt-div
131×log-pow
111×pow1/2
104×pow-to-exp pow-exp
99×associate-*l/
98×swap-sqr
97×diff-log exp-prod
92×sub-neg
80×fma-def
73×frac-2neg clear-num
71×associate-/l/ pow-unpow
60×pow-prod-up neg-mul-1
56×*-commutative
45×fma-udef associate-*r/
42×pow1/3
37×rem-sqrt-square
36×log-div tan-quot
30×pow-sqr frac-times rem-log-exp
28×cube-prod
26×sum-log
25×rec-exp 1-exp
24×complex-mul-def div-sub
22×distribute-rgt-in distribute-lft-in
17×+-commutative
15×sqrt-unprod neg-sub0
13×associate--l- pow-flip
11×inv-pow frac-add associate-+r+ neg-log
10×associate--l+
9×pow-plus frac-sub
7×pow-pow pow2
6×exp-diff *.c-commutative associate-+l-
5×associate--r+
4×pow-div rem-exp-log +.c-commutative unpow3 cube-mult complex-add-def hypot-def cbrt-div
3×rem-square-sqrt sin-mult cos-mult exp-to-pow
2×sqrt-undiv log1p-udef associate-+r- exp-neg log1p-expm1 expm1-log1p associate-*l*.c cos-sum tan-sum expm1-udef associate-+l+.c sin-sum
1×frac-2neg.c expm1-def diff-atan sin-cos-mult diff-cos difference-of-sqr-1 distribute-frac-neg sub-div diff-sin mul-1-neg

regimes2.7s (1.2%)

Accuracy

Total 24.2b remaining (11.8%)

Threshold costs 6.0b (2.9%)

4.3b84.6%quad2m (problem 3.2.1, negative)
4.3b84.7%quadm (p42, negative)
2.9b0%expq3 (problem 3.4.2)
2.8b89.4%quad2p (problem 3.2.1, positive)
1.3b84.4%2nthrt (problem 3.4.6)

localize2.1s (1.0%)

bsearch975.0ms (0.5%)

end1.0ms (0.0%)