Details

sample1.9m (53.7%)

Algorithm
56×intervals
16×halfpoints
Results
24.3s67966×body1280valid
16.6s17322×body2560valid
8.3s41813×body640valid
3.8s12981×body10240exit
2.9s93778×body80valid
2.5s20490×body320valid
1.7s64074×body80nan
834.0ms10659×body160valid
521.0ms47328×pre80true
285.0ms649×body1280nan
215.0ms665×body640nan
122.0ms471×body5120valid
70.0ms376×body320nan
21.0ms179×body160nan

prune36.3s (17.5%)

series31.3s (15.1%)

Calls

396 calls:

1.3s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
633.0ms
(cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0))))
457.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
457.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
426.0ms
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite12.5s (6.0%)

Algorithm
121×rewrite-expression-head
Calls

396 calls:

301.0ms
(/ (- (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)))))
277.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
206.0ms
(* (sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))) (sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))))
198.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
186.0ms
(/ (* (+ (exp x) 2.0) (* (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)) (sqrt (+ (* (exp x) (- (exp x) 2.0)) 1)))) (* (+ (exp x) 2.0) (exp x)))
Rules
7692×times-frac
6932×*-un-lft-identity
6566×add-sqr-sqrt
4229×add-cube-cbrt
2599×sqrt-prod
1462×add-exp-log
1089×add-cbrt-cube
1047×associate-*r*
946×associate-*l*
844×distribute-lft-out
827×difference-of-squares
721×pow1
700×add-log-exp
690×unpow-prod-down
586×distribute-lft-out--
554×cbrt-prod
540×associate-/l*
396×div-inv
374×associate-/r*
369×prod-exp
367×div-exp
321×unswap-sqr
320×flip3-- flip--
314×associate-/r/
307×sqr-pow associate-*l/
265×sqrt-div
256×flip-+ flip3-+
255×swap-sqr
224×cbrt-undiv
221×frac-times
219×cbrt-unprod
213×log-prod
184×cube-prod
181×log-pow
163×associate-*r/
161×frac-add
158×unpow2
147×exp-prod
145×sub-neg
142×associate-/l/
122×diff-log
116×pow-unpow
96×pow-exp
93×pow-to-exp
88×cbrt-div pow-prod-down
77×*-commutative
76×sqrt-pow1
74×clear-num frac-2neg
66×pow1/2
48×1-exp
47×distribute-rgt-in distribute-lft-in
45×pow1/3
44×sum-log log-div
41×unpow3 rec-exp
40×distribute-rgt-neg-in
39×frac-sub
36×cube-mult
35×exp-sum
34×tan-quot
32×associate-+l+ rem-sqrt-square
28×+-commutative
25×pow-prod-up div-sub
24×complex-mul-def pow-flip associate--l+ rem-log-exp
19×pow-sqr
18×exp-diff
16×associate--r+
13×pow-pow
12×neg-sub0
11×associate--l-
10×pow-div inv-pow pow-plus pow2
8×neg-log sin-mult associate-+l-
7×rem-exp-log
6×distribute-rgt-out-- *.c-commutative cos-mult
5×rem-cube-cbrt difference-of-sqr-1
4×cube-div associate--r- +.c-commutative associate-+r+ complex-add-def
3×un-div-inv sqr-sin sqrt-unprod sin-cos-mult rem-square-sqrt
2×associate-+l+.c exp-neg associate-*l*.c cos-sum tan-sum rem-cbrt-cube frac-2neg.c exp-to-pow sin-sum
1×sqrt-undiv difference-cubes diff-atan diff-cos sub-div diff-sin associate-+r-

simplify9.8s (4.7%)

Algorithm
193×egg-herbie

regimes2.9s (1.4%)

Accuracy

Total 27.9b remaining (12.3%)

Threshold costs 7.0b (3.1%)

4.8b81.8%quadm (p42, negative)
4.4b84.7%quadp (p42, positive)
3.2b0%expq3 (problem 3.4.2)
2.6b91%quad2p (problem 3.2.1, positive)
1.8b80.8%2nthrt (problem 3.4.6)

localize2.0s (0.9%)

bsearch1.2s (0.6%)

end1.0ms (0.0%)