Details

sample1.9m (53.7%)

Algorithm
56×intervals
16×halfpoints
Results
24.9s67029×body1280valid
17.4s17378×body2560valid
8.6s42585×body640valid
4.0s12887×body10240exit
3.2s93517×body80valid
2.7s20689×body320valid
1.7s62674×body80nan
915.0ms10728×body160valid
601.0ms47410×pre80true
315.0ms655×body1280nan
238.0ms672×body640nan
136.0ms461×body5120valid
78.0ms380×body320nan
23.0ms192×body160nan

prune40.7s (19.4%)

series33.1s (15.7%)

Calls

375 calls:

499.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
474.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
448.0ms
(fma (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (pow (cbrt (cbrt (+ x 1.0))) 4))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))
412.0ms
(/ (sqrt (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
372.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify11.3s (5.4%)

Algorithm
192×egg-herbie

rewrite6.3s (3.0%)

Algorithm
120×rewrite-expression-head
Calls

375 calls:

226.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
186.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
113.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
112.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
107.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
Rules
11056×*-un-lft-identity
10382×times-frac
9333×add-sqr-sqrt
7241×add-cube-cbrt
3927×sqrt-prod
3812×prod-diff
1299×distribute-lft-out
1258×add-exp-log
1253×unpow-prod-down
924×add-cbrt-cube
844×difference-of-squares
746×pow1
734×associate-*l*
701×distribute-lft-out--
635×add-log-exp
581×associate-*r*
575×div-inv
494×fma-neg
485×associate-/r*
483×associate-/l*
460×sqr-pow
458×associate-/r/
395×log-prod
369×div-exp
361×log1p-expm1-u
360×expm1-log1p-u
358×cbrt-prod
311×cube-prod
298×associate-+l+
261×flip-- distribute-rgt-neg-in flip3--
228×prod-exp
212×flip-+ flip3-+
203×cbrt-undiv
197×unswap-sqr
186×sqrt-div
174×distribute-lft-neg-in
153×cbrt-unprod
148×unpow2
145×sqrt-pow1
144×log-pow
130×exp-sum
128×fma-def
127×swap-sqr
114×sub-neg
110×diff-log
105×distribute-rgt-in distribute-lft-in
101×pow1/2
97×associate-*l/
96×associate-+r+
83×pow-unpow
81×pow-prod-down
77×cbrt-div
76×associate-/l/
72×frac-2neg clear-num
66×pow1/3
62×exp-prod
61×associate-*r/
59×pow-prod-up
58×unpow3 cube-mult neg-mul-1 frac-times
53×pow-exp
52×pow-to-exp
51×1-exp
49×*-commutative
48×rec-exp
38×frac-add
36×log-div
35×rem-sqrt-square
34×tan-quot
32×sum-log
29×pow-sqr
28×pow-flip
26×pow-pow
25×fma-udef
24×complex-mul-def div-sub
23×+-commutative
22×rem-log-exp
18×frac-sub
17×neg-sub0
16×pow-plus
14×inv-pow
12×associate--l-
10×pow-div sum-cubes pow2 neg-log
exp-diff associate--l+
difference-cubes hypot-def associate-+l- associate--r+
sqrt-unprod
associate-+r- *.c-commutative
rem-cube-cbrt
+.c-commutative cos-mult complex-add-def
rem-exp-log expm1-udef sin-mult
associate-+l+.c expm1-def exp-neg sub-div difference-of-sqr-1 expm1-log1p unsub-neg rem-square-sqrt associate-*l*.c cos-sum tan-sum distribute-rgt-out-- sin-sum
sin-cos-mult sqrt-pow2 log1p-udef associate--r- diff-atan log1p-expm1 diff-cos sqrt-undiv frac-2neg.c exp-to-pow diff-sin

regimes2.9s (1.4%)

Accuracy

Total 31.2b remaining (13.6%)

Threshold costs 8.7b (3.8%)

4.5b84.3%quad2m (problem 3.2.1, negative)
4.4b84.7%quadm (p42, negative)
3.7b86.9%quad2p (problem 3.2.1, positive)
3.7b87.2%quadp (p42, positive)
3.3b0%expq3 (problem 3.4.2)

localize1.9s (0.9%)

bsearch1.1s (0.5%)

end1.0ms (0.0%)