Details

sample1.8m (51.9%)

Algorithm
56×intervals
16×halfpoints
Results
24.4s66678×body1280valid
17.5s17568×body2560valid
8.3s42367×body640valid
3.0s93875×body80valid
2.6s20497×body320valid
1.7s63442×body80nan
881.0ms10616×body160valid
656.0ms16339×body80overflowed
570.0ms49716×pre80true
159.0ms173×body1280nan
137.0ms284×body640nan
128.0ms453×body5120valid
38.0ms162×body320nan
12.0ms88×body160nan

prune40.1s (19.1%)

series34.8s (16.5%)

Calls

372 calls:

1.0s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
937.0ms
(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
916.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
916.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
908.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify10.4s (4.9%)

Algorithm
189×egg-herbie

rewrite9.5s (4.5%)

Algorithm
117×rewrite-expression-head
Calls

372 calls:

324.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
309.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (log1p (expm1 (/ 1.0 (- x 1.0)))))
177.0ms
(* (- (exp (* a eps)) 1.0) (- (pow (exp (* b eps)) 3) (pow 1.0 3)))
130.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
92.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
Rules
10266×*-un-lft-identity
8911×add-sqr-sqrt
8909×times-frac
6800×add-cube-cbrt
4080×prod-diff
2458×sqrt-prod
1317×add-exp-log
1159×unpow-prod-down
1111×distribute-lft-out
918×add-cbrt-cube
905×difference-of-squares
737×pow1
675×distribute-lft-out--
627×add-log-exp
621×cube-prod
566×associate-*r*
521×associate-/r*
488×sqr-pow
487×fma-neg
483×associate-+l+
474×associate-/l*
465×associate-*l*
452×div-inv
398×div-exp
397×cbrt-prod
364×associate-/r/
359×log1p-expm1-u
357×expm1-log1p-u
346×distribute-rgt-neg-in
326×pow-unpow
279×distribute-lft-neg-in log-prod
263×prod-exp
228×flip-- flip3--
197×cbrt-undiv
186×log-pow
183×exp-prod
181×unswap-sqr
180×distribute-rgt-in distribute-lft-in
155×cbrt-unprod
144×sqrt-div
137×flip-+ flip3-+
122×unpow3 cube-mult
116×sqrt-pow1
111×diff-log
104×sub-neg
98×unpow2
97×pow-prod-down
93×neg-mul-1
91×pow1/2
87×tan-quot
79×1-exp
70×frac-2neg clear-num
64×associate-/l/ rec-exp
61×associate-*r/
58×fma-def pow-to-exp associate-*l/ pow-exp
51×pow-prod-up *-commutative
50×pow1/3 frac-times
44×exp-sum
37×swap-sqr
36×rem-sqrt-square
29×rem-log-exp
28×div-sub
26×pow-flip
25×pow-pow
24×complex-mul-def log-div
23×pow-sqr
21×difference-of-sqr-1 sum-log
19×difference-cubes fma-udef inv-pow neg-sub0
16×associate--l-
15×neg-log
13×exp-diff
12×rem-exp-log cbrt-div
11×associate-+r+
10×+-commutative associate--l+ exp-to-pow
9×frac-add
8×cube-div sqrt-unprod pow-plus hypot-def frac-sub
7×pow2 associate-+l- associate--r+
6×log1p-udef *.c-commutative
4×rem-cube-cbrt expm1-def pow-div log1p-expm1 +.c-commutative rem-cbrt-cube complex-add-def
3×expm1-log1p expm1-udef
2×associate-+l+.c associate-+r- exp-neg rem-square-sqrt associate-*l*.c cos-sum cos-mult tan-sum frac-2neg.c sin-sum log-rec
1×sin-cos-mult sqrt-pow2 un-div-inv diff-atan diff-cos distribute-rgt-out-- diff-sin

regimes3.2s (1.5%)

Accuracy

Total 25.0b remaining (9.3%)

Threshold costs 5.2b (1.9%)

4.4b84.5%quadm (p42, negative)
4.3b85%quad2m (problem 3.2.1, negative)
3.3b23.6%expq3 (problem 3.4.2)
2.1b79.3%2cos (problem 3.3.5)
1.5b83.6%2nthrt (problem 3.4.6)

localize2.0s (0.9%)

bsearch1.4s (0.6%)

end1.0ms (0.0%)