Details

sample1.8m (49.7%)

Algorithm
56×intervals
16×halfpoints
Results
24.7s66674×body1280valid
17.6s17684×body2560valid
8.8s42276×body640valid
3.0s93824×body80valid
2.6s20242×body320valid
1.7s64337×body80nan
879.0ms10742×body160valid
650.0ms16259×body80overflowed
632.0ms49557×pre80true
134.0ms274×body640nan
129.0ms130×body1280nan
123.0ms444×body5120valid
40.0ms167×body320nan
13.0ms97×body160nan

prune45.8s (21.5%)

series36.9s (17.3%)

Calls

400 calls:

884.0ms
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))
502.0ms
(exp (- (log 1.0) (log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))))
484.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
471.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
444.0ms
(* (/ 1 (sqrt (fma (fma eps eps (fma (/ eps 1.0) (/ eps 1.0) eps)) (fma (/ eps 1.0) (/ eps 1.0) eps) (pow eps 4)))) (/ (- (pow (pow eps 2) 3) (pow (fma (/ eps 1.0) (/ eps 1.0) eps) 3)) (sqrt (fma (fma eps eps (fma (/ eps 1.0) (/ eps 1.0) eps)) (fma (/ eps 1.0) (/ eps 1.0) eps) (pow eps 4)))))

simplify11.3s (5.3%)

Algorithm
194×egg-herbie

rewrite6.6s (3.1%)

Algorithm
122×rewrite-expression-head
Calls

400 calls:

251.0ms
(* (/ 1 (sqrt (fma (fma eps eps (fma (/ eps 1.0) (/ eps 1.0) eps)) (fma (/ eps 1.0) (/ eps 1.0) eps) (pow eps 4)))) (/ (- (pow (pow eps 2) 3) (pow (fma (/ eps 1.0) (/ eps 1.0) eps) 3)) (sqrt (fma (fma eps eps (fma (/ eps 1.0) (/ eps 1.0) eps)) (fma (/ eps 1.0) (/ eps 1.0) eps) (pow eps 4)))))
237.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
195.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
120.0ms
(/ (- (pow (pow eps 2) 3) (pow (fma (/ eps 1.0) (/ eps 1.0) eps) 3)) (sqrt (fma (fma eps eps (fma (/ eps 1.0) (/ eps 1.0) eps)) (fma (/ eps 1.0) (/ eps 1.0) eps) (pow eps 4))))
117.0ms
(/ (- (pow (pow eps 2) 3) (pow (fma (/ eps 1.0) (/ eps 1.0) eps) 3)) (fma (fma eps eps (fma (/ eps 1.0) (/ eps 1.0) eps)) (fma (/ eps 1.0) (/ eps 1.0) eps) (pow eps 4)))
Rules
11253×add-sqr-sqrt
11146×*-un-lft-identity
11050×times-frac
8231×add-cube-cbrt
5075×prod-diff
3381×sqrt-prod
2147×unpow-prod-down
1656×difference-of-squares
1347×add-exp-log
1291×cube-prod
979×add-cbrt-cube
912×sqr-pow
795×distribute-lft-out--
717×associate-/l*
714×associate-*r*
694×cbrt-prod
688×pow1
683×distribute-lft-out
676×add-log-exp
646×associate-*l*
572×fma-neg
545×distribute-rgt-neg-in
496×div-inv
402×distribute-lft-neg-in
386×log1p-expm1-u
385×expm1-log1p-u
378×div-exp
345×associate-/r*
340×associate-+l+
300×associate-/r/
293×prod-exp
279×distribute-rgt-in distribute-lft-in
254×log-prod
242×flip-+ flip3-+
230×unpow2
219×flip-- flip3--
211×cbrt-undiv
167×cbrt-unprod
161×pow-unpow unswap-sqr
134×neg-mul-1 exp-sum
124×cbrt-div
121×sqrt-div unpow3 cube-mult sub-neg
120×log-pow
112×diff-log
108×fma-def
99×associate-*l/ associate-*r/
93×exp-prod
89×log-div
82×sqrt-pow1
81×frac-times pow-exp
78×pow-to-exp
76×pow-prod-down
74×associate-/l/
72×frac-2neg clear-num
63×frac-add pow1/3
62×pow1/2
53×1-exp
49×tan-quot
48×*-commutative swap-sqr
38×rec-exp
37×sum-log
36×difference-cubes fma-udef
35×rem-sqrt-square
33×div-sub
27×+-commutative
24×complex-mul-def
23×rem-log-exp
22×pow-flip
19×pow-pow
18×associate--r-
17×neg-sub0
16×pow-prod-up frac-sub
15×associate--l-
14×pow-sqr
13×associate-+r+
12×associate--l+
11×exp-diff
10×pow-div neg-log
associate-+l-
rem-cube-cbrt
pow2 pow-plus
rem-exp-log inv-pow *.c-commutative
associate--r+
sqrt-unprod sub-div +.c-commutative complex-add-def hypot-def
cube-div un-div-inv difference-of-sqr-1 sin-mult cos-mult
associate-+l+.c expm1-def associate-+r- exp-neg associate-*l*.c tan-sum cos-sum exp-to-pow sin-sum
sin-cos-mult diff-atan diff-cos expm1-log1p rem-square-sqrt distribute-rgt-out-- expm1-udef frac-2neg.c diff-sin

regimes3.3s (1.6%)

Accuracy

Total 22.5b remaining (8.9%)

Threshold costs 5.4b (2.1%)

4.4b84.5%quadm (p42, negative)
4.4b84.6%quad2m (problem 3.2.1, negative)
1.9b29.6%expq3 (problem 3.4.2)
1.5b82.4%2nthrt (problem 3.4.6)
1.3b86.9%2cos (problem 3.3.5)

localize2.0s (0.9%)

bsearch1.1s (0.5%)

end1.0ms (0.0%)