Details

prune55.1s (31.9%)

sample47.6s (27.6%)

Algorithm
75×intervals
Results
19.9s310980×body80valid
5.5s13868×body1280valid
3.0s16842×body160valid
2.9s108664×pre80true
2.8s3835×body2560valid
2.3s9374×body640valid
1.0s6894×body320valid
1.0s19532×body80nan
948.0ms1861×body10240exit
193.0ms8256×pre80overflowed
97.0ms227×body5120valid
6.0ms100×pre80false

series31.1s (18.0%)

Calls

317 calls:

1.2s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
983.0ms
(fma (sqrt (pow x 4.0)) (sqrt (pow x 4.0)) (- (pow y 4.0)))
479.0ms
(fma x (* (- (* (* (* (* 11.0 x) x) y) y) (+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))) x) (+ (* 333.75 (pow y 6.0)) (fma (pow y 8.0) 5.5 (/ x (* 2.0 y)))))
410.0ms
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4.0)) 3))
408.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))

rewrite13.4s (7.8%)

Algorithm
109×rewrite-expression-head
Calls

317 calls:

620.0ms
(- (exp (+ (* (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0))))) (fma 0.5 (/ 1 y) (fma 2.0 y (fabs (- y (sqrt (+ (pow y 2) 1.0))))))) (pow (pow 10.0 -300.0) (* 10000.0 (+ y 1.0))))) 1.0)
611.0ms
(- (exp (+ (* (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0))))) (fma 0.5 (/ 1 y) (fma 2.0 y (fabs (- y (sqrt (+ (pow y 2) 1.0))))))) (pow (pow 10.0 -300.0) (* 10000.0 (+ y 1.0))))) 1.0)
609.0ms
(- (exp (+ (* (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0))))) (fma 0.5 (/ 1 y) (fma 2.0 y (fabs (- y (sqrt (+ (pow y 2) 1.0))))))) (pow (pow 10.0 -300.0) (* 10000.0 (+ y 1.0))))) 1.0)
434.0ms
(- (exp (* (fma 0.5 (/ 1 y) (fma 2.0 y (fabs (- y (sqrt (+ (pow y 2) 1.0)))))) (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0))))))) 1.0)
434.0ms
(- (exp (* (fma 0.5 (/ 1 y) (fma 2.0 y (fabs (- y (sqrt (+ (pow y 2) 1.0)))))) (- (fabs (- y (sqrt (+ (* y y) 1.0)))) (/ 1.0 (+ y (sqrt (+ (* y y) 1.0))))))) 1.0)
Rules
19105×times-frac
17389×*-un-lft-identity
15926×add-sqr-sqrt
13077×add-cube-cbrt
10124×prod-diff
3220×unpow-prod-down
2589×cube-prod
2087×distribute-rgt-in distribute-lft-in
1792×add-exp-log
1469×distribute-lft-out
1453×difference-of-squares
1356×exp-sum
1209×add-cbrt-cube
1145×div-inv
1009×sqr-pow
768×associate-*l*
751×fma-neg
715×associate-/l*
712×associate-*r*
699×associate-/r/
696×distribute-lft-out--
656×associate-/r*
653×add-log-exp
625×pow1
600×prod-exp
517×div-exp
420×flip-+ flip3-+
319×log1p-expm1-u
317×expm1-log1p-u
310×cbrt-unprod
297×distribute-rgt-neg-in
293×unpow3 cube-mult
284×distribute-lft-neg-in
283×cbrt-undiv
252×sqrt-prod
191×flip-- flip3--
177×cbrt-prod
170×frac-times
151×1-exp
149×unswap-sqr
133×pow-prod-down
124×associate-*r/
123×sub-neg
116×fma-def
111×sum-log
103×frac-sub
98×associate-*l/
89×rec-exp
83×diff-log
80×exp-neg
77×neg-mul-1
71×*-commutative
70×neg-sub0
67×associate-/l/
65×clear-num frac-2neg
60×exp-diff
54×log-prod
44×fma-udef
42×swap-sqr
35×unpow2
32×pow-exp
30×pow-to-exp pow1/3
24×div-sub
23×un-div-inv +-commutative
17×sqrt-div log-pow
16×pow-prod-up log-div
15×cbrt-div rem-sqrt-square
14×pow-plus
13×pow-flip
12×distribute-lft-neg-out pow-sqr
10×difference-cubes pow1/2 sqrt-pow1 pow2
associate-+l+ inv-pow
associate-+r+ associate--l- neg-log rem-log-exp
associate--l+
pow-unpow
distribute-frac-neg
frac-add associate-+l-
cube-div log1p-udef log1p-expm1 expm1-log1p expm1-udef sum-cubes distribute-neg-frac associate--r+ pow-pow
rem-cube-cbrt pow3 hypot-udef rem-cbrt-cube distribute-rgt-neg-out

simplify12.3s (7.1%)

Algorithm
183×egg-herbie

localize8.0s (4.6%)

regimes4.0s (2.3%)

Accuracy

Total 45.0b remaining (14.7%)

Threshold costs 2.5b (0.8%)

10.6b51.7%Compound Interest
8.0b36.2%Complex division, imag part
6.9b36.3%Complex division, real part
4.4b84.7%The quadratic formula (r2)
4.1b9.5%Kahan's Unum-Targeted Monster

bsearch1.1s (0.6%)

end1.0ms (0.0%)