Details

sample5.0m (69.0%)

Algorithm
78×intervals
Results
3.1m21016×body10240exit
39.6s43815×body1280valid
14.2s30426×body640valid
12.7s204983×body80valid
8.8s152576×body80nan
6.9s27627×body320valid
5.4s36349×body160valid
5.3s202129×pre80true
4.4s36935×body80overflowed
1.2s3095×body2560valid
691.0ms7991×body160nan
158.0ms8371×pre80false
139.0ms225×body5120valid

prune58.1s (13.4%)

series42.6s (9.8%)

Calls

488 calls:

716.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
589.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
439.0ms
(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)
431.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
406.0ms
(expm1 (log1p (- (log (+ 1.0 (exp x))) (* x y))))

simplify13.1s (3.0%)

Algorithm
221×egg-herbie

regimes9.4s (2.2%)

Accuracy

Total 39.0b remaining (28.7%)

Threshold costs 6.4b (4.7%)

5.9b56.4%Cubic critical, narrow range
5.2b81%Cubic critical
5.1b49.8%Quotient of products
5.0b82.6%Quadratic roots, full range
4.8b28.8%Cubic critical, medium range

rewrite8.3s (1.9%)

Algorithm
143×rewrite-expression-head
Calls

488 calls:

321.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
243.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
230.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
207.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (/ (sqrt (- (* (* b b) (* b b)) (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
139.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (/ (sqrt (- (* (* b b) (* b b)) (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))
Rules
13720×times-frac
12068×*-un-lft-identity
11717×add-sqr-sqrt
8930×add-cube-cbrt
4778×prod-diff
3083×add-exp-log
2858×sqrt-prod
1864×add-cbrt-cube
1574×unpow-prod-down
1200×associate-*r*
1170×pow1
1035×div-exp
988×associate--r+
977×distribute-rgt-neg-in
971×prod-exp
951×difference-of-squares
897×distribute-lft-out
807×distribute-lft-neg-in
698×associate-/r*
693×add-log-exp
686×div-inv
683×associate-/l*
669×distribute-lft-out--
609×fma-neg
549×sqr-pow
501×associate-/r/
493×cbrt-undiv
491×expm1-log1p-u
490×log1p-expm1-u
487×associate-*l*
437×cbrt-unprod
391×cube-prod
380×pow-exp
304×distribute-rgt-in distribute-lft-in
286×pow-to-exp
284×flip--
283×flip3--
269×neg-mul-1
256×cbrt-prod
251×fma-def
238×flip-+
237×flip3-+
227×pow-prod-down
226×unswap-sqr
168×log-prod
166×sqrt-div
158×associate-*r/
148×unpow2
131×clear-num frac-2neg
128×log-pow
110×associate-*l/
109×frac-times
100×unpow3 cube-mult
96×sub-neg
92×*-commutative
91×swap-sqr
88×associate-/l/
77×1-exp
75×pow-unpow
74×rec-exp
65×exp-prod diff-log
64×pow-prod-up
63×log-div
61×exp-sum
51×pow1/2 sqrt-pow1
47×cos-sum
46×pow-sqr
45×sum-log
44×div-sub
42×rem-log-exp
38×pow1/3
35×rem-sqrt-square
34×sin-sum
32×neg-sub0 associate--l+
31×frac-add pow-plus
30×+-commutative cbrt-div
28×fma-udef tan-quot
27×pow-flip pow-pow
24×pow2
22×inv-pow frac-sub cos-mult
20×sin-mult associate-+l-
19×sin-diff
16×neg-log
15×sin-cos-mult
14×cos-diff
13×distribute-rgt-out associate--r-
11×associate--l-
9×rem-exp-log acos-asin
8×distribute-frac-neg
7×rem-cube-cbrt un-div-inv sum-cubes expm1-udef
6×cube-div sub-div asin-acos
5×exp-diff expm1-log1p associate-+r+
4×associate-+r- associate-+l+
3×acos-neg log1p-udef sqrt-unprod log1p-expm1
2×sin-neg distribute-lft1-in hypot-udef rem-square-sqrt hypot-def distribute-rgt-neg-out
1×rem-cbrt-cube

localize2.3s (0.5%)

bsearch906.0ms (0.2%)

end1.0ms (0.0%)