Details

sample4.5m (67.3%)

Algorithm
78×intervals
Results
2.7m18077×body10240exit
39.4s44499×body1280valid
13.9s30180×body640valid
12.9s205088×body80valid
8.5s151185×body80nan
6.7s27311×body320valid
5.2s35984×body160valid
5.1s195175×pre80true
3.9s33937×body80overflowed
1.2s3136×body2560valid
637.0ms7632×body160nan
204.0ms227×body5120valid
148.0ms8052×pre80false

prune54.6s (13.5%)

series42.8s (10.6%)

Calls

491 calls:

765.0ms
(* (cbrt (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))) (cbrt (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))))
743.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
575.0ms
(/ (* (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)))
528.0ms
(cbrt (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))
528.0ms
(- (pow (cos delta) 3) (log1p (expm1 (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))))

simplify13.5s (3.3%)

Algorithm
224×egg-herbie

regimes10.1s (2.5%)

Accuracy

Total 30.4b remaining (24.7%)

Threshold costs 6.2b (5%)

5.6b59.5%Cubic critical, narrow range
5.1b28.6%Cubic critical, medium range
3.8b67.2%Quotient of products
3.4b0%Cubic critical, wide range
2.8b87.6%Cubic critical

rewrite8.7s (2.2%)

Algorithm
146×rewrite-expression-head
Calls

491 calls:

348.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
318.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
263.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
200.0ms
(sin (/ (- phi1 phi2) 2.0))
191.0ms
(pow (- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))) 3)
Rules
12996×*-un-lft-identity
11537×times-frac
11472×add-sqr-sqrt
7954×add-cube-cbrt
6288×prod-diff
2857×add-exp-log
2800×cbrt-prod
2653×unpow-prod-down
1995×cube-prod
1809×add-cbrt-cube
1450×distribute-lft-out
1421×difference-of-squares
996×distribute-lft-out--
995×pow1
966×associate--r+
950×prod-exp
885×div-exp
867×sqrt-prod
838×associate-/r/
726×associate-*r*
711×add-log-exp
683×div-inv
664×distribute-rgt-neg-in
622×associate-/l*
580×sqr-pow
513×distribute-lft-neg-in
494×log1p-expm1-u
491×expm1-log1p-u
473×associate-/r*
456×cbrt-unprod
435×cbrt-undiv
376×associate-*l*
374×fma-neg
326×flip--
325×flip3--
314×pow-exp
308×flip-+
307×flip3-+
284×log-prod
244×log-pow
230×unpow3 cube-mult
229×pow-to-exp
226×distribute-rgt-in distribute-lft-in
218×fma-def
201×exp-prod
171×pow-prod-down neg-mul-1
153×unswap-sqr
119×associate-*r/
114×clear-num frac-2neg
102×pow-unpow
96×associate-/l/
91×*-commutative
90×sub-neg
84×sqrt-pow1
75×cbrt-div
71×diff-log
70×1-exp
63×pow1/2
61×associate-*l/
60×pow1/3 rec-exp
59×frac-times
56×sqrt-div
49×cos-sum
47×div-sub swap-sqr
45×fma-udef sum-log
38×cube-div
34×sin-sum distribute-rgt-out
33×pow-pow
32×rem-sqrt-square
30×unpow2
29×+-commutative
27×associate-+l+ sin-mult
26×neg-sub0 frac-sub
25×log-div
24×rem-log-exp
22×associate-+l-
21×cos-mult
20×pow-prod-up
19×pow-flip associate--l+ sin-diff
18×tan-quot
17×neg-log
16×pow-sqr
15×rem-cube-cbrt
12×associate--l- cos-diff exp-sum
11×inv-pow
9×pow2 pow-plus distribute-frac-neg
8×sin-cos-mult associate-+r+ acos-asin rem-cbrt-cube
7×expm1-udef
6×difference-cubes distribute-lft1-in frac-add associate-+r-
5×rem-exp-log expm1-log1p
4×acos-neg distribute-rgt1-in sub-div
3×distribute-lft-neg-out distribute-rgt-neg-out
2×un-div-inv log1p-udef count-2 rem-square-sqrt sqrt-unprod asin-acos associate--r- exp-to-pow
1×unsub-neg unpow1/3 log1p-expm1 hypot-udef hypot-def

localize2.3s (0.6%)

bsearch748.0ms (0.2%)

end1.0ms (0.0%)