Details

sample11.3m (82.9%)

Algorithm
78×intervals
Results
9.9m62369×body10240exit
34.3s44547×body1280valid
10.9s30277×body640valid
6.9s205455×body80valid
4.6s153935×body80nan
4.4s27366×body320valid
3.2s202443×pre80true
3.1s36159×body160valid
759.0ms3203×body2560valid
356.0ms4050×pre10240exit
337.0ms7860×body160nan
137.0ms227×body5120valid
91.0ms8235×pre80false

prune58.6s (7.2%)

series41.5s (5.1%)

Calls

475 calls:

2.1s
(* (/ (* (- (/ (* m (- 1.0 m)) v) 1.0) (fma m (sqrt m) (pow (sqrt 1.0) 3))) (+ (* (sqrt 1.0) (sqrt 1.0)) (- (* (sqrt m) (sqrt m)) (* (sqrt 1.0) (sqrt m))))) (- (sqrt 1.0) (sqrt m)))
1.0s
(/ (* (- (/ (* m (- 1.0 m)) v) 1.0) (fma m (sqrt m) (pow (sqrt 1.0) 3))) (+ (* (sqrt 1.0) (sqrt 1.0)) (- (* (sqrt m) (sqrt m)) (* (sqrt 1.0) (sqrt m)))))
940.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
645.0ms
(/ (* (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)))
583.0ms
(/ (* (fma (log 0.5) c_p (fma 0.5 (* s c_p) 1)) (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)))

rewrite14.4s (1.8%)

Algorithm
144×rewrite-expression-head
Calls

475 calls:

389.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
292.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
233.0ms
(* (/ (* (- (/ (* m (- 1.0 m)) v) 1.0) (fma m (sqrt m) (pow (sqrt 1.0) 3))) (+ (* (sqrt 1.0) (sqrt 1.0)) (- (* (sqrt m) (sqrt m)) (* (sqrt 1.0) (sqrt m))))) (- (sqrt 1.0) (sqrt m)))
209.0ms
(* (- (/ (/ (* m (- 1.0 m)) (sqrt v)) (sqrt v)) 1.0) m)
191.0ms
(/ (* (fma (log 0.5) c_p (fma 0.5 (* s c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (* (* (cbrt (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1))) (cbrt (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)))) (cbrt (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)))) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
Rules
11493×*-un-lft-identity
11108×add-sqr-sqrt
11099×times-frac
8296×add-cube-cbrt
5963×prod-diff
3520×add-exp-log
1941×add-cbrt-cube
1433×unpow-prod-down
1321×prod-exp
1161×associate-*r*
1148×distribute-rgt-neg-in
1121×div-exp
1047×sqrt-prod
1028×pow1
999×distribute-lft-neg-in
977×difference-of-squares
973×associate--r+
822×distribute-lft-out
767×distribute-lft-out--
709×div-inv
708×add-log-exp
590×associate-/r/
581×cbrt-unprod
569×associate-*l*
514×sqr-pow
500×fma-neg
488×cbrt-prod
479×cbrt-undiv
475×log1p-expm1-u associate-/l* expm1-log1p-u
461×distribute-rgt-in distribute-lft-in
431×cube-prod
410×pow-exp
403×associate-/r*
333×neg-mul-1
311×flip--
310×flip3--
302×pow-to-exp
248×flip-+
247×flip3-+
230×unswap-sqr
204×log-prod
191×pow-prod-down
174×associate-*r/
172×fma-def
163×swap-sqr
138×unpow2
137×frac-times
123×1-exp
115×*-commutative
114×unpow3 cube-mult
112×sub-neg
109×associate-*l/
107×log-pow
102×cbrt-div
100×clear-num frac-2neg
91×cos-sum
87×pow-unpow
86×diff-log
82×associate-/l/
77×rec-exp
74×sqrt-div
65×exp-prod tan-quot
54×pow1/3 div-sub
42×pow1/2 sqrt-pow1
41×log-div
40×exp-sum
38×sum-log
37×neg-sub0 pow-pow
35×frac-sub
34×sin-sum
30×rem-sqrt-square sin-mult
28×rem-log-exp
25×+-commutative
24×associate-+l+ pow-prod-up associate--l+
23×cube-div rem-cube-cbrt
22×pow-sqr associate-+l-
20×fma-udef
18×sin-diff
17×neg-log
16×pow-plus
15×cos-diff pow2
14×associate--l-
13×distribute-rgt-out
11×acos-asin cos-mult
10×associate-+r- frac-add pow-flip distribute-frac-neg
rem-exp-log sin-cos-mult un-div-inv inv-pow associate-+r+
associate--r-
exp-diff acos-neg rem-cbrt-cube
sub-div distribute-rgt-neg-out
sin-neg hypot-udef hypot-def asin-acos expm1-udef
distribute-lft1-in sqrt-unprod pow3
expm1-log1p rem-square-sqrt log-rec distribute-rgt-out-- exp-to-pow

simplify13.1s (1.6%)

Algorithm
222×egg-herbie

regimes9.3s (1.1%)

Accuracy

Total 35.4b remaining (27.3%)

Threshold costs 6.3b (4.9%)

5.9b56.7%Cubic critical, narrow range
5.2b25.3%Cubic critical, medium range
4.4b84.6%Cubic critical
4.4b84.7%Quadratic roots, full range
3.5b0%Cubic critical, wide range

localize2.4s (0.3%)

bsearch542.0ms (0.1%)

end1.0ms (0.0%)