Details

sample6.2m (72.2%)

Algorithm
78×intervals
Results
4.8m36837×body10240exit
33.7s43302×body1280valid
11.7s31372×body640valid
7.2s203774×body80valid
4.6s152485×body80nan
4.5s27485×body320valid
3.0s35984×body160valid
2.7s174889×pre80true
723.0ms3010×body2560valid
377.0ms4050×pre10240exit
365.0ms7988×body160nan
94.0ms241×body5120valid
88.0ms8370×pre80false

prune58.1s (11.3%)

series44.6s (8.7%)

Calls

483 calls:

742.0ms
(fma (pow (cos phi2) 3) (pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3) (pow (cos phi1) 3))
726.0ms
(/ (* (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)))
658.0ms
(/ (* (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)))
598.0ms
(/ (* (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)))
557.0ms
(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))

rewrite15.0s (2.9%)

Algorithm
146×rewrite-expression-head
Calls

483 calls:

605.0ms
(* (+ (- (* (* (/ 1 v) m) (- 1.0 m)) 1.0) (fma (- 1.0) 1 1.0)) m)
400.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
383.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
311.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
298.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
Rules
12803×*-un-lft-identity
11790×add-sqr-sqrt
11738×times-frac
8442×add-cube-cbrt
6117×prod-diff
2746×add-exp-log
1887×sqrt-prod
1711×add-cbrt-cube
1299×difference-of-squares
1070×associate--r+
1069×unpow-prod-down
1066×distribute-lft-out--
1033×distribute-lft-out
977×pow1
900×prod-exp
883×log-prod
881×distribute-rgt-neg-in
862×div-exp
791×associate-/r/
775×associate-*r*
761×add-log-exp
687×distribute-lft-neg-in
679×div-inv
667×associate-/l*
560×exp-sum
546×associate-/r*
519×fma-neg
503×cbrt-prod
495×distribute-rgt-in distribute-lft-in
485×log1p-expm1-u
484×expm1-log1p-u
462×flip--
461×flip3--
406×cbrt-unprod
404×cbrt-undiv
386×sqr-pow
377×associate-*l*
364×pow-exp
360×cube-prod
272×cbrt-div
269×pow-to-exp
266×flip-+
265×flip3-+
229×neg-mul-1
202×sin-sum
189×frac-times
187×fma-def
179×pow-prod-down
176×unswap-sqr
160×associate-*r/
129×associate-*l/
121×clear-num frac-2neg
120×sub-neg
104×log-pow
100×diff-log
96×associate-/l/
92×unpow3 cube-mult
91×*-commutative
88×sqrt-div
87×sqrt-pow1
79×exp-prod
75×swap-sqr
66×pow-unpow
62×pow1/2
58×pow1/3
52×associate-+r+
49×1-exp sum-log
48×cos-sum
42×div-sub
41×rem-log-exp
38×neg-sub0
37×associate--l+
36×rem-sqrt-square log-div
33×rec-exp
29×cube-div pow-flip +-commutative
28×unpow2 sin-mult pow-prod-up
26×neg-log cos-mult
25×associate-+l+
24×tan-quot frac-sub
23×pow-pow
22×pow-sqr
21×fma-udef
20×cos-diff sin-diff
17×acos-asin associate-+l-
16×associate--l-
12×pow-div pow2 pow-plus associate--r-
11×sin-cos-mult distribute-rgt-out
9×rem-exp-log rem-cube-cbrt inv-pow
8×frac-add
7×associate-+r- sum-cubes
6×exp-diff distribute-frac-neg expm1-udef
4×acos-neg sub-div rem-cbrt-cube
3×sqrt-unprod expm1-log1p hypot-def
2×log1p-udef distribute-lft1-in log1p-expm1 unpow-prod-up pow-sub hypot-udef rem-square-sqrt asin-acos cos-neg
1×un-div-inv sin-asin log-rec

simplify13.0s (2.5%)

Algorithm
224×egg-herbie

regimes9.2s (1.8%)

Accuracy

Total 28.6b remaining (25.7%)

Threshold costs 4.9b (4.4%)

7.3b47.2%Cubic critical, narrow range
5.1b26.4%Cubic critical, medium range
3.4b0%Cubic critical, wide range
2.5b90.6%Cubic critical
2.2b69%Quotient of products

localize2.3s (0.4%)

bsearch732.0ms (0.1%)

end1.0ms (0.0%)