Details

simplify6.9m (46.5%)

sample4.9m (32.9%)

Algorithm
78×intervals
Results
1.6m20426×body10240exit
1.3m43746×body1280valid
28.2s30691×body640valid
19.2s202771×body80valid
13.1s153013×body80nan
11.0s27748×body320valid
8.3s158253×pre80true
7.9s35760×body160valid
3.0s3100×body2560valid
1.1s7869×body160nan
682.0ms4116×pre10240exit
223.0ms8292×pre80false
133.0ms220×body5120valid
1.0ms1×body640nan

prune1.2m (8.2%)

series59.5s (6.7%)

Calls

465 calls:

864.0ms
(sqrt (/ (* (pow (/ 1.0 (+ (exp (- s)) 1.0)) c_p) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) (fma c_p (+ (log 0.5) (* 0.5 t)) 1)))
856.0ms
(sqrt (/ (* (pow (/ 1.0 (+ (exp (- s)) 1.0)) c_p) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) (fma c_p (+ (log 0.5) (* 0.5 t)) 1)))
792.0ms
(/ (* (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)))
751.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
722.0ms
(log (+ 1.0 (sqrt (- 1.0 (* x x)))))

rewrite23.9s (2.7%)

Algorithm
147×rewrite-expression-head
Calls

465 calls:

1.2s
(* (- (/ (+ (* (* 1.0 1.0) m) (- (pow m 3))) (* v (+ 1.0 m))) 1.0) (- 1.0 m))
866.0ms
(* (- (/ (* m (- (* 1.0 1.0) (* m m))) (* (sqrt (* v (+ 1.0 m))) (sqrt (* v (+ 1.0 m))))) 1.0) m)
555.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
517.0ms
(- (/ (+ (* (* 1.0 1.0) m) (- (pow m 3))) (* v (+ 1.0 m))) 1.0)
318.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) (* 2.0 a))
Rules
11261×*-un-lft-identity
8801×add-sqr-sqrt
8624×times-frac
6653×add-cube-cbrt
5188×prod-diff
2578×add-exp-log
1603×add-cbrt-cube
1405×distribute-lft-out
1210×sqrt-prod
950×pow1
936×difference-of-squares
857×prod-exp
853×distribute-lft-out--
796×div-exp
781×associate-/r/
774×log-prod
692×add-log-exp
600×associate-*r*
583×div-inv
555×associate-/l*
546×cbrt-prod
511×exp-sum
469×expm1-log1p-u
467×log1p-expm1-u
454×associate-/r*
423×fma-neg
411×unpow-prod-down
388×associate-*l*
383×cbrt-unprod
361×cube-prod
358×cbrt-undiv
348×distribute-rgt-in distribute-lft-in
339×distribute-rgt-neg-in
333×pow-exp
326×flip-+
325×flip3-+
314×flip--
313×flip3--
247×distribute-lft-neg-in
234×pow-to-exp
201×pow-prod-down
169×fma-def
160×sqr-pow
138×associate-*r/
135×unswap-sqr
124×unpow3
118×clear-num cube-mult frac-2neg
113×sub-neg
105×log-pow
97×associate-/l/
95×sqrt-div
91×*-commutative
84×diff-log
79×neg-mul-1
77×sqrt-pow1
68×associate-+r+
67×associate-*l/
56×frac-times
53×pow1/2 exp-prod
52×1-exp
50×cos-sum
48×div-sub swap-sqr
45×log-div
37×associate--l+
36×cbrt-div
35×sum-log
33×sin-sum
32×fma-udef
31×rem-log-exp
30×rem-sqrt-square rec-exp
27×pow1/3 +-commutative
21×sin-mult
20×pow-prod-up
19×sin-diff
18×pow-unpow neg-sub0
16×frac-sub
15×cube-div
14×sin-cos-mult cos-diff pow-sqr associate-+l+ tan-quot
13×associate--l- associate-+l-
12×neg-log pow-pow
11×cos-mult
10×rem-cube-cbrt acos-asin
9×pow-flip
8×exp-diff frac-add distribute-rgt-out associate--r+
7×inv-pow
6×associate-+r- pow2 pow-plus
5×associate--r-
4×acos-neg log1p-udef sqrt-unprod log1p-expm1 unsub-neg distribute-frac-neg rem-cbrt-cube distribute-rgt-neg-out expm1-udef rem-exp-log
3×distribute-neg-in expm1-log1p asin-acos log-rec
2×e-exp-1 hypot-udef rem-square-sqrt distribute-neg-frac
1×distribute-neg-out difference-cubes distribute-lft-neg-out un-div-inv tanh-undef exp-to-pow tanh-def

regimes17.3s (1.9%)

Accuracy

Total 32.1b remaining (26.5%)

Threshold costs 6.2b (5.1%)

7.6b45.4%Cubic critical, narrow range
3.7b0%Cubic critical, wide range
3.7b0%Quadratic roots, wide range
3.3b85.7%Cubic critical
2.7b75.9%Quotient of products

bsearch5.1s (0.6%)

localize4.0s (0.5%)

end0.0ms (0.0%)