Details

simplify5.9m (45.3%)

sample4.8m (37.2%)

Algorithm
64×intervals
Results
3.1m25174×body10240exit
41.8s28488×body1280valid
14.8s19845×body640valid
10.0s139208×body80valid
9.2s113335×body80nan
5.5s14621×body320valid
3.7s94074×pre80true
3.1s17645×body160valid
1.3s7830×body160nan
592.0ms4154×pre10240exit
544.0ms940×body2560valid
18.0ms7×body5120valid

prune58.4s (7.5%)

series41.6s (5.3%)

Calls

373 calls:

1.7s
(+ (* (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1))))
1.4s
(- (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
670.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
664.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
623.0ms
(/ (* (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)))

rewrite16.8s (2.1%)

Algorithm
117×rewrite-expression-head
Calls

373 calls:

875.0ms
(* (- (/ 1 (/ (/ v (- 1.0 m)) m)) 1.0) m)
494.0ms
(+ (* (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1))))
401.0ms
(log (+ x (+ (- (/ 0.5 x) (/ 0.125 (* x (* x x)))) x)))
359.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) m)
349.0ms
(log (exp (cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
Rules
4451×*-un-lft-identity
4255×times-frac
3906×add-sqr-sqrt
2629×add-cube-cbrt
1919×add-exp-log
1285×add-cbrt-cube
917×pow1
641×prod-exp
610×associate-*r/
583×add-log-exp
554×associate-*l*
547×div-exp
541×difference-of-squares
485×distribute-lft-out--
433×associate-/r*
432×associate-/l*
419×sqrt-prod
403×distribute-lft-out
373×associate-*r*
368×log-prod
311×cbrt-unprod
296×flip--
295×flip3--
267×pow-exp
266×cbrt-undiv associate-/r/
258×frac-times
255×frac-add
254×div-inv
248×flip-+
247×flip3-+
236×associate-*l/
201×pow-prod-down
187×pow-to-exp
172×cos-mult
145×sqrt-div
144×cbrt-prod
135×distribute-rgt-in distribute-lft-in
133×sin-mult
118×exp-prod
108×unswap-sqr
103×log-pow
94×frac-2neg clear-num
93×sub-neg
92×*-commutative
86×associate-+l+
70×diff-log
69×frac-sub
68×associate--l+
67×pow-prod-up
63×swap-sqr
62×unpow-prod-down
59×associate-/l/
49×log-div
48×associate-+r+
42×div-sub
41×sum-log pow-sqr
35×cbrt-div
34×distribute-rgt-out
32×rem-log-exp
27×sqrt-pow1 pow1/2
26×pow1/3 +-commutative
25×cube-unmult
24×pow-plus
23×tan-quot
21×pow2
17×rem-sqrt-square sin-diff
16×sqr-pow cos-diff
15×cos-sum
14×exp-sum associate--r+
13×1-exp rec-exp
9×distribute-lft-neg-in sin-cos-mult difference-cubes distribute-rgt-neg-in associate--r-
8×associate-+r- acos-asin
7×exp-diff
6×distribute-lft1-in pow-unpow exp-to-pow sub-div
5×pow-flip sin-sum associate--l-
4×inv-pow
3×distribute-lft-neg-out distribute-frac-neg pow3 un-div-inv asin-acos neg-mul-1 rem-exp-log acos-neg
2×distribute-rgt-out-- distribute-rgt-neg-out sqrt-unprod pow-pow sqr-cos rem-cbrt-cube
1×unsub-neg tanh-undef tanh-def sum-cubes associate-+l- rem-square-sqrt

regimes13.7s (1.8%)

Accuracy

Total 25.5b remaining (39.2%)

Threshold costs 4.4b (6.8%)

7.6b45%Cubic critical, narrow range
6.8b0%Cubic critical, medium range
3.4b0%Cubic critical, wide range
3.3b70.3%Quotient of products
1.0b0%(- (/ x0 (- 1 x1)) x0)

localize6.1s (0.8%)

bsearch161.0ms (0.0%)

end1.0ms (0.0%)