Details

sample7.5m (47.5%)

Algorithm
78×intervals
Results
4.2m32432×body10240exit
1.3m43940×body1280valid
28.1s30143×body640valid
18.0s203955×body80valid
13.9s151660×body80nan
12.7s27473×body320valid
9.8s36261×body160valid
8.7s169001×pre80true
2.1s3018×body2560valid
1.3s7989×body160nan
575.0ms4073×pre10240exit
548.0ms230×body5120valid
170.0ms8470×pre80false

simplify4.7m (29.9%)

prune1.3m (8.0%)

series1.0m (6.6%)

Calls

512 calls:

927.0ms
(- (log (pow (pow (exp 1) (/ (sqrt 2.0) (pow (+ (exp (* -2.0 x)) 1.0) 2))) (/ (sqrt 2.0) (/ 1 2.0)))) (* 1.0 1.0))
795.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
793.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
729.0ms
(/ (- (log (pow (exp 1) (/ 2.0 (/ (pow (+ (exp (* -2.0 x)) 1.0) 2) 2.0)))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
700.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite57.0s (6.0%)

Algorithm
147×rewrite-expression-head
Calls

512 calls:

22.5s
(- (- (+ (+ (* 1.0 (+ (/ x (pow (sqrt 1.0) 2)) x)) (+ (log (sqrt 1.0)) (log (* 1.0 (sqrt 1.0))))) (* 1.0 (pow x 2))) (* 0.125 (/ (pow x 2) (* (pow (sqrt 1.0) 4) (pow 1.0 2))))) (+ (+ (* (/ 0.5 1.0) (/ (pow x 2) (pow 1.0 2))) (* 0.5 (/ (pow x 2) (pow 1.0 2)))) (* 0.375 (/ (pow x 2) (pow (sqrt 1.0) 4)))))
4.9s
(- (+ (+ (* 1.0 (+ (/ x (pow (sqrt 1.0) 2)) x)) (+ (log (sqrt 1.0)) (log (* 1.0 (sqrt 1.0))))) (* 1.0 (pow x 2))) (* 0.125 (/ (pow x 2) (* (pow (sqrt 1.0) 4) (pow 1.0 2)))))
812.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
768.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
539.0ms
(* (- (/ (* 1 (* (sqrt m) (* (sqrt m) (- 1.0 m)))) v) 1.0) m)
Rules
8097×times-frac
6847×*-un-lft-identity
6707×add-sqr-sqrt
4656×add-cube-cbrt
2893×add-exp-log
1780×add-cbrt-cube
1409×sqrt-prod
1252×associate-*r*
1098×pow1
972×prod-exp
935×add-log-exp
863×flip--
862×flip3--
861×div-exp
817×difference-of-squares
775×associate-*l/
726×associate-/l*
697×unpow-prod-down
634×distribute-lft-out--
584×associate-*l*
567×associate-/r*
551×frac-times
454×sqrt-div
442×cbrt-unprod
437×distribute-lft-out
405×associate-*r/
402×div-inv
393×cbrt-undiv
380×frac-add
377×pow-exp
374×cbrt-prod
306×cube-prod
302×distribute-rgt-neg-in
279×pow-to-exp
250×pow-prod-down
247×log-prod
246×sqr-pow
236×unswap-sqr
226×associate-/r/
220×pow-unpow
193×flip-+
192×cbrt-div flip3-+
130×sum-log
128×diff-log
124×associate-/l/
122×sub-neg
117×distribute-lft-neg-in clear-num frac-2neg
114×*-commutative
83×swap-sqr
72×sqrt-pow1
71×unpow2
64×frac-sub
60×associate-+r+
59×div-sub
58×pow1/3
57×1-exp +-commutative
55×unpow3 log-pow cube-mult
54×log-div
52×pow1/2 exp-prod
47×distribute-rgt-in distribute-lft-in
46×associate--l+
45×rec-exp
39×neg-mul-1
34×neg-sub0
33×distribute-rgt-out
32×associate-+l-
28×pow-prod-up rem-log-exp
27×rem-sqrt-square
22×pow-sqr neg-log
21×associate-+l+ pow-pow
18×associate--l- cos-diff sin-diff
16×tan-quot
15×cos-sum
13×sin-mult exp-sum
11×pow-plus
10×cube-div pow2
rem-cube-cbrt sin-sum rem-cbrt-cube associate--r+
difference-cubes rem-exp-log pow-flip acos-asin distribute-rgt-neg-out
sin-cos-mult un-div-inv inv-pow distribute-frac-neg
associate-+r- cos-mult
sin-neg distribute-lft1-in associate--r-
exp-diff distribute-lft-neg-out tanh-def
acos-neg sqrt-undiv sqrt-unprod
unsub-neg rem-square-sqrt asin-acos
tanh-undef exp-to-pow

regimes12.7s (1.3%)

Accuracy

Total 28.3b remaining (23.6%)

Threshold costs 6.8b (5.7%)

9.0b33.8%Equirectangular approximation to distance on a great circle
4.5b55.8%Quotient of products
3.2b88.6%Cubic critical
3.2b88.8%Quadratic roots, full range
1.6b-73.4%(- (/ x0 (- 1 x1)) x0)

localize4.8s (0.5%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)