Details

simplify3.9m (46.8%)

sample2.4m (29.2%)

Algorithm
78×intervals
Results
1.0m18426×body10240exit
34.0s43877×body1280valid
11.0s30495×body640valid
6.8s202184×body80valid
4.6s152280×body80nan
4.3s27365×body320valid
2.9s36049×body160valid
2.4s155798×pre80true
717.0ms3060×body2560valid
383.0ms8047×body160nan
356.0ms4143×pre10240exit
94.0ms8472×pre80false
69.0ms235×body5120valid
2.0msbody640nan

series43.8s (8.8%)

Calls

481 calls:

871.0ms
(cbrt (/ (pow (- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3) (pow (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)))
759.0ms
(pow (- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3)
753.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
723.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
704.0ms
(- (log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3))) (log (- (* 2 (* x x)) (+ 1.0 (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))))

prune43.2s (8.7%)

rewrite16.3s (3.3%)

Algorithm
145×rewrite-expression-head
Calls

481 calls:

717.0ms
(* (/ (pow x 2) (log 2.0)) (- (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2))) 0.25))
463.0ms
(log (exp (- (/ (pow x0 3) (pow (- 1.0 x1) 6)) (pow x0 3))))
372.0ms
(* (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))) (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))))
246.0ms
(* (* 1 (- (/ m (/ v (- 1.0 m))) 1.0)) (- 1.0 m))
245.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
Rules
12610×times-frac
8530×*-un-lft-identity
8456×add-sqr-sqrt
5559×add-cube-cbrt
3052×add-exp-log
1855×add-cbrt-cube
1510×sqrt-prod
1262×difference-of-squares
1104×div-exp
1028×distribute-lft-out--
1004×pow1
974×div-inv
920×prod-exp
772×associate-*r*
735×flip--
734×flip3--
733×add-log-exp
712×associate-/r*
660×associate-/l*
597×associate-*l/
517×associate-*l*
499×cbrt-undiv
469×cbrt-prod
464×unpow-prod-down
436×distribute-lft-out
430×associate-/r/
418×cbrt-unprod
381×log-prod
364×pow-exp
362×sqrt-div
350×frac-times
329×distribute-rgt-neg-in
282×frac-add
263×associate-*r/
261×pow-to-exp
256×cube-prod
199×pow-prod-down sqr-pow
195×log-pow
160×unswap-sqr
153×flip-+
152×flip3-+
142×exp-prod
119×clear-num frac-2neg
118×sub-neg
100×*-commutative
98×associate-/l/
85×1-exp
84×diff-log
64×swap-sqr
63×cbrt-div
60×pow-unpow div-sub
54×unpow3 cube-mult
52×log-div
51×pow1/3
50×rec-exp
47×sum-log
46×distribute-rgt-in distribute-lft-in
44×associate-+r+
37×+-commutative
33×pow1/2 sqrt-pow1
32×rem-log-exp
30×rem-sqrt-square
27×pow-pow
26×unpow2
24×tan-quot
23×exp-sum
22×cos-mult
19×cos-diff neg-sub0 sin-mult
18×pow-prod-up cube-div pow-sqr sin-diff
16×associate-+l-
15×acos-asin frac-sub
14×neg-log distribute-rgt-out associate--l+
13×rem-cube-cbrt pow-plus cos-sum
12×associate-+l+ pow2
11×associate--l- distribute-frac-neg sin-cos-mult
10×associate-+r-
acos-neg
distribute-neg-in associate--r+
exp-diff pow-flip sum-cubes
inv-pow associate--r-
sin-sum
rem-exp-log
distribute-rgt-out-- asin-acos distribute-rgt-neg-out
sub0-neg distribute-lft1-in sub-div sqrt-undiv rem-cbrt-cube
difference-cubes un-div-inv sqrt-unprod sqr-sin tanh-undef tanh-def

regimes9.1s (1.8%)

Accuracy

Total 40.0b remaining (27.2%)

Threshold costs 5.0b (3.4%)

7.4b46%Quadratic roots, narrow range
6.0b14.3%Cubic critical, medium range
5.0b82.4%Cubic critical
4.9b81.9%Quadratic roots, full range
3.8b0%Cubic critical, wide range

bsearch4.6s (0.9%)

localize2.2s (0.4%)

end1.0ms (0.0%)