Details

sample7.4m (76.8%)

Algorithm
78×intervals
Results
6.0m29210×body10240exit
34.5s43438×body1280valid
12.1s30721×body640valid
7.3s204649×body80valid
4.8s152821×body80nan
4.7s27181×body320valid
3.3s180950×pre80true
3.1s35962×body160valid
790.0ms3100×body2560valid
415.0ms14758×body80overflowed
388.0ms4141×pre10240exit
366.0ms7935×body160nan
99.0ms7928×pre80false
59.0ms205×body5120valid
0.0msbody320nan

prune52.8s (9.2%)

series43.8s (7.6%)

Calls

480 calls:

1.1s
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
808.0ms
(/ (fma (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))))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
694.0ms
(/ (- (- (pow (cos delta) 2) (fma (* (pow (sin phi1) 2) (pow (cos phi1) 2)) (* (pow (cos theta) 2) (pow (sin delta) 2)) (* (pow (sin phi1) 4) (pow (cos delta) 2)))) (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
691.0ms
(/ (* (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)))
571.0ms
(/ (* (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)))

simplify12.7s (2.2%)

Algorithm
221×egg-herbie

regimes10.2s (1.8%)

Accuracy

Total 31.4b remaining (27.7%)

Threshold costs 4.6b (4.1%)

5.7b57.9%Cubic critical, narrow range
5.6b50.5%Quotient of products
4.9b29.3%Cubic critical, medium range
3.3b11.3%Cubic critical, wide range
2.2b0%(- (/ x0 (- 1 x1)) x0)

rewrite9.6s (1.7%)

Algorithm
143×rewrite-expression-head
Calls

480 calls:

580.0ms
(* (+ (sqrt (/ m (/ v (- 1.0 m)))) (sqrt 1.0)) (* (- (sqrt (/ m (/ v (- 1.0 m)))) (sqrt 1.0)) m))
561.0ms
(- (- (+ (/ 1.0 (pow x 2)) (/ 3.0 x))) (* 3.0 (/ 1 (pow x 3))))
326.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
300.0ms
(* (- (sqrt (/ m (/ v (- 1.0 m)))) (sqrt 1.0)) m)
208.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) m)
Rules
9605×*-un-lft-identity
9043×add-sqr-sqrt
8774×times-frac
6784×add-cube-cbrt
4026×prod-diff
2864×add-exp-log
1751×add-cbrt-cube
1577×unpow-prod-down
1067×sqrt-prod
1002×associate-*r*
978×cube-prod
958×pow1
933×prod-exp
913×div-exp
874×difference-of-squares
718×add-log-exp
713×distribute-lft-out--
694×distribute-lft-out
653×associate-/l*
569×associate-/r/
560×fma-neg
554×associate-/r*
551×distribute-rgt-neg-in
537×div-inv
497×sqr-pow
482×log1p-expm1-u
480×expm1-log1p-u
465×cbrt-prod
446×distribute-rgt-in distribute-lft-in
433×associate-*l*
418×distribute-lft-neg-in
415×cbrt-undiv
406×pow-exp
398×cbrt-unprod
304×pow-to-exp
294×flip--
293×flip3--
240×unswap-sqr
237×flip-+
236×flip3-+
197×unpow3 cube-mult
185×fma-def
165×pow-prod-down
163×log-prod
146×unpow2
138×neg-mul-1
126×clear-num frac-2neg
125×associate-*r/
110×sub-neg
109×associate-/l/
102×pow-unpow
97×*-commutative
82×diff-log
78×sin-sum
75×log-pow
73×swap-sqr
69×frac-times
65×associate-*l/
62×1-exp
56×div-sub
55×sqrt-pow1
54×rec-exp
50×sqrt-div exp-prod
49×pow-pow
48×cos-sum
46×pow1/2
42×sum-log
39×pow1/3
35×rem-sqrt-square
33×cbrt-div
32×associate-+l+
31×fma-udef sin-mult log-div
28×+-commutative neg-sub0 cos-mult
24×tan-quot frac-sub
23×associate--l+
21×associate-+r+ pow-prod-up
20×rem-cube-cbrt pow-flip
19×neg-log exp-sum associate-+l- sin-diff
18×pow-sqr rem-log-exp
15×associate--l-
14×cos-diff distribute-rgt-out
13×inv-pow
12×pow-plus distribute-frac-neg
11×associate-+r- pow2 frac-add acos-asin
10×associate--r+
cube-div
un-div-inv
rem-exp-log acos-neg sin-cos-mult
difference-cubes sub-div rem-cbrt-cube expm1-udef distribute-neg-frac
expm1-log1p associate--r- distribute-rgt-neg-out exp-to-pow
hypot-udef asin-acos
exp-diff distribute-lft1-in
expm1-def sqrt-pow2 pow3 distribute-lft-neg-out distribute-neg-in sqr-sin difference-of-sqr-1 rem-square-sqrt hypot-def sqrt-unprod distribute-rgt-out-- sum-cubes

localize2.3s (0.4%)

bsearch2.2s (0.4%)

end1.0ms (0.0%)