Herbie run

Date:Thursday, May 22nd, 2025
Commit:089dffb0 on main
Seed:2025142
Parameters:256 points for 4 iterations
Flags:
reduce:regimesreduce:binary-searchreduce:branch-expressionssetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:proofs
default
Memory:235 551.9 MB

Time bar (total: 3.0min)

sample1.2min (40.3%)

Memory
412.0MiB live, 89 373.9MiB allocated; 33.7s collecting garbage
Samples
29.0s224 625×0valid
10.3s65 899×0invalid
6.5s23 436×1valid
3.7s14 667×1invalid
2.9s6 360×3valid
2.7s9 757×2valid
191.0ms591×2invalid
162.0ms267×0exit
21.0ms14×4valid
1.0ms2×5exit
Precisions
Click to see histograms. Total time spent on operations: 41.5s
ival-mult!: 9.1s (22% of total)
ival-div!: 5.6s (13.6% of total)
adjust: 3.3s (8% of total)
ival-sin: 2.9s (7% of total)
ival-pow: 2.9s (6.9% of total)
ival-pow2: 2.8s (6.8% of total)
ival-sqrt: 2.8s (6.7% of total)
ival-sub!: 2.6s (6.2% of total)
ival-exp: 2.3s (5.5% of total)
ival-add!: 1.9s (4.7% of total)
ival-cos: 1.0s (2.4% of total)
ival-tan: 910.0ms (2.2% of total)
ival-asin: 900.0ms (2.2% of total)
ival-neg: 626.0ms (1.5% of total)
ival-acos: 551.0ms (1.3% of total)
ival-hypot: 382.0ms (0.9% of total)
ival-log: 358.0ms (0.9% of total)
ival-tanu: 271.0ms (0.7% of total)
ival-atan: 138.0ms (0.3% of total)
ival-fabs: 48.0ms (0.1% of total)
ival-<: 1.0ms (0% of total)
ival-and: 1.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-pi: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
Bogosity

rewrite29.9s (16.5%)

Memory
789.4MiB live, 35 874.7MiB allocated; 9.6s collecting garbage
Stop Event
274×iter-limit
128×node-limit
Counts
24 732 → 49 459

regimes16.0s (8.8%)

Memory
22.0MiB live, 24 128.5MiB allocated; 5.1s collecting garbage
Counts
10 678 → 772
Calls

156 calls:

972.0ms
l
650.0ms
t
539.0ms
F
521.0ms
v
438.0ms
k
Compiler

Compiled 11 709 to 11 625 computations (0.7% saved)

series15.8s (8.7%)

Memory
372.0MiB live, 22 870.1MiB allocated; 6.8s collecting garbage
Counts
4 767 → 19 965
Calls

1200 calls:

TimeVariablePointExpression
947.0ms
kx
@inf
((sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) (/ 1 2) 1 2 (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (/ (* 2 l) Om) 2) (/ (* 2 l) Om) (* 2 l) l Om (+ (pow (sin kx) 2) (pow (sin ky) 2)) (+ (* kx kx) (- 1/2 (* 1/2 (cos (* 2 ky))))) kx (- 1/2 (* 1/2 (cos (* 2 ky)))) 1/2 (* 1/2 (cos (* 2 ky))) (cos (* 2 ky)) (* 2 ky) ky (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) (* (+ 1 (/ 1 (sqrt (+ (* (* (* l l) (/ (- 1/2 (* 1/2 (cos (* 2 kx)))) (* Om Om))) 4) 1)))) 1/2) (+ 1 (/ 1 (sqrt (+ (* (* (* l l) (/ (- 1/2 (* 1/2 (cos (* 2 kx)))) (* Om Om))) 4) 1)))) (/ 1 (sqrt (+ (* (* (* l l) (/ (- 1/2 (* 1/2 (cos (* 2 kx)))) (* Om Om))) 4) 1))) (sqrt (+ (* (* (* l l) (/ (- 1/2 (* 1/2 (cos (* 2 kx)))) (* Om Om))) 4) 1)) (+ (* (* (* l l) (/ (- 1/2 (* 1/2 (cos (* 2 kx)))) (* Om Om))) 4) 1) (* (* l l) (/ (- 1/2 (* 1/2 (cos (* 2 kx)))) (* Om Om))) (* l l) (/ (- 1/2 (* 1/2 (cos (* 2 kx)))) (* Om Om)) (- 1/2 (* 1/2 (cos (* 2 kx)))) (* 1/2 (cos (* 2 kx))) (cos (* 2 kx)) (* 2 kx) (* Om Om) 4 (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (+ (pow (sin kx) 2) (pow (sin ky) 2)) (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) (+ (* -1/2 (/ (* (* l l) (+ (- 1/2 (* 1/2 (cos (* 2 ky)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* Om Om))) 1) -1/2 (/ (* (* l l) (+ (- 1/2 (* 1/2 (cos (* 2 ky)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* Om Om)) (* (* l l) (+ (- 1/2 (* 1/2 (cos (* 2 ky)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (- 1/2 (* 1/2 (cos (* 2 ky)))) (- 1/2 (* 1/2 (cos (* 2 kx))))))
663.0ms
k
@inf
((/ 2 (* (* (* (exp (- (* (log t) 3) (* (log l) 2))) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))) 2 (* (* (* (exp (- (* (log t) 3) (* (log l) 2))) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)) (* (* (exp (- (* (log t) 3) (* (log l) 2))) (sin k)) (tan k)) (* (exp (- (* (log t) 3) (* (log l) 2))) (sin k)) (exp (- (* (log t) 3) (* (log l) 2))) (- (* (log t) 3) (* (log l) 2)) (* (log t) 3) (log t) t 3 (* (log l) 2) (log l) l (sin k) k (tan k) (+ (+ 1 (pow (/ k t) 2)) 1) (+ 1 (pow (/ k t) 2)) 1 (pow (/ k t) 2) (/ k t) (/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (/ (* l l) (* (* k k) (* (* t t) t))) (* l l) (* (* k k) (* (* t t) t)) (* k k) (* (* t t) t) (* t t) (/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)) (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (* (/ (pow t 3) (* l l)) (sin k)) (/ (* (* (* t t) t) k) (* l l)) (* (* (* t t) t) k) (/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)) (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (* (/ (pow t 3) (* l l)) (sin k)) (/ (pow t 3) (* l l)) (pow t 3) (sin k) (/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (* (/ (* (cos k) (* l l)) (* (* (+ (* (/ k t) (/ k t)) 2) (- 1/2 (* 1/2 (cos (* 2 k))))) (* (* t t) t))) 2) (/ (* (cos k) (* l l)) (* (* (+ (* (/ k t) (/ k t)) 2) (- 1/2 (* 1/2 (cos (* 2 k))))) (* (* t t) t))) (* (cos k) (* l l)) (cos k) (* (* (+ (* (/ k t) (/ k t)) 2) (- 1/2 (* 1/2 (cos (* 2 k))))) (* (* t t) t)) (* (+ (* (/ k t) (/ k t)) 2) (- 1/2 (* 1/2 (cos (* 2 k))))) (+ (* (/ k t) (/ k t)) 2) (- 1/2 (* 1/2 (cos (* 2 k)))) 1/2 (* 1/2 (cos (* 2 k))) (cos (* 2 k)) (* 2 k))
255.0ms
f
@inf
((neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (/ (log (/ (* 2 (cosh (* (* (PI) f) -1/4))) (* 2 (sinh (* (* (PI) f) 1/4))))) (PI)) -4) (/ (log (/ (* 2 (cosh (* (* (PI) f) -1/4))) (* 2 (sinh (* (* (PI) f) 1/4))))) (PI)) (log (/ (* 2 (cosh (* (* (PI) f) -1/4))) (* 2 (sinh (* (* (PI) f) 1/4))))) (/ (* 2 (cosh (* (* (PI) f) -1/4))) (* 2 (sinh (* (* (PI) f) 1/4)))) (* 2 (cosh (* (* (PI) f) -1/4))) 2 (cosh (* (* (PI) f) -1/4)) (* (* (PI) f) -1/4) (* (PI) f) (PI) f -1/4 (* 2 (sinh (* (* (PI) f) 1/4))) (sinh (* (* (PI) f) 1/4)) (* (* (PI) f) 1/4) 1/4 -4 (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (/ (log (/ 2 (* (* (PI) 1/2) f))) (PI)) -4) (/ (log (/ 2 (* (* (PI) 1/2) f))) (PI)) (log (/ 2 (* (* (PI) 1/2) f))) (/ 2 (* (* (PI) 1/2) f)) (* (* (PI) 1/2) f) (* (PI) 1/2) 1/2 (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))) (/ 1 (/ (PI) 4)) 1 (/ (PI) 4) 4 (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))) (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))) (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))) (neg (* (/ (PI) 4) f)) (* (/ (PI) 4) f) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (neg (log (pow (* 1 (/ (cosh (* f (/ (PI) 4))) (sinh (* f (/ (PI) 4))))) (* (/ 1 (PI)) 4)))) (log (pow (* 1 (/ (cosh (* f (/ (PI) 4))) (sinh (* f (/ (PI) 4))))) (* (/ 1 (PI)) 4))) (pow (* 1 (/ (cosh (* f (/ (PI) 4))) (sinh (* f (/ (PI) 4))))) (* (/ 1 (PI)) 4)) (* 1 (/ (cosh (* f (/ (PI) 4))) (sinh (* f (/ (PI) 4))))) (/ (cosh (* f (/ (PI) 4))) (sinh (* f (/ (PI) 4)))) (cosh (* f (/ (PI) 4))) (* f (/ (PI) 4)) (sinh (* f (/ (PI) 4))) (* (/ 1 (PI)) 4) (/ 1 (PI)) (neg (* (/ 1 (/ (PI) 4)) (/ (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3)) (+ (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))) (+ (* (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4))))))))))) (* (/ 1 (/ (PI) 4)) (/ (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3)) (+ (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))) (+ (* (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))))))) (/ (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3)) (+ (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))) (+ (* (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4))))))))) (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3)) (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (log (* 2 (cosh (* f (/ (PI) 4))))) (* 2 (cosh (* f (/ (PI) 4)))) 3 (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3) (log (* 2 (sinh (* f (/ (PI) 4))))) (* 2 (sinh (* f (/ (PI) 4)))) (+ (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))) (+ (* (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))))) (+ (* (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4))))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))))
244.0ms
f
@-inf
((neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (/ (log (/ (* 2 (cosh (* (* (PI) f) -1/4))) (* 2 (sinh (* (* (PI) f) 1/4))))) (PI)) -4) (/ (log (/ (* 2 (cosh (* (* (PI) f) -1/4))) (* 2 (sinh (* (* (PI) f) 1/4))))) (PI)) (log (/ (* 2 (cosh (* (* (PI) f) -1/4))) (* 2 (sinh (* (* (PI) f) 1/4))))) (/ (* 2 (cosh (* (* (PI) f) -1/4))) (* 2 (sinh (* (* (PI) f) 1/4)))) (* 2 (cosh (* (* (PI) f) -1/4))) 2 (cosh (* (* (PI) f) -1/4)) (* (* (PI) f) -1/4) (* (PI) f) (PI) f -1/4 (* 2 (sinh (* (* (PI) f) 1/4))) (sinh (* (* (PI) f) 1/4)) (* (* (PI) f) 1/4) 1/4 -4 (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (/ (log (/ 2 (* (* (PI) 1/2) f))) (PI)) -4) (/ (log (/ 2 (* (* (PI) 1/2) f))) (PI)) (log (/ 2 (* (* (PI) 1/2) f))) (/ 2 (* (* (PI) 1/2) f)) (* (* (PI) 1/2) f) (* (PI) 1/2) 1/2 (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))) (/ 1 (/ (PI) 4)) 1 (/ (PI) 4) 4 (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))) (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))) (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))) (neg (* (/ (PI) 4) f)) (* (/ (PI) 4) f) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (neg (log (pow (* 1 (/ (cosh (* f (/ (PI) 4))) (sinh (* f (/ (PI) 4))))) (* (/ 1 (PI)) 4)))) (log (pow (* 1 (/ (cosh (* f (/ (PI) 4))) (sinh (* f (/ (PI) 4))))) (* (/ 1 (PI)) 4))) (pow (* 1 (/ (cosh (* f (/ (PI) 4))) (sinh (* f (/ (PI) 4))))) (* (/ 1 (PI)) 4)) (* 1 (/ (cosh (* f (/ (PI) 4))) (sinh (* f (/ (PI) 4))))) (/ (cosh (* f (/ (PI) 4))) (sinh (* f (/ (PI) 4)))) (cosh (* f (/ (PI) 4))) (* f (/ (PI) 4)) (sinh (* f (/ (PI) 4))) (* (/ 1 (PI)) 4) (/ 1 (PI)) (neg (* (/ 1 (/ (PI) 4)) (/ (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3)) (+ (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))) (+ (* (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4))))))))))) (* (/ 1 (/ (PI) 4)) (/ (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3)) (+ (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))) (+ (* (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))))))) (/ (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3)) (+ (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))) (+ (* (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4))))))))) (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3)) (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (log (* 2 (cosh (* f (/ (PI) 4))))) (* 2 (cosh (* f (/ (PI) 4)))) 3 (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3) (log (* 2 (sinh (* f (/ (PI) 4))))) (* 2 (sinh (* f (/ (PI) 4)))) (+ (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))) (+ (* (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))))) (+ (* (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4))))))) (* (log (* 2 (cosh (* f (/ (PI) 4))))) (log (* 2 (sinh (* f (/ (PI) 4)))))))
229.0ms
f
@0
((neg (/ (* (/ 4 (PI)) (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3))) (+ (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 2) (* (log (* 2 (sinh (* f (/ (PI) 4))))) (+ (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))))))) (/ (* (/ 4 (PI)) (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3))) (+ (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 2) (* (log (* 2 (sinh (* f (/ (PI) 4))))) (+ (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4))))))))) (* (/ 4 (PI)) (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3))) (/ 4 (PI)) 4 (PI) (- (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3)) (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 3) (log (* 2 (cosh (* f (/ (PI) 4))))) (* 2 (cosh (* f (/ (PI) 4)))) 2 (cosh (* f (/ (PI) 4))) (* f (/ (PI) 4)) f (/ (PI) 4) 3 (pow (log (* 2 (sinh (* f (/ (PI) 4))))) 3) (log (* 2 (sinh (* f (/ (PI) 4))))) (* 2 (sinh (* f (/ (PI) 4)))) (sinh (* f (/ (PI) 4))) (+ (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 2) (* (log (* 2 (sinh (* f (/ (PI) 4))))) (+ (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))))) (pow (log (* 2 (cosh (* f (/ (PI) 4))))) 2) (* (log (* 2 (sinh (* f (/ (PI) 4))))) (+ (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4))))))) (+ (log (* 2 (sinh (* f (/ (PI) 4))))) (log (* 2 (cosh (* f (/ (PI) 4)))))) (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (/ (log (/ 2 (* (* (PI) 1/2) f))) (PI)) -4) (/ (log (/ 2 (* (* (PI) 1/2) f))) (PI)) (log (/ 2 (* (* (PI) 1/2) f))) (+ (log (/ 4 (PI))) (neg (log f))) (log (/ 4 (PI))) (neg (log f)) (log f) -4 (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (/ (* (log (/ (cosh (* (* (PI) f) -1/4)) (sinh (* (* (PI) f) 1/4)))) -4) (PI)) (* (log (/ (cosh (* (* (PI) f) -1/4)) (sinh (* (* (PI) f) 1/4)))) -4) (log (/ (cosh (* (* (PI) f) -1/4)) (sinh (* (* (PI) f) 1/4)))) (/ (cosh (* (* (PI) f) -1/4)) (sinh (* (* (PI) f) 1/4))) (cosh (* (* (PI) f) -1/4)) (+ (* (* 1/32 (* f f)) (* (PI) (PI))) 1) (* 1/32 (* f f)) 1/32 (* f f) (* (PI) (PI)) 1 (sinh (* (* (PI) f) 1/4)) (* (* (PI) f) 1/4) (* (PI) f) 1/4 (* (/ 4 (PI)) (neg (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f)))) (- (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f)))))))) (neg (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f)))) (- (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f))))))) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f)))) (- (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f)))))) (/ (+ (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f)))) (- (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f))))) (+ (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f)))) (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f))) (* (/ (PI) 4) (neg f)) (neg f) (- (exp (* (/ (PI) 4) f)) (exp (* (/ (PI) 4) (neg f)))) (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))))) (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))) (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))))) (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))) (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (exp (* (/ (PI) 4) f)) (* (/ (PI) 4) f) (exp (neg (* (/ (PI) 4) f))) (neg (* (/ (PI) 4) f)) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (* (- (+ (* (- (+ (* (* (pow (PI) 5) 1/61440) (* f f)) (* (* (* (PI) (PI)) (PI)) 1/384)) (* -1/384 (* (* (PI) (PI)) (PI)))) (* f f)) (* 1/4 (PI))) (* -1/4 (PI))) f) (- (+ (* (- (+ (* (* (pow (PI) 5) 1/61440) (* f f)) (* (* (* (PI) (PI)) (PI)) 1/384)) (* -1/384 (* (* (PI) (PI)) (PI)))) (* f f)) (* 1/4 (PI))) (* -1/4 (PI))) (+ (* (- (+ (* (* (pow (PI) 5) 1/61440) (* f f)) (* (* (* (PI) (PI)) (PI)) 1/384)) (* -1/384 (* (* (PI) (PI)) (PI)))) (* f f)) (* 1/4 (PI))) (- (+ (* (* (pow (PI) 5) 1/61440) (* f f)) (* (* (* (PI) (PI)) (PI)) 1/384)) (* -1/384 (* (* (PI) (PI)) (PI)))) (+ (* (* (pow (PI) 5) 1/61440) (* f f)) (* (* (* (PI) (PI)) (PI)) 1/384)) (* (pow (PI) 5) 1/61440) (pow (PI) 5) 5 1/61440 (* (* (* (PI) (PI)) (PI)) 1/384) (* (* (PI) (PI)) (PI)) 1/384 (* -1/384 (* (* (PI) (PI)) (PI))) -1/384 (* 1/4 (PI)) (* -1/4 (PI)) -1/4)

derivations11.9s (6.6%)

Memory
-15.4MiB live, 11 465.3MiB allocated; 2.4s collecting garbage
Stop Event
32×fuel
Compiler

Compiled 36 660 to 4 164 computations (88.6% saved)

preprocess9.3s (5.1%)

Memory
-129.3MiB live, 14 039.5MiB allocated; 2.9s collecting garbage
Stop Event
31×node-limit
1×saturated
Compiler

Compiled 221 401 to 86 791 computations (60.8% saved)

eval8.2s (4.5%)

Memory
202.4MiB live, 13 008.4MiB allocated; 2.6s collecting garbage
Compiler

Compiled 3 090 275 to 283 797 computations (90.8% saved)

analyze8.1s (4.5%)

Memory
214.7MiB live, 10 505.9MiB allocated; 2.8s collecting garbage
Algorithm
32×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%98.2%1.8%0%0%0%0
22.2%21.8%76.4%1.8%0%0%0%1
22.6%21.8%74.8%1.8%0%1.6%0%2
28.6%26.5%66.3%1.8%0%5.5%0%3
32.6%29.6%61.2%1.8%0%7.4%0%4
35.8%32.3%58%1.8%0%8%0%5
40.1%36.1%54%1.8%0%8.1%0%6
45.5%40.6%48.7%1.8%0%8.9%0%7
47.9%42.1%45.8%1.8%0%10.3%0%8
51%44.6%43%1.8%0%10.6%0%9
52.1%45.5%41.8%1.8%0%11%0%10
53.9%46.7%40%1.8%0%11.5%0%11
55.6%47.9%38.2%1.8%0%12.1%0%12
Compiler

Compiled 798 to 574 computations (28.1% saved)

prune4.9s (2.7%)

Memory
-179.0MiB live, 8 517.9MiB allocated; 1.5s collecting garbage
Counts
51 262 → 3 101
Compiler

Compiled 313 781 to 152 558 computations (51.4% saved)

bsearch4.0s (2.2%)

Memory
279.2MiB live, 5 763.8MiB allocated; 1.3s collecting garbage
Algorithm
235×binary-search
175×left-value
Stop Event
224×narrow-enough
8×predicate-same
3×predicate-failed
Samples
2.0s12 694×0valid
170.0ms1 811×0invalid
111.0ms734×1valid
64.0ms208×2valid
51.0ms141×1invalid
39.0ms139×3valid
2.0ms8×2invalid
0.0ms1×4valid
Compiler

Compiled 157 776 to 106 680 computations (32.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.8s
ival-mult!: 410.0ms (22.9% of total)
ival-div!: 308.0ms (17.2% of total)
ival-pow: 229.0ms (12.8% of total)
ival-sin: 205.0ms (11.4% of total)
ival-tan: 173.0ms (9.6% of total)
ival-pow2: 121.0ms (6.7% of total)
ival-add!: 110.0ms (6.1% of total)
ival-neg: 56.0ms (3.1% of total)
adjust: 52.0ms (2.9% of total)
ival-sqrt: 40.0ms (2.2% of total)
ival-sub!: 39.0ms (2.2% of total)
ival-exp: 20.0ms (1.1% of total)
ival-hypot: 14.0ms (0.8% of total)
ival-tanu: 9.0ms (0.5% of total)
ival-cos: 3.0ms (0.2% of total)
ival-fabs: 1.0ms (0.1% of total)
ival-log: 1.0ms (0.1% of total)
ival-pi: 0.0ms (0% of total)
ival-atan: 0.0ms (0% of total)

start11.0ms (0%)

Memory
-40.8MiB live, 3.4MiB allocated; 9ms collecting garbage

end0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Profiling

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