Herbie run

Date:Thursday, May 22nd, 2025
Commit:d1858d41 on fighting-unsoundness
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:128 568.9 MB

Time bar (total: 2.2min)

sample1.6min (69.7%)

Memory
2 018.6MiB live, 87 466.1MiB allocated; 30.7s collecting garbage
Samples
24.7s44 738×2valid
16.0s145 411×0invalid
15.7s96 886×1valid
10.9s6 115×5exit
6.5s85 956×0valid
2.5s3 579×3valid
627.0ms4 256×0exit
139.0ms1 068×1exit
134.0ms139×4exit
16.0ms9×4valid
9.0ms3×3exit
Precisions
Click to see histograms. Total time spent on operations: 1.1min
ival-tan: 11.2s (17.8% of total)
ival-pow: 11.1s (17.6% of total)
adjust: 6.5s (10.2% of total)
ival-mult!: 5.1s (8.1% of total)
ival-cos: 4.7s (7.4% of total)
ival-log: 3.7s (5.9% of total)
ival-div!: 2.9s (4.5% of total)
ival-sin: 2.8s (4.4% of total)
ival-add!: 2.3s (3.6% of total)
ival-expm1: 2.2s (3.5% of total)
ival-sub!: 1.9s (3% of total)
ival-exp: 1.8s (2.9% of total)
ival-fabs: 1.8s (2.8% of total)
ival-sqrt: 1.2s (2% of total)
ival-log1p: 1.2s (1.9% of total)
ival-neg: 738.0ms (1.2% of total)
ival-<: 435.0ms (0.7% of total)
ival-<=: 390.0ms (0.6% of total)
ival-atan: 363.0ms (0.6% of total)
ival-and: 321.0ms (0.5% of total)
ival-cbrt: 304.0ms (0.5% of total)
ival-assert: 65.0ms (0.1% of total)
ival-fmin: 64.0ms (0.1% of total)
ival->: 1.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

rewrite14.3s (10.7%)

Memory
216.9MiB live, 11 754.5MiB allocated; 2.5s collecting garbage
Stop Event
200×iter-limit
110×saturated
95×node-limit
15×unsound
Counts
2 659 → 29 494

eval6.2s (4.6%)

Memory
-125.0MiB live, 7 444.8MiB allocated; 2.5s collecting garbage
Compiler

Compiled 515 086 to 172 357 computations (66.5% saved)

series4.8s (3.6%)

Memory
230.1MiB live, 6 170.3MiB allocated; 1.2s collecting garbage
Stop Event
110×iter-limit
Counts
2 659 → 8 504
Calls

510 calls:

TimeVariablePointExpression
95.0ms
x
@-inf
((- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (neg (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3))) eps) (- (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) 1/6)) eps) (* (+ (pow (tan x) 2) 1) (tan x))) eps) 1) eps) (* (pow (tan x) 2) eps)) (+ (* (+ (* (+ (* (neg (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3))) eps) (- (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) 1/6)) eps) (* (+ (pow (tan x) 2) 1) (tan x))) eps) 1) (+ (* (+ (* (neg (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3))) eps) (- (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) 1/6)) eps) (* (+ (pow (tan x) 2) 1) (tan x))) (+ (* (neg (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3))) eps) (- (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) 1/6)) (neg (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3))) (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3)) (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (+ (pow (tan x) 2) 1) (pow (tan x) 2) (tan x) x 2 1 -1/2 (* 1/6 (pow (tan x) 2)) 1/6 (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) -1/6 (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3) (* (+ (pow (tan x) 2) 1) (tan x)) -1/3 eps (- (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) 1/6) (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2)) (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2) (* (pow (tan x) 2) eps) (- (tan (+ x eps)) (tan x)) (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1 (* 1/3 (pow eps 2))) (* 1/3 (pow eps 2)) 1/3 (pow eps 2) (- (tan (+ (+ (PI) x) eps)) (tan x)) (tan (+ (+ (PI) x) eps)) (+ (+ (PI) x) eps) (+ (PI) x) (PI) (- (tan (+ (+ (+ (PI) x) eps) (PI))) (/ (sin (+ (+ (PI) x) (PI))) (cos x))) (tan (+ (+ (+ (PI) x) eps) (PI))) (+ (+ (+ (PI) x) eps) (PI)) (/ (sin (+ (+ (PI) x) (PI))) (cos x)) (sin (+ (+ (PI) x) (PI))) (+ (+ (PI) x) (PI)) (cos x) (- (tan (+ x eps)) (tan x)) (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) -1 (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (pow (cos x) 2))
79.0ms
n
@-inf
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (* -1 (/ (- (+ (* -1 (log (+ 1 x))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/6 (pow (log (+ 1 x)) 3)) (* -1/6 (pow (log x) 3))) n)) (* 1/2 (pow (log (+ 1 x)) 2))) (* 1/2 (pow (log x) 2))) n))) (* -1 (log x))) n)) -1 (/ (- (+ (* -1 (log (+ 1 x))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/6 (pow (log (+ 1 x)) 3)) (* -1/6 (pow (log x) 3))) n)) (* 1/2 (pow (log (+ 1 x)) 2))) (* 1/2 (pow (log x) 2))) n))) (* -1 (log x))) n) (- (+ (* -1 (log (+ 1 x))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/6 (pow (log (+ 1 x)) 3)) (* -1/6 (pow (log x) 3))) n)) (* 1/2 (pow (log (+ 1 x)) 2))) (* 1/2 (pow (log x) 2))) n))) (* -1 (log x))) (+ (* -1 (log (+ 1 x))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/6 (pow (log (+ 1 x)) 3)) (* -1/6 (pow (log x) 3))) n)) (* 1/2 (pow (log (+ 1 x)) 2))) (* 1/2 (pow (log x) 2))) n))) (log (+ 1 x)) (+ 1 x) 1 x (* -1 (/ (- (+ (* -1 (/ (- (* -1/6 (pow (log (+ 1 x)) 3)) (* -1/6 (pow (log x) 3))) n)) (* 1/2 (pow (log (+ 1 x)) 2))) (* 1/2 (pow (log x) 2))) n)) (/ (- (+ (* -1 (/ (- (* -1/6 (pow (log (+ 1 x)) 3)) (* -1/6 (pow (log x) 3))) n)) (* 1/2 (pow (log (+ 1 x)) 2))) (* 1/2 (pow (log x) 2))) n) (- (+ (* -1 (/ (- (* -1/6 (pow (log (+ 1 x)) 3)) (* -1/6 (pow (log x) 3))) n)) (* 1/2 (pow (log (+ 1 x)) 2))) (* 1/2 (pow (log x) 2))) (+ (* -1 (/ (- (* -1/6 (pow (log (+ 1 x)) 3)) (* -1/6 (pow (log x) 3))) n)) (* 1/2 (pow (log (+ 1 x)) 2))) (/ (- (* -1/6 (pow (log (+ 1 x)) 3)) (* -1/6 (pow (log x) 3))) n) (- (* -1/6 (pow (log (+ 1 x)) 3)) (* -1/6 (pow (log x) 3))) (* -1/6 (pow (log (+ 1 x)) 3)) -1/6 (pow (log (+ 1 x)) 3) 3 (* -1/6 (pow (log x) 3)) (pow (log x) 3) (log x) n (* 1/2 (pow (log (+ 1 x)) 2)) 1/2 (pow (log (+ 1 x)) 2) 2 (* 1/2 (pow (log x) 2)) (pow (log x) 2) (* -1 (log x)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (+ 1 (/ x n)) (/ x n) (pow x (/ 1 n)) (/ 1 n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (+ x 1) (pow x (/ 1 n)) (+ 1 (/ (log x) n)) (/ (log x) n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (+ (log (+ 1 x)) (* 1/2 (/ (pow (log (+ 1 x)) 2) n))) (+ (log x) (* 1/2 (/ (pow (log x) 2) n)))) n) (- (+ (log (+ 1 x)) (* 1/2 (/ (pow (log (+ 1 x)) 2) n))) (+ (log x) (* 1/2 (/ (pow (log x) 2) n)))) (+ (log (+ 1 x)) (* 1/2 (/ (pow (log (+ 1 x)) 2) n))) (* 1/2 (/ (pow (log (+ 1 x)) 2) n)) (/ (pow (log (+ 1 x)) 2) n) (+ (log x) (* 1/2 (/ (pow (log x) 2) n))) (* 1/2 (/ (pow (log x) 2) n)) (/ (pow (log x) 2) n))
75.0ms
n
@-inf
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (log (/ (- x -1) x)) n) (log (/ (- x -1) x)) (/ (- x -1) x) (- x -1) x -1 n (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (/ 1 (* n x)) 1 (* n x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (* (/ 1 n) (log (/ (- x -1) x))) (/ 1 n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (+ (log (+ 1 x)) (* 1/2 (/ (pow (log (+ 1 x)) 2) n))) (+ (log x) (* 1/2 (/ (pow (log x) 2) n)))) n) (* -1 (/ (+ 1 (* -1 (/ (log (/ 1 x)) n))) (* n x))) (/ (+ 1 (* -1 (/ (log (/ 1 x)) n))) (* n x)) (+ 1 (* -1 (/ (log (/ 1 x)) n))) (* -1 (/ (log (/ 1 x)) n)) (/ (log (/ 1 x)) n) (log (/ 1 x)) (/ 1 x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (/ (- (+ 1 (/ 1/3 (pow x 2))) (* 1/2 (/ 1 x))) x) (- (+ 1 (/ 1/3 (pow x 2))) (* 1/2 (/ 1 x))) (+ 1 (/ 1/3 (pow x 2))) (/ 1/3 (pow x 2)) 1/3 (pow x 2) 2 (* 1/2 (/ 1 x)) 1/2)
71.0ms
n
@0
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (log (/ (- x -1) x)) n) (log (/ (- x -1) x)) (/ (- x -1) x) (- x -1) x -1 n (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (/ 1 (* n x)) 1 (* n x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (* (/ 1 n) (log (/ (- x -1) x))) (/ 1 n) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (+ (log (+ 1 x)) (* 1/2 (/ (pow (log (+ 1 x)) 2) n))) (+ (log x) (* 1/2 (/ (pow (log x) 2) n)))) n) (* -1 (/ (+ 1 (* -1 (/ (log (/ 1 x)) n))) (* n x))) (/ (+ 1 (* -1 (/ (log (/ 1 x)) n))) (* n x)) (+ 1 (* -1 (/ (log (/ 1 x)) n))) (* -1 (/ (log (/ 1 x)) n)) (/ (log (/ 1 x)) n) (log (/ 1 x)) (/ 1 x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (- (log (+ 1 x)) (log x)) (/ (- (+ 1 (/ 1/3 (pow x 2))) (* 1/2 (/ 1 x))) x) (- (+ 1 (/ 1/3 (pow x 2))) (* 1/2 (/ 1 x))) (+ 1 (/ 1/3 (pow x 2))) (/ 1/3 (pow x 2)) 1/3 (pow x 2) 2 (* 1/2 (/ 1 x)) 1/2)
68.0ms
x
@0
((- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (neg (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3))) eps) (- (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) 1/6)) eps) (* (+ (pow (tan x) 2) 1) (tan x))) eps) 1) eps) (* (pow (tan x) 2) eps)) (+ (* (+ (* (+ (* (neg (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3))) eps) (- (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) 1/6)) eps) (* (+ (pow (tan x) 2) 1) (tan x))) eps) 1) (+ (* (+ (* (neg (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3))) eps) (- (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) 1/6)) eps) (* (+ (pow (tan x) 2) 1) (tan x))) (+ (* (neg (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3))) eps) (- (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) 1/6)) (neg (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3))) (+ (* (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (tan x)) (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3)) (- (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) -1/6) (- (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (* (+ (pow (tan x) 2) 1) (pow (tan x) 2))) (+ (* (+ (pow (tan x) 2) 1) -1/2) (* 1/6 (pow (tan x) 2))) (+ (pow (tan x) 2) 1) (pow (tan x) 2) (tan x) x 2 1 -1/2 (* 1/6 (pow (tan x) 2)) 1/6 (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) -1/6 (* (* (+ (pow (tan x) 2) 1) (tan x)) -1/3) (* (+ (pow (tan x) 2) 1) (tan x)) -1/3 eps (- (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) 1/6) (+ (* (+ (pow (tan x) 2) 1) (pow (tan x) 2)) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2))) (- (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2)) (* -1/6 (pow (tan x) 2)) (* (+ (pow (tan x) 2) 1) -1/2) (* (pow (tan x) 2) eps) (- (tan (+ x eps)) (tan x)) (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1 (* 1/3 (pow eps 2))) (* 1/3 (pow eps 2)) 1/3 (pow eps 2) (- (tan (+ (+ (PI) x) eps)) (tan x)) (tan (+ (+ (PI) x) eps)) (+ (+ (PI) x) eps) (+ (PI) x) (PI) (- (tan (+ (+ (+ (PI) x) eps) (PI))) (/ (sin (+ (+ (PI) x) (PI))) (cos x))) (tan (+ (+ (+ (PI) x) eps) (PI))) (+ (+ (+ (PI) x) eps) (PI)) (/ (sin (+ (+ (PI) x) (PI))) (cos x)) (sin (+ (+ (PI) x) (PI))) (+ (+ (PI) x) (PI)) (cos x) (- (tan (+ x eps)) (tan x)) (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) -1 (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (pow (cos x) 2))

preprocess4.6s (3.4%)

Memory
-270.9MiB live, 4 037.5MiB allocated; 2.0s collecting garbage
Stop Event
28×node-limit
Compiler

Compiled 5 954 to 4 252 computations (28.6% saved)

regimes3.0s (2.2%)

Memory
-215.1MiB live, 3 856.8MiB allocated; 1.4s collecting garbage
Counts
2 935 → 267
Calls

43 calls:

643.0ms
x
412.0ms
eps
170.0ms
(/.f64 #s(literal 1 binary64) n)
126.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 1 525 to 1 661 computations (-8.9% saved)

derivations2.8s (2.1%)

Memory
-39.1MiB live, 1 940.6MiB allocated; 1.1s collecting garbage
Stop Event
23×fuel
5×done
Compiler

Compiled 2 892 to 1 571 computations (45.7% saved)

prune2.2s (1.6%)

Memory
467.6MiB live, 2 932.0MiB allocated; 396ms collecting garbage
Counts
36 595 → 1 462
Compiler

Compiled 57 254 to 43 794 computations (23.5% saved)

analyze1.9s (1.4%)

Memory
-64.8MiB live, 1 994.7MiB allocated; 1.2s collecting garbage
Algorithm
28×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%61.1%38.9%0%0%0%0
7.4%4.5%56.6%38.9%0%0%0%1
22.3%13.6%47.5%38.9%0%0%0%2
40.2%23.5%34.9%38.9%0%2.7%0%3
53.4%31.1%27.2%38.9%0%2.8%0%4
63%36.3%21.3%38.9%0%3.6%0%5
65.9%37.5%19.4%38.9%0%4.2%0%6
70.4%38.8%16.3%38.9%0%6%0%7
73.6%40.2%14.4%38.9%0%6.5%0%8
76.3%40.9%12.7%38.9%0%7.5%0%9
78.4%41.4%11.4%38.9%0%8.3%0%10
81.1%42.4%9.9%38.9%0%8.8%0%11
82.3%42.7%9.2%38.9%0%9.3%0%12
Compiler

Compiled 483 to 337 computations (30.2% saved)

bsearch802.0ms (0.6%)

Memory
29.1MiB live, 969.4MiB allocated; 184ms collecting garbage
Algorithm
68×binary-search
23×left-value
Stop Event
65×narrow-enough
3×predicate-same
Samples
251.0ms3 623×0valid
87.0ms301×2valid
69.0ms555×1valid
49.0ms744×0invalid
3.0ms35×0exit
0.0ms1×3valid
0.0ms1×1exit
Compiler

Compiled 15 539 to 16 301 computations (-4.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 299.0ms
ival-mult!: 63.0ms (21.1% of total)
ival-pow: 59.0ms (19.8% of total)
adjust: 34.0ms (11.4% of total)
ival-div!: 33.0ms (11.1% of total)
ival-sqrt: 32.0ms (10.7% of total)
ival-sub!: 24.0ms (8% of total)
ival-neg: 23.0ms (7.7% of total)
ival-cos: 12.0ms (4% of total)
ival-add!: 8.0ms (2.7% of total)
ival-cbrt: 6.0ms (2% of total)
ival-log1p: 2.0ms (0.7% of total)
ival-expm1: 2.0ms (0.7% of total)
ival-log: 1.0ms (0.3% of total)

start1.0ms (0%)

Memory
1.9MiB live, 1.9MiB allocated; 0ms collecting garbage

end0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Profiling

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