Herbie run

Date:Tuesday, April 15th, 2025
Commit:5565a39e on main
Seed:2025105
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:146 866.2 MB

Time bar (total: 2.4min)

sample1.5min (63.5%)

Memory
627.2MiB live, 90 012.4MiB allocated; 29.2s collecting garbage
Samples
23.3s44 710×2valid
15.9s97 004×1valid
15.5s146 809×0invalid
10.2s5 905×5exit
6.5s85 840×0valid
2.8s3 610×3valid
344.0ms4 040×0exit
135.0ms1 112×1exit
117.0ms140×4exit
14.0ms2×3exit
4.0ms4×4valid
Precisions
Click to see histograms. Total time spent on operations: 1.0min
ival-tan: 10.6s (17.6% of total)
ival-pow: 10.4s (17.4% of total)
adjust: 6.0s (10% of total)
ival-cos: 4.4s (7.2% of total)
ival-mult!: 4.0s (6.6% of total)
ival-log: 3.4s (5.7% of total)
ival-div!: 2.9s (4.9% of total)
ival-sin: 2.9s (4.8% of total)
ival-sub!: 2.8s (4.7% of total)
ival-add!: 2.4s (3.9% of total)
ival-exp: 2.3s (3.8% of total)
ival-expm1: 1.8s (2.9% of total)
ival-fabs: 1.4s (2.4% of total)
ival-sqrt: 1.3s (2.1% of total)
ival-log1p: 1.2s (2.1% of total)
ival-<=: 475.0ms (0.8% of total)
ival-<: 452.0ms (0.8% of total)
ival-atan: 364.0ms (0.6% of total)
ival-cbrt: 352.0ms (0.6% of total)
ival-and: 336.0ms (0.6% of total)
ival-neg: 307.0ms (0.5% of total)
ival-assert: 70.0ms (0.1% of total)
ival-fmin: 63.0ms (0.1% of total)
ival->: 1.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

rewrite21.4s (14.8%)

Memory
320.9MiB live, 20 865.9MiB allocated; 5.0s collecting garbage
Stop Event
255×iter-limit
107×node-limit
Counts
15 522 → 31 872

derivations6.0s (4.1%)

Memory
-161.8MiB live, 4 816.9MiB allocated; 1.8s collecting garbage
Stop Event
25×fuel
3×done
Compiler

Compiled 7 568 to 1 740 computations (77% saved)

eval5.9s (4.1%)

Memory
260.0MiB live, 7 581.0MiB allocated; 2.6s collecting garbage
Compiler

Compiled 1 555 397 to 169 109 computations (89.1% saved)

explain5.1s (3.5%)

Memory
108.0MiB live, 5 896.7MiB allocated; 1.1s collecting garbage
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64#fcancellation420325
log.f64#fsensitivity7661
sqrt.f64#foflow-rescue4440
/.f64#fu/u4330
+.f64#fcancellation3171
/.f64#fu/n1300
pow.f64(pow.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))sensitivity620
/.f64(/.f64 (*.f64 eps (-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))n/u270
↳(*.f64 b eps)underflow121
↳(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))underflow137
↳(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))underflow121
↳(*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))underflow230
↳(*.f64 a eps)underflow137
-.f64#fnan-rescue270
sqrt.f64#fuflow-rescue180
/.f64(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))n/o40
↳(*.f64 x x)overflow52
exp.f64(exp.f64 (*.f64 a x))sensitivity21
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/o20
↳(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow3
↳(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow3
↳(exp.f64 x)overflow2
↳(-.f64 (exp.f64 x) #s(literal 1 binary64))overflow2
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/n10
↳(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow3
↳(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow3
sin.f64(sin.f64 (+.f64 x eps))sensitivity10
tan.f64(tan.f64 (+.f64 x eps))sensitivity10
Confusion
Predicted +Predicted -
+522015
-1551778
Precision
0.9711627906976744
Recall
0.997134670487106
Confusion?
Predicted +Predicted MaybePredicted -
+5220105
-155201758
Precision?
0.967622571692877
Recall?
0.9990448901623686
Freqs
test
numberfreq
01793
14552
2646
3114
463
Total Confusion?
Predicted +Predicted MaybePredicted -
+2800
-000
Precision?
1.0
Recall?
1.0
Samples
1.4s2 828×2valid
1.1s6 076×1valid
405.0ms5 146×0valid
174.0ms286×3valid
Compiler

Compiled 2 154 to 763 computations (64.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.3s
ival-tan: 474.0ms (20.2% of total)
adjust: 286.0ms (12.2% of total)
ival-cos: 276.0ms (11.8% of total)
ival-log: 239.0ms (10.2% of total)
ival-div!: 186.0ms (7.9% of total)
ival-exp: 132.0ms (5.6% of total)
ival-sin: 131.0ms (5.6% of total)
ival-pow: 110.0ms (4.7% of total)
ival-mult!: 107.0ms (4.6% of total)
ival-sub!: 87.0ms (3.7% of total)
ival-sqrt: 79.0ms (3.4% of total)
ival-neg: 64.0ms (2.7% of total)
ival-log1p: 59.0ms (2.5% of total)
ival-add!: 53.0ms (2.3% of total)
ival-expm1: 24.0ms (1% of total)
ival-atan: 20.0ms (0.9% of total)
ival-cbrt: 16.0ms (0.7% of total)

series3.9s (2.7%)

Memory
262.9MiB live, 5 098.0MiB allocated; 964ms collecting garbage
Counts
2 680 → 12 842
Calls

501 calls:

TimeVariablePointExpression
114.0ms
n
@-inf
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (/ (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))))) n)) (/ (/ (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))))) n) (/ (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))))) (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)) (log (+ 1 x)) x (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n) (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)) (pow (log (+ 1 x)) 3) 3 (pow (log x) 3) (log x) n (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) (pow (log (+ 1 x)) 2) 2 (pow (log x) 2) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (+ 1 (/ x n)) 1 (/ x n) (pow x (/ 1 n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (/ (- (/ (+ (* 1/3 n) (* (* n (* x x)) 1)) (* (* n (* x x)) n)) (/ 1/2 (* n x))) x) (- (/ (+ (* 1/3 n) (* (* n (* x x)) 1)) (* (* n (* x x)) n)) (/ 1/2 (* n x))) (/ (+ (* 1/3 n) (* (* n (* x x)) 1)) (* (* n (* x x)) n)) (+ (* 1/3 n) (* (* n (* x x)) 1)) 1/3 (* (* n (* x x)) 1) (* n (* x x)) (* x x) (* (* n (* x x)) n) (/ 1/2 (* n x)) (* n x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (log (/ (+ 1 x) x)) n) (log (/ (+ 1 x) x)) (/ (+ 1 x) x) (+ 1 x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) n)) (/ (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) n) (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)) (+ (* -1 (/ (+ (* 1/24 (/ (pow (log x) 4) n)) (* 1/6 (pow (log x) 3))) (* n n))) (* -1/2 (/ (pow (log x) 2) n))) (/ (+ (* 1/24 (/ (pow (log x) 4) n)) (* 1/6 (pow (log x) 3))) (* n n)) (+ (* 1/24 (/ (pow (log x) 4) n)) (* 1/6 (pow (log x) 3))) 1/24 (/ (pow (log x) 4) n) (pow (log x) 4) 4 (* 1/6 (pow (log x) 3)) 1/6 (* n n) (* -1/2 (/ (pow (log x) 2) n)) -1/2 (/ (pow (log x) 2) n))
104.0ms
n
@0
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (/ (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))))) n)) (/ (/ (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))))) n) (/ (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))))) (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)) (log (+ 1 x)) x (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n) (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)) (pow (log (+ 1 x)) 3) 3 (pow (log x) 3) (log x) n (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) (pow (log (+ 1 x)) 2) 2 (pow (log x) 2) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (+ 1 (/ x n)) 1 (/ x n) (pow x (/ 1 n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (/ (- (/ (+ (* 1/3 n) (* (* n (* x x)) 1)) (* (* n (* x x)) n)) (/ 1/2 (* n x))) x) (- (/ (+ (* 1/3 n) (* (* n (* x x)) 1)) (* (* n (* x x)) n)) (/ 1/2 (* n x))) (/ (+ (* 1/3 n) (* (* n (* x x)) 1)) (* (* n (* x x)) n)) (+ (* 1/3 n) (* (* n (* x x)) 1)) 1/3 (* (* n (* x x)) 1) (* n (* x x)) (* x x) (* (* n (* x x)) n) (/ 1/2 (* n x)) (* n x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (log (/ (+ 1 x) x)) n) (log (/ (+ 1 x) x)) (/ (+ 1 x) x) (+ 1 x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) n)) (/ (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) n) (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)) (+ (* -1 (/ (+ (* 1/24 (/ (pow (log x) 4) n)) (* 1/6 (pow (log x) 3))) (* n n))) (* -1/2 (/ (pow (log x) 2) n))) (/ (+ (* 1/24 (/ (pow (log x) 4) n)) (* 1/6 (pow (log x) 3))) (* n n)) (+ (* 1/24 (/ (pow (log x) 4) n)) (* 1/6 (pow (log x) 3))) 1/24 (/ (pow (log x) 4) n) (pow (log x) 4) 4 (* 1/6 (pow (log x) 3)) 1/6 (* n n) (* -1/2 (/ (pow (log x) 2) n)) -1/2 (/ (pow (log x) 2) n))
97.0ms
b
@inf
((/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ (+ b a) (* b a)) (+ b a) a (* b a) b (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (/ (+ b a) (* b a)) (+ b a))
89.0ms
x
@-inf
((- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (/ (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))))) n)) (/ (/ (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))))) n) (/ (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))))) (+ (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (pow (log x) 3)) (pow (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) 3) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)) (log (+ 1 x)) x (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n) (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)) (pow (log (+ 1 x)) 3) 3 (pow (log x) 3) (log x) n (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2))) 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)) (pow (log (+ 1 x)) 2) 2 (pow (log x) 2) (+ (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)))) (- (pow (log x) 2) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x))) (* (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (pow (+ x 1) (/ 1 n)) (+ 1 (/ x n)) 1 (/ x n) (pow x (/ 1 n)) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (- (log (+ 1 x)) (log x)) n) (/ (- (/ (+ (* 1/3 n) (* (* n (* x x)) 1)) (* (* n (* x x)) n)) (/ 1/2 (* n x))) x) (- (/ (+ (* 1/3 n) (* (* n (* x x)) 1)) (* (* n (* x x)) n)) (/ 1/2 (* n x))) (/ (+ (* 1/3 n) (* (* n (* x x)) 1)) (* (* n (* x x)) n)) (+ (* 1/3 n) (* (* n (* x x)) 1)) 1/3 (* (* n (* x x)) 1) (* n (* x x)) (* x x) (* (* n (* x x)) n) (/ 1/2 (* n x)) (* n x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (/ (log (/ (+ 1 x) x)) n) (log (/ (+ 1 x) x)) (/ (+ 1 x) x) (+ 1 x) (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))) (neg (/ (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) n)) (/ (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) n) (+ (* -1 (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n))) (log x)) (+ (log (+ 1 x)) (/ (+ (* (/ (+ (* (/ (* 1/24 (- (pow (log (+ 1 x)) 4) (pow (log x) 4))) n) -1) (* -1/6 (- (pow (log (+ 1 x)) 3) (pow (log x) 3)))) n) -1) (* 1/2 (- (pow (log (+ 1 x)) 2) (pow (log x) 2)))) n)) (+ (* -1 (/ (+ (* 1/24 (/ (pow (log x) 4) n)) (* 1/6 (pow (log x) 3))) (* n n))) (* -1/2 (/ (pow (log x) 2) n))) (/ (+ (* 1/24 (/ (pow (log x) 4) n)) (* 1/6 (pow (log x) 3))) (* n n)) (+ (* 1/24 (/ (pow (log x) 4) n)) (* 1/6 (pow (log x) 3))) 1/24 (/ (pow (log x) 4) n) (pow (log x) 4) 4 (* 1/6 (pow (log x) 3)) 1/6 (* n n) (* -1/2 (/ (pow (log x) 2) n)) -1/2 (/ (pow (log x) 2) n))
78.0ms
x
@inf
((/ (- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1)) (* (sqrt x) (sqrt (+ x 1)))) (- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1)) (/ (+ (* -1/8 (pow x -1/2)) (+ (* -5/128 (pow x -5/2)) (+ (* 1/16 (pow x -3/2)) (* 1/2 (sqrt x))))) x) (+ (* -1/8 (pow x -1/2)) (+ (* -5/128 (pow x -5/2)) (+ (* 1/16 (pow x -3/2)) (* 1/2 (sqrt x))))) -1/8 (pow x -1/2) x -1/2 (+ (* -5/128 (pow x -5/2)) (+ (* 1/16 (pow x -3/2)) (* 1/2 (sqrt x)))) -5/128 (pow x -5/2) -5/2 (+ (* 1/16 (pow x -3/2)) (* 1/2 (sqrt x))) 1/16 (pow x -3/2) -3/2 (* 1/2 (sqrt x)) 1/2 (sqrt x) (* (sqrt x) (sqrt (+ x 1))) (sqrt (+ x 1)) (+ x 1) 1 (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (+ (* -1 x) (sqrt x)) x) (+ (* -1 x) (sqrt x)) -1 (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (* -1/2 (- (/ 1 (sqrt x)) (sqrt x))) (* x x)) (* -1/2 (- (/ 1 (sqrt x)) (sqrt x))) (- (/ 1 (sqrt x)) (sqrt x)) (/ 1 (sqrt x)) (* x x) (/ (- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1)) (* (sqrt x) (sqrt (+ x 1)))) (- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1)) (* 1 (sqrt (+ x 1))) (* (sqrt x) 1) (* (sqrt x) (sqrt (+ x 1))) (* (neg x) (+ (* (/ (+ (+ 1/2 (/ 1/16 (* (* x x) 1))) (/ 1/8 (neg x))) x) -1) -1)) (neg x) (+ (* (/ (+ (+ 1/2 (/ 1/16 (* (* x x) 1))) (/ 1/8 (neg x))) x) -1) -1) (/ (+ (+ 1/2 (/ 1/16 (* (* x x) 1))) (/ 1/8 (neg x))) x) (+ (+ 1/2 (/ 1/16 (* (* x x) 1))) (/ 1/8 (neg x))) (+ 1/2 (/ 1/16 (* (* x x) 1))) (/ 1/16 (* (* x x) 1)) (* (* x x) 1) (/ 1/8 (neg x)) 1/8 (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (* -1/2 (- (pow (sqrt x) -1) (sqrt x))) (* x x)) (* -1/2 (- (pow (sqrt x) -1) (sqrt x))) (- (pow (sqrt x) -1) (sqrt x)) (/ (+ (* (pow x 3/2) -1) (sqrt x)) x) (+ (* (pow x 3/2) -1) (sqrt x)) (pow x 3/2) 3/2)

preprocess3.1s (2.1%)

Memory
-406.4MiB live, 2 810.8MiB allocated; 717ms collecting garbage
Stop Event
26×node-limit
2×saturated
Compiler

Compiled 19 354 to 6 084 computations (68.6% saved)

regimes2.4s (1.6%)

Memory
151.8MiB live, 3 789.8MiB allocated; 445ms collecting garbage
Counts
2 763 → 305
Calls

43 calls:

673.0ms
x
220.0ms
eps
112.0ms
a
109.0ms
b_2
87.0ms
(/.f64 #s(literal 1 binary64) n)
Compiler

Compiled 1 884 to 1 792 computations (4.9% saved)

analyze2.0s (1.4%)

Memory
79.2MiB live, 1 653.8MiB allocated; 1.1s 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)

prune1.9s (1.3%)

Memory
-223.3MiB live, 2 939.3MiB allocated; 468ms collecting garbage
Counts
34 305 → 1 433
Compiler

Compiled 79 230 to 41 115 computations (48.1% saved)

bsearch1.2s (0.8%)

Memory
-53.7MiB live, 1 399.0MiB allocated; 238ms collecting garbage
Algorithm
81×binary-search
26×left-value
Stop Event
79×narrow-enough
2×predicate-same
Samples
393.0ms5 230×0valid
112.0ms750×1valid
98.0ms1 257×0invalid
96.0ms398×2valid
2.0ms30×0exit
1.0ms6×3valid
0.0ms1×1exit
Compiler

Compiled 27 889 to 21 065 computations (24.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 447.0ms
ival-mult!: 98.0ms (21.9% of total)
ival-div!: 74.0ms (16.5% of total)
ival-pow: 67.0ms (15% of total)
ival-sub!: 53.0ms (11.9% of total)
ival-sqrt: 48.0ms (10.7% of total)
adjust: 38.0ms (8.5% of total)
ival-neg: 28.0ms (6.3% of total)
ival-add!: 14.0ms (3.1% of total)
ival-cos: 11.0ms (2.5% of total)
ival-expm1: 9.0ms (2% of total)
ival-exp: 4.0ms (0.9% of total)
ival-cbrt: 4.0ms (0.9% of total)

start1.0ms (0%)

Memory
2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

end0.0ms (0%)

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

Profiling

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