Metrics for ln(1 + x)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze1.0ms (0.1%)

Memory

2.4MiB live, 2.4MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
83.3%	62.5%	12.5%	0%	0%	25%	0%	4
91.7%	68.7%	6.2%	0%	0%	25%	0%	5
95.8%	71.8%	3.1%	0%	0%	25%	0%	6
97.9%	73.4%	1.6%	0%	0%	25%	0%	7
99%	74.2%	0.8%	0%	0%	25%	0%	8
99.5%	74.6%	0.4%	0%	0%	25%	0%	9
99.7%	74.8%	0.2%	0%	0%	25%	0%	10
99.9%	74.9%	0.1%	0%	0%	25%	0%	11
99.9%	74.9%	0%	0%	0%	25%	0%	12

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample628.0ms (48.6%)

Memory

-4.8MiB live, 695.9MiB allocated; 216ms collecting garbage

Samples

311.0ms	8 256×	0	valid
0.0ms	2×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 163.0ms

ival-log1p: 162.0ms (99.2% of total)

adjust: 1.0ms (0.6% of total)

Bogosity

preprocess51.0ms (4%)

Memory

-15.4MiB live, 27.1MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	23	13
2	65	13
3	206	13
4	1244	13

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.0%	(log.f64 (+.f64 #s(literal 1 binary64) x))

Compiler

Compiled 8 to 8 computations (0% saved)

series2.0ms (0.2%)

Memory

3.8MiB live, 3.8MiB allocated; 0ms collecting garbage

Counts

4 → 15

Calls

Call 1

Inputs
(log.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x

Outputs
#s(approx (log (+ 1 x)) #s(hole binary64 x))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* -1/2 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* 1/3 x) 1/2))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))))
#s(approx (+ 1 x) #s(hole binary64 1))
#s(approx (+ 1 x) #s(hole binary64 (+ 1 x)))
#s(approx (log (+ 1 x)) #s(hole binary64 (* -1 (log (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (* -1 (log (/ 1 x))) (/ 1 x))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))))
#s(approx (+ 1 x) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((log (+ 1 x)) (+ 1 x) 1 x)
1.0ms	x	@	inf	((log (+ 1 x)) (+ 1 x) 1 x)
0.0ms	x	@	0	((log (+ 1 x)) (+ 1 x) 1 x)

rewrite69.0ms (5.3%)

Memory

9.5MiB live, 101.2MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	252
0	81	227
0	570	192
1	1624	192

Stop Event

1×	saturated
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

19 → 23

Calls

Call 1

Inputs
(log.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (log (+ 1 x)) #s(hole binary64 x))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* -1/2 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* 1/3 x) 1/2))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))))
#s(approx (+ 1 x) #s(hole binary64 1))
#s(approx (+ 1 x) #s(hole binary64 (+ 1 x)))
#s(approx (log (+ 1 x)) #s(hole binary64 (* -1 (log (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (* -1 (log (/ 1 x))) (/ 1 x))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))))
#s(approx (+ 1 x) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))))

Outputs
(log1p.f64 x)
(log.f64 (fabs.f64 (+.f64 x #s(literal 1 binary64))))
(log.f64 (+.f64 x #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (neg.f64 x))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (log (+ 1 x)) x)
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (+ 1 x) #s(literal 1 binary64))
#s(approx (+ 1 x) (+.f64 x #s(literal 1 binary64)))
#s(approx (log (+ 1 x)) (neg.f64 (neg.f64 (log.f64 x))))
#s(approx (log (+ 1 x)) (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (/.f64 #s(literal 1 binary64) x)))
#s(approx (log (+ 1 x)) (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
#s(approx (log (+ 1 x)) (-.f64 (+.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
#s(approx (+ 1 x) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
#s(approx (log (+ 1 x)) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)))) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x)) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)))) #s(literal 0 binary64)))

eval2.0ms (0.1%)

Memory: 4.4MiB live, 4.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 137 to 82 computations (40.1% saved)

prune2.0ms (0.1%)

Memory

3.3MiB live, 3.3MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	16	4	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	5	21

Accuracy

100.0%

Counts

21 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log1p.f64 x)
✓	39.0%	(log.f64 (+.f64 #s(literal 1 binary64) x))
▶	65.5%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
▶	33.8%	#s(approx (log (+ 1 x)) (neg.f64 (neg.f64 (log.f64 x))))
▶	66.8%	#s(approx (log (+ 1 x)) x)

Compiler

Compiled 28 to 28 computations (0% saved)

series75.0ms (5.8%)

Memory

18.9MiB live, 73.7MiB allocated; 8ms collecting garbage

Counts

12 → 23

Calls

Call 1

Inputs
#s(approx (log (+ 1 x)) x)
x
#s(approx (log (+ 1 x)) (neg.f64 (neg.f64 (log.f64 x))))
(neg.f64 (neg.f64 (log.f64 x)))
(neg.f64 (log.f64 x))
(log.f64 x)
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(log1p.f64 x)

Outputs
#s(approx (log (+ 1 x)) #s(hole binary64 x))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* -1/2 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* 1/3 x) 1/2))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))))
#s(approx (neg (neg (log x))) #s(hole binary64 (log x)))
#s(approx (neg (log x)) #s(hole binary64 (* -1 (log x))))
#s(approx (+ (* -1/2 x) 1) #s(hole binary64 1))
#s(approx (+ (* -1/2 x) 1) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* -1 (log (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (* -1 (log (/ 1 x))) (/ 1 x))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))))
#s(approx (neg (log x)) #s(hole binary64 (log (/ 1 x))))
#s(approx (* (+ (* -1/2 x) 1) x) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (* (+ (* -1/2 x) 1) x) #s(hole binary64 (* (pow x 2) (- (/ 1 x) 1/2))))
#s(approx (+ (* -1/2 x) 1) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* -1/2 x) 1) #s(hole binary64 (* x (- (/ 1 x) 1/2))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))))
#s(approx (neg (log x)) #s(hole binary64 (* -1 (+ (log -1) (* -1 (log (/ -1 x)))))))
#s(approx (+ (* -1/2 x) 1) #s(hole binary64 (* -1 (* x (- 1/2 (/ 1 x))))))

Calls

3 calls:

Time	Variable		Point	Expression
51.0ms	x	@	0	((log (+ 1 x)) x (log (+ 1 x)) (neg (neg (log x))) (neg (log x)) (log x) (log (+ 1 x)) (* (+ (* -1/2 x) 1) x) (+ (* -1/2 x) 1) -1/2 1 (log (+ 1 x)))
17.0ms	x	@	-inf	((log (+ 1 x)) x (log (+ 1 x)) (neg (neg (log x))) (neg (log x)) (log x) (log (+ 1 x)) (* (+ (* -1/2 x) 1) x) (+ (* -1/2 x) 1) -1/2 1 (log (+ 1 x)))
7.0ms	x	@	inf	((log (+ 1 x)) x (log (+ 1 x)) (neg (neg (log x))) (neg (log x)) (log x) (log (+ 1 x)) (* (+ (* -1/2 x) 1) x) (+ (* -1/2 x) 1) -1/2 1 (log (+ 1 x)))

Time

Variable

Point

Expression

51.0ms

((log (+ 1 x)) x (log (+ 1 x)) (neg (neg (log x))) (neg (log x)) (log x) (log (+ 1 x)) (* (+ (* -1/2 x) 1) x) (+ (* -1/2 x) 1) -1/2 1 (log (+ 1 x)))

17.0ms

-inf

((log (+ 1 x)) x (log (+ 1 x)) (neg (neg (log x))) (neg (log x)) (log x) (log (+ 1 x)) (* (+ (* -1/2 x) 1) x) (+ (* -1/2 x) 1) -1/2 1 (log (+ 1 x)))

7.0ms

inf

((log (+ 1 x)) x (log (+ 1 x)) (neg (neg (log x))) (neg (log x)) (log x) (log (+ 1 x)) (* (+ (* -1/2 x) 1) x) (+ (* -1/2 x) 1) -1/2 1 (log (+ 1 x)))

rewrite72.0ms (5.6%)

Memory

-6.7MiB live, 36.8MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	356
0	113	309
0	641	301
1	1759	301

Stop Event

1×	saturated
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

35 → 62

Calls

Call 1

Inputs
#s(approx (log (+ 1 x)) x)
x
#s(approx (log (+ 1 x)) (neg.f64 (neg.f64 (log.f64 x))))
(neg.f64 (neg.f64 (log.f64 x)))
(neg.f64 (log.f64 x))
(log.f64 x)
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(log1p.f64 x)
#s(approx (log (+ 1 x)) #s(hole binary64 x))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* -1/2 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* 1/3 x) 1/2))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))))
#s(approx (neg (neg (log x))) #s(hole binary64 (log x)))
#s(approx (neg (log x)) #s(hole binary64 (* -1 (log x))))
#s(approx (+ (* -1/2 x) 1) #s(hole binary64 1))
#s(approx (+ (* -1/2 x) 1) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* -1 (log (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (* -1 (log (/ 1 x))) (/ 1 x))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))))
#s(approx (neg (log x)) #s(hole binary64 (log (/ 1 x))))
#s(approx (* (+ (* -1/2 x) 1) x) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (* (+ (* -1/2 x) 1) x) #s(hole binary64 (* (pow x 2) (- (/ 1 x) 1/2))))
#s(approx (+ (* -1/2 x) 1) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* -1/2 x) 1) #s(hole binary64 (* x (- (/ 1 x) 1/2))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))))
#s(approx (neg (log x)) #s(hole binary64 (* -1 (+ (log -1) (* -1 (log (/ -1 x)))))))
#s(approx (+ (* -1/2 x) 1) #s(hole binary64 (* -1 (* x (- 1/2 (/ 1 x))))))

Outputs
#s(approx (log (+ 1 x)) x)
x
#s(approx (log (+ 1 x)) (log.f64 x))
(*.f64 #s(literal -1 binary64) (neg.f64 (log.f64 x)))
(*.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64))
(neg.f64 (neg.f64 (log.f64 x)))
(log.f64 (fabs.f64 x))
(log.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(log.f64 x)
(*.f64 (log.f64 x) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (log.f64 x))
(neg.f64 (log.f64 x))
(log.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) x)))
(log.f64 (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) (neg.f64 (log.f64 x)))
(*.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64))
(neg.f64 (neg.f64 (log.f64 x)))
(log.f64 (fabs.f64 x))
(log.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(log.f64 x)
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
(*.f64 x (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 #s(literal -1/2 binary64) x)))
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 #s(literal -1/2 binary64) x) x))
(+.f64 (.f64 x #s(literal 1 binary64)) (.f64 x (*.f64 #s(literal -1/2 binary64) x)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(-.f64 #s(literal 1 binary64) (neg.f64 (*.f64 #s(literal -1/2 binary64) x)))
(+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(log1p.f64 x)
(log.f64 (fabs.f64 (+.f64 x #s(literal 1 binary64))))
(log.f64 (+.f64 x #s(literal 1 binary64)))
#s(approx (log (+ 1 x)) x)
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (neg (neg (log x))) (log.f64 x))
#s(approx (neg (log x)) (neg.f64 (log.f64 x)))
#s(approx (+ (* -1/2 x) 1) #s(literal 1 binary64))
#s(approx (+ (* -1/2 x) 1) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
#s(approx (log (+ 1 x)) (log.f64 x))
#s(approx (log (+ 1 x)) (+.f64 (log.f64 x) (/.f64 #s(literal 1 binary64) x)))
#s(approx (log (+ 1 x)) (-.f64 (+.f64 (log.f64 x) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
#s(approx (log (+ 1 x)) (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) x)) (log.f64 x)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
#s(approx (neg (log x)) (neg.f64 (log.f64 x)))
#s(approx (* (+ (* -1/2 x) 1) x) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (* (+ (* -1/2 x) 1) x) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (+ (* -1/2 x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x))
#s(approx (log (+ 1 x)) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)))) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x)) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)))) #s(literal 0 binary64)))
#s(approx (neg (log x)) (neg.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) #s(literal 0 binary64))))
#s(approx (+ (* -1/2 x) 1) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))

eval4.0ms (0.3%)

Memory: 7.3MiB live, 7.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 259 to 166 computations (35.9% saved)

prune2.0ms (0.2%)

Memory

4.1MiB live, 4.1MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	42	5	47

Accuracy

100.0%

Counts

47 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log1p.f64 x)
✓	39.0%	(log.f64 (+.f64 #s(literal 1 binary64) x))
✓	65.5%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
▶	33.8%	#s(approx (log (+ 1 x)) (log.f64 x))
✓	66.8%	#s(approx (log (+ 1 x)) x)

Compiler

Compiled 26 to 26 computations (0% saved)

series69.0ms (5.3%)

Memory

-36.9MiB live, 53.5MiB allocated; 12ms collecting garbage

Counts

3 → 13

Calls

Call 1

Inputs
#s(approx (log (+ 1 x)) (log.f64 x))
(log.f64 x)
x

Outputs
#s(approx (log (+ 1 x)) #s(hole binary64 x))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* -1/2 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* 1/3 x) 1/2))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))))
#s(approx (log x) #s(hole binary64 (log x)))
#s(approx (log (+ 1 x)) #s(hole binary64 (* -1 (log (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (* -1 (log (/ 1 x))) (/ 1 x))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))))

Calls

3 calls:

Time	Variable		Point	Expression
32.0ms	x	@	0	((log (+ 1 x)) (log x) x)
30.0ms	x	@	-inf	((log (+ 1 x)) (log x) x)
6.0ms	x	@	inf	((log (+ 1 x)) (log x) x)

rewrite63.0ms (4.9%)

Memory

30.5MiB live, 80.8MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	235
0	78	210
0	552	175
1	1575	175

Stop Event

1×	saturated
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

16 → 17

Calls

Call 1

Inputs
#s(approx (log (+ 1 x)) (log.f64 x))
(log.f64 x)
x
#s(approx (log (+ 1 x)) #s(hole binary64 x))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* -1/2 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* 1/3 x) 1/2))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))))
#s(approx (log x) #s(hole binary64 (log x)))
#s(approx (log (+ 1 x)) #s(hole binary64 (* -1 (log (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (* -1 (log (/ 1 x))) (/ 1 x))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))))
#s(approx (log (+ 1 x)) #s(hole binary64 (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))))

Outputs
#s(approx (log (+ 1 x)) (log.f64 x))
(log.f64 (fabs.f64 x))
(log.f64 x)
x
#s(approx (log (+ 1 x)) x)
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (log x) (log.f64 x))
#s(approx (log (+ 1 x)) (neg.f64 (neg.f64 (log.f64 x))))
#s(approx (log (+ 1 x)) (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (/.f64 #s(literal 1 binary64) x)))
#s(approx (log (+ 1 x)) (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
#s(approx (log (+ 1 x)) (-.f64 (+.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
#s(approx (log (+ 1 x)) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)))) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x)) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)))) #s(literal 0 binary64)))

eval1.0ms (0.1%)

Memory: 3.0MiB live, 3.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 114 to 68 computations (40.4% saved)

prune2.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	12	0	12
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	12	5	17

Accuracy

100.0%

Counts

17 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log1p.f64 x)
✓	39.0%	(log.f64 (+.f64 #s(literal 1 binary64) x))
✓	65.5%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
✓	33.8%	#s(approx (log (+ 1 x)) (log.f64 x))
✓	66.8%	#s(approx (log (+ 1 x)) x)

Compiler

Compiled 49 to 44 computations (10.2% saved)

regimes29.0ms (2.3%)

Memory

-26.3MiB live, 20.2MiB allocated; 3ms collecting garbage

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (log (+ 1 x)) x)
#s(approx (log (+ 1 x)) (log.f64 x))
#s(approx (log (+ 1 x)) (neg.f64 (neg.f64 (log.f64 x))))
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
(log.f64 (+.f64 #s(literal 1 binary64) x))
(log1p.f64 x)

Outputs
(log1p.f64 x)

Calls

3 calls:

25.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))
2.0ms	x
2.0ms	(+.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
100.0%	1	`(+.f64 #s(literal 1 binary64) x)`
100.0%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
100.0%	1	`x`

Compiler

Compiled 8 to 8 computations (0% saved)

regimes5.0ms (0.4%)

Memory

15.7MiB live, 15.7MiB allocated; 0ms collecting garbage

Counts

5 → 2

Calls

Call 1

Inputs
#s(approx (log (+ 1 x)) x)
#s(approx (log (+ 1 x)) (log.f64 x))
#s(approx (log (+ 1 x)) (neg.f64 (neg.f64 (log.f64 x))))
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
(log.f64 (+.f64 #s(literal 1 binary64) x))

Outputs
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
(log.f64 (+.f64 #s(literal 1 binary64) x))

Calls

3 calls:

2.0ms	x
2.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))
1.0ms	(+.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
99.6%	2	`(+.f64 #s(literal 1 binary64) x)`
99.6%	2	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
99.6%	2	`x`

Compiler

Compiled 8 to 8 computations (0% saved)

regimes5.0ms (0.4%)

Memory

14.8MiB live, 14.8MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (log (+ 1 x)) x)
#s(approx (log (+ 1 x)) (log.f64 x))
#s(approx (log (+ 1 x)) (neg.f64 (neg.f64 (log.f64 x))))
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))

Outputs
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
#s(approx (log (+ 1 x)) (log.f64 x))

Calls

3 calls:

2.0ms	x
1.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))
1.0ms	(+.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
98.3%	2	`(+.f64 #s(literal 1 binary64) x)`
98.3%	2	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
98.3%	2	`x`

Compiler

Compiled 8 to 8 computations (0% saved)

regimes6.0ms (0.4%)

Memory

-31.9MiB live, 14.1MiB allocated; 2ms collecting garbage

Counts

3 → 2

Calls

Call 1

Inputs
#s(approx (log (+ 1 x)) x)
#s(approx (log (+ 1 x)) (log.f64 x))
#s(approx (log (+ 1 x)) (neg.f64 (neg.f64 (log.f64 x))))

Outputs
#s(approx (log (+ 1 x)) x)
#s(approx (log (+ 1 x)) (log.f64 x))

Calls

3 calls:

3.0ms	x
1.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))
1.0ms	(+.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
97.8%	2	`(+.f64 #s(literal 1 binary64) x)`
97.8%	2	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
97.8%	2	`x`

Compiler

Compiled 8 to 8 computations (0% saved)

regimes3.0ms (0.2%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (log (+ 1 x)) x)

Outputs
#s(approx (log (+ 1 x)) x)

Calls

3 calls:

1.0ms	x
1.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))
1.0ms	(+.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
66.8%	1	`(+.f64 #s(literal 1 binary64) x)`
66.8%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
66.8%	1	`x`

Compiler

Compiled 8 to 8 computations (0% saved)

bsearch7.0ms (0.6%)

Memory

21.3MiB live, 21.3MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	6.562341442968174e-7	1.601407375267994e-5

Samples

3.0ms

112×

valid

Compiler

Compiled 98 to 111 computations (-13.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-log1p: 1.0ms (106.9% of total)

adjust: 0.0ms (0% of total)

bsearch17.0ms (1.3%)

Memory

-6.8MiB live, 35.9MiB allocated; 8ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	1.601407375267994e-5	873.2291769086165

Samples

11.0ms

144×

valid

Compiler

Compiled 142 to 159 computations (-12% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-log1p: 2.0ms (127.5% of total)

adjust: 0.0ms (0% of total)

bsearch4.0ms (0.3%)

Memory

8.5MiB live, 8.5MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	1.601407375267994e-5	873.2291769086165

Samples

1.0ms

48×

valid

Compiler

Compiled 106 to 123 computations (-16% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-log1p: 1.0ms (196.1% of total)

adjust: 0.0ms (0% of total)

derivations7.0ms (0.5%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 28 to 24 computations (14.3% saved)

preprocess167.0ms (12.9%)

Memory: -57.9MiB live, 72.3MiB allocated; 177ms collecting garbage
Compiler: Compiled 47 to 37 computations (21.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze1.0ms (0.1%)

sample628.0ms (48.6%)

preprocess51.0ms (4%)

series2.0ms (0.2%)

rewrite69.0ms (5.3%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

series75.0ms (5.8%)

rewrite72.0ms (5.6%)

eval4.0ms (0.3%)

prune2.0ms (0.2%)

series69.0ms (5.3%)

rewrite63.0ms (4.9%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

regimes29.0ms (2.3%)

regimes5.0ms (0.4%)

regimes5.0ms (0.4%)

regimes6.0ms (0.4%)

regimes3.0ms (0.2%)

bsearch7.0ms (0.6%)

bsearch17.0ms (1.3%)

bsearch4.0ms (0.3%)

derivations7.0ms (0.5%)

preprocess167.0ms (12.9%)

end0.0ms (0%)

Profiling