Metrics for ln(1 + x)

start0.0ms (0%)

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

analyze1.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB 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)

sample530.0ms (39.6%)

Memory

47.1MiB live, 629.8MiB allocated; 289ms collecting garbage

Samples

362.0ms	8 256×	0	valid
0.0ms	1×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 117.0ms

ival-log1p: 115.0ms (98.3% of total)

adjust: 2.0ms (1.7% of total)

Bogosity

preprocess176.0ms (13.1%)

Memory

-12.2MiB live, 39.8MiB allocated; 24ms 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
▶	42.4%	(log.f64 (+.f64 #s(literal 1 binary64) x))

Compiler

Compiled 8 to 8 computations (0% saved)

series2.0ms (0.2%)

Memory

3.7MiB live, 3.7MiB 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)

rewrite148.0ms (11%)

Memory

10.9MiB live, 100.0MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	252
0	81	223
0	575	188

Stop Event

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

Counts

19 → 25

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 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (.f64 #s(literal 1 binary64) x))))
(-.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 (neg.f64 (log.f64 x))) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 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 (neg.f64 (log.f64 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 (neg.f64 (log.f64 x)))) #s(literal 0 binary64)))

eval2.0ms (0.2%)

Memory: 5.6MiB live, 5.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 150 to 87 computations (42% saved)

prune2.0ms (0.1%)

Memory

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

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	18	4	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	5	23

Accuracy

100.0%

Counts

23 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log1p.f64 x)
✓	42.4%	(log.f64 (+.f64 #s(literal 1 binary64) x))
▶	62.6%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
▶	36.7%	#s(approx (log (+ 1 x)) (neg.f64 (neg.f64 (log.f64 x))))
▶	63.8%	#s(approx (log (+ 1 x)) x)

Compiler

Compiled 28 to 28 computations (0% saved)

series131.0ms (9.8%)

Memory

13.6MiB live, 104.2MiB allocated; 30ms 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
90.0ms	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)))
35.0ms	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)))
6.0ms	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

90.0ms

-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)))

35.0ms

((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)))

6.0ms

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)))

rewrite44.0ms (3.3%)

Memory

10.5MiB live, 54.5MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	356
0	113	294
0	651	288

Stop Event

1×	iter-limit
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

35 → 71

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 (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))
(-.f64 #s(literal 0 binary64) (log.f64 x))
(log.f64 (fabs.f64 (/.f64 #s(literal -1 binary64) x)))
(log.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) x)))
(log.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 (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))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) x))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) x)) (.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) x) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))))
(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 (log.f64 x) (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) 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 (log.f64 x) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (log.f64 x) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)) (log.f64 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)) (log.f64 x)) #s(literal 0 binary64)))
#s(approx (neg (log x)) (neg.f64 (+.f64 (log.f64 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: 13.2MiB live, 13.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 310 to 203 computations (34.5% saved)

prune37.0ms (2.7%)

Memory

-40.7MiB live, 6.1MiB allocated; 3ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	50	5	55

Accuracy

100.0%

Counts

55 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log1p.f64 x)
✓	42.4%	(log.f64 (+.f64 #s(literal 1 binary64) x))
✓	62.6%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
▶	36.7%	#s(approx (log (+ 1 x)) (log.f64 x))
✓	63.8%	#s(approx (log (+ 1 x)) x)

Compiler

Compiled 26 to 26 computations (0% saved)

series23.0ms (1.7%)

Memory

2.7MiB live, 48.5MiB allocated; 4ms 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
10.0ms	x	@	-inf	((log (+ 1 x)) (log x) x)
6.0ms	x	@	inf	((log (+ 1 x)) (log x) x)
6.0ms	x	@	0	((log (+ 1 x)) (log x) x)

rewrite124.0ms (9.2%)

Memory

3.2MiB live, 104.3MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	235
0	78	206
0	557	171

Stop Event

1×	iter-limit
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 (neg.f64 (log.f64 x))) #s(literal 0 binary64)))
#s(approx (log (+ 1 x)) (+.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 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 (neg.f64 (log.f64 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 (neg.f64 (log.f64 x)))) #s(literal 0 binary64)))

eval1.0ms (0.1%)

Memory: 2.3MiB live, 2.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 113 to 63 computations (44.2% saved)

prune2.0ms (0.2%)

Memory

3.4MiB live, 3.4MiB 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)
✓	42.4%	(log.f64 (+.f64 #s(literal 1 binary64) x))
✓	62.6%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
✓	36.7%	#s(approx (log (+ 1 x)) (log.f64 x))
✓	63.8%	#s(approx (log (+ 1 x)) x)

Compiler

Compiled 51 to 44 computations (13.7% saved)

regimes6.0ms (0.5%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms 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:

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

9.2MiB live, 9.2MiB 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
99.8%	2	`(+.f64 #s(literal 1 binary64) x)`
99.8%	2	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
99.8%	2	`x`

Compiler

Compiled 8 to 8 computations (0% saved)

regimes11.0ms (0.8%)

Memory

-37.1MiB live, 10.0MiB allocated; 2ms 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:

8.0ms	(+.f64 #s(literal 1 binary64) x)
2.0ms	x
1.0ms	(log.f64 (+.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)

regimes4.0ms (0.3%)

Memory

14.1MiB live, 14.1MiB allocated; 0ms 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:

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

Results

Accuracy	Segments	Branch
97.5%	2	`(+.f64 #s(literal 1 binary64) x)`
97.5%	2	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
97.5%	2	`x`

Compiler

Compiled 8 to 8 computations (0% saved)

regimes3.0ms (0.2%)

Memory

10.2MiB live, 10.2MiB 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
63.8%	1	`(+.f64 #s(literal 1 binary64) x)`
63.8%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
63.8%	1	`x`

Compiler

Compiled 8 to 8 computations (0% saved)

bsearch7.0ms (0.5%)

Memory

18.9MiB live, 18.9MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	4.534106338517671e-7	3.9437126516706144e-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 (104.4% of total)

adjust: 0.0ms (0% of total)

bsearch12.0ms (0.9%)

Memory

-14.6MiB live, 31.4MiB allocated; 4ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	3.9437126516706144e-5	9.057459591099056

Samples

6.0ms

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 (127.2% of total)

adjust: 0.0ms (0% of total)

bsearch3.0ms (0.3%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	3.9437126516706144e-5	9.057459591099056

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

adjust: 0.0ms (0% of total)

ival-log1p: 0.0ms (0% of total)

derivations22.0ms (1.6%)

Memory

-45.2MiB live, 29.5MiB allocated; 21ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 28 to 24 computations (14.3% saved)

preprocess38.0ms (2.8%)

Memory: 29.3MiB live, 120.3MiB allocated; 14ms 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%)

sample530.0ms (39.6%)

preprocess176.0ms (13.1%)

series2.0ms (0.2%)

rewrite148.0ms (11%)

eval2.0ms (0.2%)

prune2.0ms (0.1%)

series131.0ms (9.8%)

rewrite44.0ms (3.3%)

eval4.0ms (0.3%)

prune37.0ms (2.7%)

series23.0ms (1.7%)

rewrite124.0ms (9.2%)

eval1.0ms (0.1%)

prune2.0ms (0.2%)

regimes6.0ms (0.5%)

regimes5.0ms (0.4%)

regimes11.0ms (0.8%)

regimes4.0ms (0.3%)

regimes3.0ms (0.2%)

bsearch7.0ms (0.5%)

bsearch12.0ms (0.9%)

bsearch3.0ms (0.3%)

derivations22.0ms (1.6%)

preprocess38.0ms (2.8%)

end0.0ms (0%)

Profiling