expq2 (section 3.11)

Time bar (total: 1.2s)

start0.0ms (0%)

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

analyze1.0ms (0.1%)

Memory
4.6MiB live, 4.6MiB allocated; 0ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%75.2%24.8%0%0%0%0
0%0%75.2%24.8%0%0%0%1
50%37.6%37.6%24.8%0%0%0%2
75%56.4%18.8%24.8%0%0%0%3
87.5%65.8%9.4%24.8%0%0%0%4
93.8%70.5%4.7%24.8%0%0%0%5
96.9%72.8%2.3%24.8%0%0%0%6
98.4%74%1.2%24.8%0%0%0%7
99.2%74.6%0.6%24.8%0%0%0%8
99.6%74.9%0.3%24.8%0%0%0%9
99.8%75%0.1%24.8%0%0%0%10
99.9%75.1%0.1%24.8%0%0%0%11
100%75.1%0%24.8%0%0%0%12
Compiler

Compiled 11 to 7 computations (36.4% saved)

sample554.0ms (45.9%)

Memory
31.4MiB live, 872.9MiB allocated; 205ms collecting garbage
Samples
371.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 240.0ms
ival-exp: 142.0ms (59.1% of total)
ival-expm1: 53.0ms (22.1% of total)
ival-div!: 43.0ms (17.9% of total)
adjust: 2.0ms (0.8% of total)
Bogosity

preprocess38.0ms (3.2%)

Memory
-16.1MiB live, 32.9MiB allocated; 13ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01026
14325
217625
389419
Stop Event
node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
39.4%
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 12 to 10 computations (16.7% saved)

series3.0ms (0.2%)

Memory
3.7MiB live, 3.7MiB allocated; 0ms collecting garbage
Counts
5 → 15
Calls
Call 1
Inputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(exp.f64 x)
x
(-.f64 (exp.f64 x) #s(literal 1 binary64))
#s(literal 1 binary64)
Outputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx x #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((/ (exp x) (- (exp x) 1)) (exp x) x (- (exp x) 1) 1)
1.0ms
x
@inf
((/ (exp x) (- (exp x) 1)) (exp x) x (- (exp x) 1) 1)
1.0ms
x
@0
((/ (exp x) (- (exp x) 1)) (exp x) x (- (exp x) 1) 1)

rewrite175.0ms (14.5%)

Memory
45.4MiB live, 180.1MiB allocated; 14ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
062203
067203
1443203
22990203
Stop Event
iter-limit
unsound
node-limit
iter-limit
Counts
20 → 10
Calls
Call 1
Inputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(exp.f64 x)
x
(-.f64 (exp.f64 x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx x #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(exp.f64 x)
x
(-.f64 (exp.f64 x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (exp x) #s(literal 1 binary64))
#s(approx x x)
#s(approx (/ (exp x) (- (exp x) 1)) (/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
#s(approx (exp x) (exp.f64 x))
#s(approx (- (exp x) 1) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

eval1.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated; 0ms collecting garbage
Compiler

Compiled 39 to 22 computations (43.6% saved)

prune1.0ms (0.1%)

Memory
1.5MiB live, 1.5MiB allocated; 0ms collecting garbage
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New415
Fresh000
Picked011
Done000
Total426
Accuracy
39.4%
Counts
6 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
39.4%
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
2.3%
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)))
Compiler

Compiled 14 to 11 computations (21.4% saved)

series1.0ms (0.1%)

Memory
1.7MiB live, 1.7MiB allocated; 0ms collecting garbage
Counts
4 → 15
Calls
Call 1
Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
Outputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
((/ (exp x) (- (exp x) 1)) (exp x) 1 (- (exp x) 1))
0.0ms
x
@inf
((/ (exp x) (- (exp x) 1)) (exp x) 1 (- (exp x) 1))
0.0ms
x
@0
((/ (exp x) (- (exp x) 1)) (exp x) 1 (- (exp x) 1))

rewrite163.0ms (13.6%)

Memory
3.4MiB live, 96.4MiB allocated; 15ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061213
063213
1460213
23092213
Stop Event
iter-limit
unsound
node-limit
iter-limit
Counts
19 → 6
Calls
Call 1
Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
Outputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
(-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (exp x) #s(literal 1 binary64))
#s(approx (- (exp x) 1) x)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 9 to 8 computations (11.1% saved)

prune1.0ms (0.1%)

Memory
1.1MiB live, 1.1MiB allocated; 0ms collecting garbage
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New011
Fresh000
Picked101
Done011
Total123
Accuracy
99.7%
Counts
3 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
39.4%
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
64.5%
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) x))
Compiler

Compiled 15 to 13 computations (13.3% saved)

series3.0ms (0.2%)

Memory
-43.7MiB live, 2.1MiB allocated; 3ms collecting garbage
Counts
5 → 15
Calls
Call 1
Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) x))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (exp x) 1) x)
x
Outputs
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((/ (exp x) (- (exp x) 1)) (exp x) 1 (- (exp x) 1) x)
0.0ms
x
@inf
((/ (exp x) (- (exp x) 1)) (exp x) 1 (- (exp x) 1) x)
0.0ms
x
@0
((/ (exp x) (- (exp x) 1)) (exp x) 1 (- (exp x) 1) x)

rewrite207.0ms (17.2%)

Memory
11.5MiB live, 193.8MiB allocated; 61ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
060214
061214
1444214
23009214
Stop Event
iter-limit
unsound
node-limit
iter-limit
Counts
20 → 7
Calls
Call 1
Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) x))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (exp x) 1) x)
x
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* 1/2 x)) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* 1/12 x)))) x)))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (+ 1 (* x (+ 1/2 (* x (+ 1/12 (* -1/720 (pow x 2))))))) x)))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (/ (exp x) (- (exp x) 1)) #s(hole binary64 (/ (exp x) (- (exp x) 1))))
#s(approx (exp x) #s(hole binary64 (exp x)))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
Outputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) x))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (exp x) 1) x)
x
#s(approx (exp x) #s(literal 1 binary64))
#s(approx (- (exp x) 1) x)

eval0.0ms (0%)

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

Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0.1%)

Memory
1.8MiB live, 1.8MiB allocated; 0ms collecting garbage
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Accuracy
99.7%
Counts
2 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
39.4%
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
64.5%
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) x))
Compiler

Compiled 32 to 26 computations (18.8% saved)

regimes4.0ms (0.3%)

Memory
7.9MiB live, 7.9MiB allocated; 0ms collecting garbage
Counts
3 → 2
Calls
Call 1
Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) x))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) x))
Calls

3 calls:

1.0ms
x
1.0ms
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
1.0ms
(exp.f64 x)
Results
AccuracySegmentsBranch
99.3%2(exp.f64 x)
99.4%2(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
99.3%2x
Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes3.0ms (0.3%)

Memory
7.0MiB live, 7.0MiB allocated; 0ms collecting garbage
Accuracy

Total -39.8b remaining (-175.1%)

Threshold costs -39.8b (-175.1%)

Counts
2 → 1
Calls
Call 1
Inputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) x))
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) (-.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(literal 1 binary64)))
Outputs
(/.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (- (exp x) 1) x))
Calls

3 calls:

1.0ms
x
1.0ms
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
1.0ms
(exp.f64 x)
Results
AccuracySegmentsBranch
64.5%1(exp.f64 x)
64.5%1x
64.5%1(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 9 to 8 computations (11.1% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
506471.68562088074
+inf
Compiler

Compiled 9 to 9 computations (0% saved)

derivations32.0ms (2.7%)

Memory
-15.9MiB live, 29.6MiB allocated; 4ms collecting garbage
Stop Event
done
Compiler

Compiled 16 to 14 computations (12.5% saved)

preprocess17.0ms (1.4%)

Memory
32.3MiB live, 32.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 28 to 25 computations (10.7% saved)

end0.0ms (0%)

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

Profiling

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