Details

Time bar (total: 6.6s)

analyze663.0ms (10%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%93.6%6.4%7
3.1%84.2%12.7%8
12.5%67.1%20.5%9
16%63.5%20.5%10
17.9%57.7%24.4%11
22.6%48.7%28.7%12
28.7%37.8%33.6%13
30.4%35.9%33.7%14
Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.5s (21.9%)

Results
1.0s8256×body128valid
428.0ms3913×body128invalid
Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess25.0ms (0.4%)

Algorithm
2×egg-herbie
Rules
12×*-commutative_binary64
12×associate-/r*_binary64
1×swap-V-l
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03284
15684
26484
044
144
Stop Event
1×unsound
1×saturated
Symmetry

(sort V l)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64
2×associate-/r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11312
21512
Stop Event
1×saturated
Counts
1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
17.5b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶17.5b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓1.4b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
✓4.0b
(/.f64 A (*.f64 V l))
✓16.0b
(sqrt.f64 (/.f64 A (*.f64 V l)))

series89.0ms (1.3%)

Counts
3 → 12
Calls

30 calls:

5.0ms
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
l
inf
5.0ms
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
V
0
4.0ms
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
A
0
4.0ms
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
c0
0
4.0ms
(sqrt.f64 (/.f64 A (*.f64 V l)))
l
inf

rewrite52.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
914×log1p-expm1-u_binary64
914×expm1-log1p-u_binary64
94×egg-rr
93×add-sqr-sqrt_binary64
86×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0928
118528
2247328
Stop Event
1×node limit
Counts
3 → 94

simplify10.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64
2×associate-/r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09144
113144
215144
Stop Event
1×saturated
Counts
106 → 95

prune83.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New831295
Fresh000
Picked011
Done000
Total831396
Error
3.3b
Counts
96 → 13
Alt Table
StatusErrorProgram
37.9b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
18.5b
(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
✓17.5b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
40.6b
(/.f64 (*.f64 (sqrt.f64 A) c0) (sqrt.f64 (*.f64 V l)))
40.1b
(*.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (*.f64 V l)) (sqrt.f64 A))))
40.1b
(*.f64 c0 (*.f64 (sqrt.f64 A) (/.f64 1 (sqrt.f64 (*.f64 V l)))))
47.3b
(sqrt.f64 (*.f64 (/.f64 (/.f64 A V) l) (*.f64 c0 c0)))
19.4b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l))))
33.9b
(*.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (*.f64 l (neg.f64 V)))))
18.9b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 3)
23.5b
(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
54.7b
(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
▶18.5b
(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
Compiler

Compiled 1551 to 700 computations (54.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V))))
✓1.4b
(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
✓5.3b
(/.f64 l (/.f64 A V))
✓16.0b
(sqrt.f64 (/.f64 l (/.f64 A V)))

series227.0ms (3.4%)

Counts
4 → 48
Calls

39 calls:

24.0ms
(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
V
-inf
22.0ms
(/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V))))
V
-inf
21.0ms
(/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V))))
l
-inf
20.0ms
(/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V))))
A
-inf
20.0ms
(*.f64 c0 (/.f64 1 (sqrt.f64 (/.f64 l (/.f64 A V)))))
l
-inf

rewrite74.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
620×log-prod_binary64
198×expm1-udef_binary64
198×log1p-udef_binary64
188×log-pow_binary64
163×log-div_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01140
123337
2316937
Stop Event
1×node limit
Counts
4 → 148

simplify19.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
4×*-commutative_binary64
2×associate-/r*_binary64
2×associate-/l*_binary64
2×associate-/r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010396
116396
220396
323396
424396
Stop Event
1×saturated
Counts
196 → 152

prune151.0ms (2.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1493152
Fresh3811
Picked101
Done011
Total15312165
Error
2.1b
Counts
165 → 12
Alt Table
StatusErrorProgram
37.9b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
▶18.5b
(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
✓17.5b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
40.6b
(/.f64 (*.f64 (sqrt.f64 A) c0) (sqrt.f64 (*.f64 V l)))
40.1b
(*.f64 c0 (*.f64 (sqrt.f64 A) (/.f64 1 (sqrt.f64 (*.f64 V l)))))
54.7b
(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
50.3b
(*.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 l)) (sqrt.f64 (/.f64 (neg.f64 A) V)))))
19.5b
(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))
33.9b
(*.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (*.f64 l (neg.f64 V)))))
18.9b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 3)
23.5b
(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
23.3b
(*.f64 c0 (/.f64 1 (*.f64 (sqrt.f64 l) (sqrt.f64 (/.f64 V A)))))
Compiler

Compiled 2485 to 1076 computations (56.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.5b
(pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2)
✓1.4b
(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
✓5.3b
(/.f64 (/.f64 A V) l)
✓18.0b
(pow.f64 (/.f64 (/.f64 A V) l) 1/4)

series1.3s (19.4%)

Counts
4 → 120
Calls

39 calls:

79.0ms
(pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2)
V
-inf
78.0ms
(pow.f64 (/.f64 (/.f64 A V) l) 1/4)
A
0
72.0ms
(pow.f64 (/.f64 (/.f64 A V) l) 1/4)
A
inf
72.0ms
(pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2)
l
0
72.0ms
(pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2)
l
-inf

rewrite58.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
618×log-prod_binary64
217×expm1-udef_binary64
217×log1p-udef_binary64
198×log-pow_binary64
125×log-div_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01240
126238
2329738
Stop Event
1×node limit
Counts
4 → 122

simplify58.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
312×fma-def_binary64
231×associate-+l+_binary64
210×associate-+r+_binary64
210×distribute-rgt-in_binary64
199×exp-sum_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0761880
11941784
24581652
313771208
Stop Event
1×node limit
Counts
242 → 150

prune107.0ms (1.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1473150
Fresh01010
Picked011
Done011
Total14715162
Error
1.5b
Counts
162 → 15
Alt Table
StatusErrorProgram
37.9b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
✓18.5b
(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
✓17.5b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
50.3b
(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (neg.f64 A) V)) (sqrt.f64 (neg.f64 l))))
23.5b
(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
40.6b
(/.f64 (*.f64 (sqrt.f64 A) c0) (sqrt.f64 (*.f64 V l)))
40.1b
(*.f64 c0 (*.f64 (sqrt.f64 A) (/.f64 1 (sqrt.f64 (*.f64 V l)))))
54.7b
(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
50.3b
(*.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 l)) (sqrt.f64 (/.f64 (neg.f64 A) V)))))
23.6b
(*.f64 c0 (pow.f64 (*.f64 (pow.f64 (/.f64 A V) 1/4) (pow.f64 (/.f64 1 l) 1/4)) 2))
19.5b
(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))
33.9b
(*.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (*.f64 l (neg.f64 V)))))
▶18.9b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 3)
23.3b
(*.f64 c0 (/.f64 1 (*.f64 (sqrt.f64 l) (sqrt.f64 (/.f64 V A)))))
25.7b
(*.f64 c0 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (*.f64 -1 (/.f64 A l))) (log.f64 (/.f64 -1 V))))) 2))
Compiler

Compiled 2756 to 1397 computations (49.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓1.4b
(*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)
5.3b
(/.f64 (/.f64 A V) l)
✓7.5b
(cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0))
✓16.0b
(sqrt.f64 (/.f64 (/.f64 A V) l))

series607.0ms (9.1%)

Counts
3 → 36
Calls

33 calls:

86.0ms
(cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0))
A
inf
86.0ms
(cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0))
A
0
77.0ms
(cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0))
l
0
77.0ms
(cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0))
l
inf
71.0ms
(cbrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0))
V
inf

rewrite51.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
575×log-prod_binary64
189×expm1-udef_binary64
189×log1p-udef_binary64
179×log-pow_binary64
142×log-div_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01035
121035
2287235
Stop Event
1×node limit
Counts
3 → 81

simplify44.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
359×fma-neg_binary64
330×unswap-sqr_binary64
247×div-sub_binary64
218×fma-def_binary64
201×*-commutative_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
052696
1116648
2249648
3621504
41624504
53547504
Stop Event
1×node limit
Counts
117 → 90

prune87.0ms (1.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1401141
Fresh01212
Picked101
Done022
Total14115156
Error
1.5b
Counts
156 → 15
Alt Table
StatusErrorProgram
37.9b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 A V) l)) c0)) 2)
✓18.5b
(*.f64 c0 (pow.f64 (pow.f64 (/.f64 (/.f64 A V) l) 1/4) 2))
✓17.5b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
50.3b
(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (neg.f64 A) V)) (sqrt.f64 (neg.f64 l))))
23.5b
(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
40.6b
(/.f64 (*.f64 (sqrt.f64 A) c0) (sqrt.f64 (*.f64 V l)))
40.1b
(*.f64 c0 (*.f64 (sqrt.f64 A) (/.f64 1 (sqrt.f64 (*.f64 V l)))))
54.7b
(log.f64 (pow.f64 (exp.f64 c0) (sqrt.f64 (/.f64 (/.f64 A V) l))))
50.3b
(*.f64 c0 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 l)) (sqrt.f64 (/.f64 (neg.f64 A) V)))))
23.6b
(*.f64 c0 (pow.f64 (*.f64 (pow.f64 (/.f64 A V) 1/4) (pow.f64 (/.f64 1 l) 1/4)) 2))
24.9b
(pow.f64 (cbrt.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 A V)) c0) (sqrt.f64 l))) 3)
23.3b
(*.f64 c0 (/.f64 1 (*.f64 (sqrt.f64 l) (sqrt.f64 (/.f64 V A)))))
19.5b
(/.f64 c0 (sqrt.f64 (*.f64 V (/.f64 l A))))
33.9b
(*.f64 c0 (/.f64 (sqrt.f64 (neg.f64 A)) (sqrt.f64 (*.f64 l (neg.f64 V)))))
25.7b
(*.f64 c0 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (*.f64 -1 (/.f64 A l))) (log.f64 (/.f64 -1 V))))) 2))
Compiler

Compiled 2527 to 1199 computations (52.6% saved)

regimes1.1s (16.8%)

Accuracy

Total 5.7b remaining (73.9%)

Threshold costs 0b (0%)

Counts
59 → 4
Compiler

Compiled 7528 to 5342 computations (29% saved)

bsearch2.0ms (0%)

Algorithm
3×left-value
Calls

3 calls:

0.0ms
(*.f64 V l)
0.0ms
(*.f64 V l)
0.0ms
(*.f64 V l)
Steps
ItersPointRange
1.3567910861171497e+299
∈ [
1.3567910861171497e+299
, 
6.985848795505889e+302
]
-0.0
∈ [
-0.0
, 
1.9820986054209347e-306
]
-1.417736747975075e-309
∈ [
-1.417736747975075e-309
, 
-5.4258645e-317
]
Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
12×*-commutative_binary64
6×+-commutative_binary64
5×sub-neg_binary64
5×neg-sub0_binary64
4×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045102
161102
272102
379102
483102
584102
Stop Event
1×saturated

end330.0ms (5%)

Stop Event
1×fuel
Compiler

Compiled 508 to 344 computations (32.3% saved)

Profiling

Loading profile data...