Details

Time bar (total: 8.9s)

analyze2.6s (29.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
15.6%84.3%0.1%8
15.6%84.3%0.1%9
15.6%84.3%0.1%10
30.4%69.4%0.1%11
30.4%69.4%0.1%12
30.4%69.4%0.1%13
39.6%60.3%0.1%14
Compiler

Compiled 28 to 23 computations (17.9% saved)

sample4.5s (50.6%)

Alt Table
StatusErrorProgram
▶19.1b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
Results
2.4s2135×body1024valid
1.1s4569×body128valid
730.0ms1048×body512valid
260.0ms501×body256valid
7.0ms3×body2048valid
1.0ms5×body128invalid
Compiler

Compiled 137 to 112 computations (18.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓0.2b
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
✓8.5b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓9.3b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series368.0ms (4.1%)

Counts
4 → 132
Calls

4 calls:

209.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
91.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
58.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
9.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

rewrite89.0ms (1%)

Algorithm
2×batch-egg-rewrite
Rules
614×prod-diff_binary64
180×add-sqr-sqrt_binary64
171×log1p-expm1-u_binary64
171×expm1-log1p-u_binary64
168×add-log-exp_binary64
Counts
4 → 104
Calls

4 calls:

85.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
85.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
85.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
85.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01890
138080
2408780
3513180
000
100

prune235.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2333236
Fresh000
Picked011
Done000
Total2334237
Error
0.0b
Counts
237 → 4
Alt Table
StatusErrorProgram
✓19.1b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
47.4b
(*.f64 -1 U)
▶39.2b
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
47.7b
U
Compiler

Compiled 7687 to 6118 computations (20.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
✓5.4b
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓7.7b
(*.f64 (pow.f64 K 2) J)
✓9.3b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series281.0ms (3.1%)

Counts
4 → 108
Calls

4 calls:

124.0ms
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
92.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
54.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
10.0ms
(*.f64 (pow.f64 K 2) J)

rewrite83.0ms (0.9%)

Algorithm
2×batch-egg-rewrite
Rules
479×prod-diff_binary64
207×add-sqr-sqrt_binary64
202×log1p-expm1-u_binary64
202×expm1-log1p-u_binary64
196×add-log-exp_binary64
Counts
4 → 84
Calls

4 calls:

78.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
78.0ms
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
78.0ms
(*.f64 (pow.f64 K 2) J)
78.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02089
143977
2473477
3564977
000
100

prune243.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1920192
Fresh022
Picked011
Done011
Total1924196
Error
0.0b
Counts
196 → 4
Alt Table
StatusErrorProgram
✓19.1b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
▶47.4b
(*.f64 -1 U)
✓39.2b
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
47.7b
U
Compiler

Compiled 7870 to 6132 computations (22.1% saved)

localize2.0ms (0%)

prune3.0ms (0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked011
Done022
Total044
Error
0.0b
Counts
4 → 4
Alt Table
StatusErrorProgram
✓19.1b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓47.4b
(*.f64 -1 U)
✓39.2b
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
▶47.7b
U
Compiler

Compiled 71 to 57 computations (19.7% saved)

localize1.0ms (0%)

prune4.0ms (0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done033
Total044
Error
0.0b
Counts
4 → 4
Alt Table
StatusErrorProgram
✓19.1b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓47.4b
(*.f64 -1 U)
✓39.2b
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓47.7b
U
Compiler

Compiled 67 to 54 computations (19.4% saved)

regimes338.0ms (3.8%)

Accuracy

Total 9.2b remaining (99.3%)

Threshold costs 0b (0%)

Counts
39 → 2
Compiler

Compiled 5666 to 4548 computations (19.7% saved)

bsearch51.0ms (0.6%)

Steps
ItersRangePoint
5
1.8496974450358866e+172
7.358482293982686e+172
7.165885222303086e+172
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02343
13243
23343
33443
43543
53443

end88.0ms (1%)

Compiler

Compiled 129 to 102 computations (20.9% saved)

Profiling

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