Details

Time bar (total: 10.6s)

analyze2.6s (24.3%)

Algorithm
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)

sample207.0ms (1.9%)

Algorithm
intervals
Results
70.0ms70×body1024valid
20.0ms142×body128valid
17.0ms34×body512valid
3.0ms10×body256valid
0.0msbody128invalid
Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify72.0ms (0.7%)

Algorithm
egg-herbie
Rules
1043×associate-*l/_binary64
692×associate-/l/_binary64
651×associate-/r/_binary64
474×associate-/l*_binary64
398×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01837
13732
28332
320832
474232
5227332
6247432
7287532
8301532
9312632
10323432
11483532
12495332
13488032

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
8.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
8.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Compiler

Compiled 96 to 76 computations (20.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))
0.1b
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))
0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
7.5b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series199.0ms (1.9%)

Counts
4 → 120
Calls

4 calls:

128.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
47.0ms
(/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))
14.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
10.0ms
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))

rewrite23.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube_binary64
32×add-exp-log_binary64
23×pow1_binary64
15×cbrt-unprod_binary64
15×prod-exp_binary64
Counts
4 → 88
Calls

4 calls:

6.0ms
(/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))
5.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
4.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
4.0ms
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))

simplify159.0ms (1.5%)

Algorithm
egg-herbie
Rules
836×fma-def_binary64
375×associate-*l*_binary64
303×fma-neg_binary64
300×associate-*r*_binary64
204×*-commutative_binary64
Counts
208 → 190
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03235501
18544903
233684868
349004868
449814868
549564868

prune225.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1819190
Fresh000
Picked101
Done000
Total1829191
Error
0.0b
Counts
191 → 9
Alt Table
StatusErrorProgram
42.8b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 -2 J)) (*.f64 -2 J)) (*.f64 (*.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
45.9b
U
8.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 U (/.f64 1 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
36.5b
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
22.2b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
9.3b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
8.4b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
8.2b
(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
45.8b
(neg.f64 U)
Compiler

Compiled 6744 to 5059 computations (25% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
0.1b
(/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))
0.1b
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))
7.6b
(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))

series229.0ms (2.2%)

Counts
2 → 72
Calls

2 calls:

135.0ms
(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
94.0ms
(*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
16×pow1_binary64
cbrt-unprod_binary64
prod-exp_binary64
Counts
2 → 44
Calls

2 calls:

6.0ms
(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
3.0ms
(*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

simplify138.0ms (1.3%)

Algorithm
egg-herbie
Rules
421×cancel-sign-sub-inv_binary64
309×fma-neg_binary64
287×associate-*l*_binary64
281×associate-*r*_binary64
213×*-commutative_binary64
Counts
116 → 132
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03205675
18705137
234075125
349845125
449745125

prune297.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2152217
Fresh268
Picked101
Done000
Total2188226
Error
0.0b
Counts
226 → 8
Alt Table
StatusErrorProgram
42.8b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 -2 J)) (*.f64 -2 J)) (*.f64 (*.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
45.9b
U
8.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 U (/.f64 1 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
22.2b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
8.4b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
24.4b
(*.f64 (*.f64 -2 J) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))))) 3)))
45.8b
(neg.f64 U)
34.2b
(*.f64 (*.f64 -2 J) (log1p.f64 (expm1.f64 (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))))
Compiler

Compiled 8320 to 6156 computations (26% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))
0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.2b
(*.f64 U (/.f64 1 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))
7.5b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 U (/.f64 1 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))

series180.0ms (1.7%)

Counts
2 → 72
Calls

2 calls:

137.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 U (/.f64 1 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
43.0ms
(*.f64 U (/.f64 1 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
43×add-exp-log_binary64
25×add-cbrt-cube_binary64
25×prod-exp_binary64
13×cbrt-unprod_binary64
13×pow1_binary64
Counts
2 → 61
Calls

2 calls:

8.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 U (/.f64 1 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
7.0ms
(*.f64 U (/.f64 1 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))

simplify154.0ms (1.4%)

Algorithm
egg-herbie
Rules
705×fma-def_binary64
395×associate-*l*_binary64
320×associate-*r*_binary64
261×cancel-sign-sub-inv_binary64
233×fma-neg_binary64
Counts
133 → 132
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03214382
18223891
232373870
348933870
449813870
549973870
649463870

prune241.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2060206
Fresh077
Picked011
Done000
Total2068214
Error
0.0b
Counts
214 → 8
Alt Table
StatusErrorProgram
42.8b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 -2 J)) (*.f64 -2 J)) (*.f64 (*.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
45.9b
U
8.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 U (/.f64 1 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
22.2b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
8.4b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
24.4b
(*.f64 (*.f64 -2 J) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))))) 3)))
45.8b
(neg.f64 U)
34.2b
(*.f64 (*.f64 -2 J) (log1p.f64 (expm1.f64 (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))))
Compiler

Compiled 7438 to 5680 computations (23.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.2b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
0.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
7.6b
(sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series417.0ms (3.9%)

Counts
3 → 84
Calls

3 calls:

182.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
127.0ms
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
107.0ms
(sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

rewrite24.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
27×pow1_binary64
26×add-cbrt-cube_binary64
26×add-exp-log_binary64
16×cbrt-unprod_binary64
16×prod-exp_binary64
Counts
3 → 70
Calls

3 calls:

8.0ms
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
7.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
1.0ms
(sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

simplify143.0ms (1.3%)

Algorithm
egg-herbie
Rules
483×associate-*l*_binary64
379×associate-*r*_binary64
379×fma-neg_binary64
281×*-commutative_binary64
240×fma-def_binary64
Counts
154 → 169
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03767658
110566900
243216874
349816874

prune361.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2490249
Fresh066
Picked011
Done011
Total2498257
Error
0.0b
Counts
257 → 8
Alt Table
StatusErrorProgram
42.8b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 -2 J)) (*.f64 -2 J)) (*.f64 (*.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
45.9b
U
8.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 U (/.f64 1 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
22.2b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
8.4b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) (sqrt.f64 (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
24.4b
(*.f64 (*.f64 -2 J) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))))) 3)))
45.8b
(neg.f64 U)
34.2b
(*.f64 (*.f64 -2 J) (log1p.f64 (expm1.f64 (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))))
Compiler

Compiled 13822 to 10539 computations (23.8% saved)

regimes930.0ms (8.8%)

Accuracy

Total 8.2b remaining (99.4%)

Threshold costs 0b (0%)

Counts
106 → 2
Compiler

Compiled 17558 to 13938 computations (20.6% saved)

bsearch70.0ms (0.7%)

Steps
ItersRangePoint
9
3.569017089538664e+226
4.1523917369092484e+232
3.616021255462154e+229
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02141
13141
23341
33441
43341

end1.0ms (0%)

Compiler

Compiled 30 to 23 computations (23.3% saved)

sample3.9s (36.5%)

Algorithm
intervals
Results
1.9s2071×body1024valid
722.0ms4402×body128valid
566.0ms1051×body512valid
185.0ms475×body256valid
3.0msbody2048valid
0.0msbody128invalid
Compiler

Compiled 262 to 210 computations (19.8% saved)

Profiling

Loading profile data...