Details

Time bar (total: 11.6s)

analyze2.9s (24.8%)

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)

sample220.0ms (1.9%)

Algorithm
intervals
Results
56.0ms57×body1024valid
26.0ms147×body128valid
22.0ms38×body512valid
5.0ms14×body256valid
Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify95.0ms (0.8%)

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
7.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
7.1b
(*.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)

localize14.0ms (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)))
6.7b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series284.0ms (2.4%)

Counts
4 → 120
Calls

4 calls:

135.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
86.0ms
(/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))
52.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
11.0ms
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))

rewrite25.0ms (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 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
5.0ms
(/.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))

simplify181.0ms (1.6%)

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

prune241.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1837190
Fresh000
Picked101
Done000
Total1847191
Error
0.0b
Counts
191 → 7
Alt Table
StatusErrorProgram
7.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 (/.f64 1 (cos.f64 (/.f64 K 2))) (/.f64 U (*.f64 J 2)))))
48.1b
U
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)))))
7.6b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
34.6b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
41.9b
(*.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)))))
47.3b
(neg.f64 U)
Compiler

Compiled 6618 to 4961 computations (25% 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)))
0.1b
(/.f64 1 (cos.f64 (/.f64 K 2)))
0.1b
(*.f64 (/.f64 1 (cos.f64 (/.f64 K 2))) (/.f64 U (*.f64 J 2)))
6.7b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 (/.f64 1 (cos.f64 (/.f64 K 2))) (/.f64 U (*.f64 J 2)))))

series196.0ms (1.7%)

Counts
3 → 84
Calls

3 calls:

140.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 (/.f64 1 (cos.f64 (/.f64 K 2))) (/.f64 U (*.f64 J 2)))))
48.0ms
(*.f64 (/.f64 1 (cos.f64 (/.f64 K 2))) (/.f64 U (*.f64 J 2)))
7.0ms
(/.f64 1 (cos.f64 (/.f64 K 2)))

rewrite27.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
55×add-exp-log_binary64
35×add-cbrt-cube_binary64
28×add-sqr-sqrt_binary64
23×times-frac_binary64
22×*-un-lft-identity_binary64
Counts
3 → 111
Calls

3 calls:

9.0ms
(*.f64 (/.f64 1 (cos.f64 (/.f64 K 2))) (/.f64 U (*.f64 J 2)))
6.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 (/.f64 1 (cos.f64 (/.f64 K 2))) (/.f64 U (*.f64 J 2)))))
2.0ms
(/.f64 1 (cos.f64 (/.f64 K 2)))

simplify182.0ms (1.6%)

Algorithm
egg-herbie
Rules
781×fma-def_binary64
386×associate-*l*_binary64
320×associate-*r*_binary64
236×fma-neg_binary64
235×*-commutative_binary64
Counts
195 → 207
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03595402
19164795
235954772
349654772
449984772
549554772

prune296.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2431244
Fresh156
Picked011
Done000
Total2447251
Error
0.0b
Counts
251 → 7
Alt Table
StatusErrorProgram
7.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 (/.f64 1 (cos.f64 (/.f64 K 2))) (/.f64 U (*.f64 J 2)))))
48.1b
U
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)))))
7.6b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
34.6b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
47.3b
(neg.f64 U)
42.5b
(cbrt.f64 (pow.f64 (*.f64 (*.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 (*.f64 1/2 (/.f64 U J)) (cos.f64 (/.f64 K 2))))) 3))
Compiler

Compiled 8554 to 6556 computations (23.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
0.3b
(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
0.3b
(cbrt.f64 (cos.f64 (/.f64 K 2)))
6.7b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series587.0ms (5%)

Counts
4 → 84
Calls

4 calls:

241.0ms
(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
188.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))
145.0ms
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
13.0ms
(*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))

rewrite44.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
54×pow1_binary64
49×add-exp-log_binary64
34×pow-prod-down_binary64
33×cbrt-unprod_binary64
33×prod-exp_binary64
Counts
4 → 119
Calls

4 calls:

14.0ms
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
11.0ms
(*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
5.0ms
(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
1.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify160.0ms (1.4%)

Algorithm
egg-herbie
Rules
852×fma-def_binary64
491×associate-*l*_binary64
370×associate-*r*_binary64
270×fma-neg_binary64
205×*-commutative_binary64
Counts
203 → 214
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03365881
18365091
233324908
349614908
449954908

prune401.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2584262
Fresh235
Picked101
Done011
Total2618269
Error
0.0b
Counts
269 → 8
Alt Table
StatusErrorProgram
7.3b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
7.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 (/.f64 1 (cos.f64 (/.f64 K 2))) (/.f64 U (*.f64 J 2)))))
48.1b
U
7.4b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (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)))))
7.7b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
47.3b
(neg.f64 U)
7.6b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (expm1.f64 (log1p.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Compiler

Compiled 11322 to 8929 computations (21.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 (*.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2))))
0.3b
(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)
0.3b
(cbrt.f64 (cos.f64 (/.f64 K 2)))
6.7b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series157.0ms (1.3%)

Counts
3 → 64
Calls

3 calls:

140.0ms
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
11.0ms
(*.f64 (*.f64 (*.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2))))
5.0ms
(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)

rewrite35.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
83×add-exp-log_binary64
64×prod-exp_binary64
28×cbrt-unprod_binary64
28×add-cbrt-cube_binary64
17×pow-exp_binary64
Counts
3 → 88
Calls

3 calls:

12.0ms
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
9.0ms
(*.f64 (*.f64 (*.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2))))
2.0ms
(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)

simplify215.0ms (1.9%)

Algorithm
egg-herbie
Rules
834×fma-def_binary64
452×associate-*l*_binary64
308×associate-*r*_binary64
281×fma-neg_binary64
236×unswap-sqr_binary64
Counts
152 → 161
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03245836
18075096
231245058
348805008
449555008
549905008
649435008

prune261.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1823185
Fresh246
Picked101
Done011
Total1858193
Error
0.0b
Counts
193 → 8
Alt Table
StatusErrorProgram
7.4b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
7.4b
(*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
7.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (*.f64 (/.f64 1 (cos.f64 (/.f64 K 2))) (/.f64 U (*.f64 J 2)))))
48.1b
U
7.3b
(*.f64 (*.f64 (*.f64 -2 J) (*.f64 (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
7.3b
(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 6)) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (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)))))
47.3b
(neg.f64 U)
Compiler

Compiled 7869 to 6213 computations (21% saved)

regimes1.0s (9%)

Accuracy

Total 8.5b remaining (99.6%)

Threshold costs 0b (0%)

Counts
92 → 3
Compiler

Compiled 20410 to 16512 computations (19.1% saved)

bsearch141.0ms (1.2%)

Steps
ItersRangePoint
10
1.8372090598137216e-273
3.266012968895409e-260
3.848224094713413e-273
7
-5.298269824217728e-232
-2.411802399617781e-234
-9.456952117734688e-234
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
03372
15370
26770
37770
48970
59670
610170
710370
810170

end1.0ms (0%)

Compiler

Compiled 49 to 38 computations (22.4% saved)

sample3.9s (33.4%)

Algorithm
intervals
Results
1.8s1881×body1024valid
767.0ms4618×body128valid
553.0ms978×body512valid
193.0ms518×body256valid
10.0msbody2048valid
1.0msbody128invalid
Compiler

Compiled 281 to 228 computations (18.9% saved)

Profiling

Loading profile data...