Details

Time bar (total: 8.6s)

analyze1.8s (21.3%)

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 25 to 23 computations (8% saved)

sample79.0ms (0.9%)

Algorithm
1×intervals
Results
31.0ms57×body1024valid
22.0ms155×body128valid
10.0ms27×body512valid
4.0ms17×body256valid
Compiler

Compiled 49 to 48 computations (2% saved)

simplify168.0ms (1.9%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
0487137
1487137

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 19.4b

Counts
2 → 1
Compiler

Compiled 48 to 44 computations (8.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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)
8.3b
(*.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))))
9.8b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite47.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
28×add-exp-log_binary64_798
20×pow1_binary64_821
18×add-cbrt-cube_binary64_796
15×*-un-lft-identity_binary64_760
12×prod-exp_binary64_809 add-sqr-sqrt_binary64_782
11×add-cube-cbrt_binary64_795
10×associate-*r*_binary64_700
9×cbrt-unprod_binary64_793 pow-prod-down_binary64_831
8×sqrt-prod_binary64_776
7×unpow-prod-down_binary64_839
4×add-log-exp_binary64_799 pow-exp_binary64_828 sqrt-div_binary64_777
3×div-exp_binary64_811 pow-unpow_binary64_837 times-frac_binary64_766
2×distribute-lft-out_binary64_711 flip3-+_binary64_763 flip-+_binary64_734 associate-*l*_binary64_701 associate-*r/_binary64_702 *-commutative_binary64_691
1×rem-sqrt-square_binary64_773 unpow2_binary64_825 sqrt-pow1_binary64_778 div-inv_binary64_757 pow-to-exp_binary64_829 sqr-pow_binary64_732 pow1/2_binary64_840 pow-pow_binary64_832
Counts
4 → 86
Calls

4 calls:

18.0ms
(*.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))))
8.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

series453.0ms (5.3%)

Counts
4 → 12
Calls

4 calls:

165.0ms
(*.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))))
144.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
109.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
35.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify59.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
052572394

prune183.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New90898
Fresh000
Picked011
Done000
Total90999

Merged error: 14.4b

Counts
99 → 9
Compiler

Compiled 3170 to 2551 computations (19.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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)
8.3b
(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
9.8b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite44.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
31×add-exp-log_binary64_798
23×pow1_binary64_821
21×add-cbrt-cube_binary64_796
14×prod-exp_binary64_809
11×*-un-lft-identity_binary64_760 cbrt-unprod_binary64_793 pow-prod-down_binary64_831
10×add-sqr-sqrt_binary64_782
9×add-cube-cbrt_binary64_795
7×unpow-prod-down_binary64_839
4×sqrt-prod_binary64_776 add-log-exp_binary64_799 pow-exp_binary64_828 sqrt-div_binary64_777 associate-*r*_binary64_700 associate-*r/_binary64_702
3×div-exp_binary64_811 pow-unpow_binary64_837 times-frac_binary64_766
2×flip3-+_binary64_763 flip-+_binary64_734 associate-*l*_binary64_701 *-commutative_binary64_691
1×rem-sqrt-square_binary64_773 distribute-lft-out_binary64_711 unpow2_binary64_825 sqrt-pow1_binary64_778 div-inv_binary64_757 pow-to-exp_binary64_829 sqr-pow_binary64_732 pow1/2_binary64_840 pow-pow_binary64_832
Counts
4 → 83
Calls

4 calls:

14.0ms
(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
8.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.0ms
(*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))

series469.0ms (5.4%)

Counts
4 → 12
Calls

4 calls:

179.0ms
(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
151.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
105.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
34.0ms
(*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))

simplify62.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
056212306

prune161.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New93295
Fresh167
Picked011
Done011
Total9410104

Merged error: 14.4b

Counts
104 → 10
Compiler

Compiled 3006 to 2418 computations (19.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b
(cbrt.f64 (cos.f64 (/.f64 K 2)))
8.3b
(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.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))))) 2)))))
9.8b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.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))))) 2)))

rewrite38.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
17×pow1_binary64_821
16×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
9×*-un-lft-identity_binary64_760
8×prod-exp_binary64_809 cbrt-unprod_binary64_793 pow-prod-down_binary64_831 add-sqr-sqrt_binary64_782
7×add-cube-cbrt_binary64_795
6×cbrt-prod_binary64_791
4×sqrt-prod_binary64_776 add-log-exp_binary64_799 sqrt-div_binary64_777 associate-*r/_binary64_702
2×pow1/3_binary64_842 flip3-+_binary64_763 flip-+_binary64_734
1×rem-sqrt-square_binary64_773 distribute-lft-out_binary64_711 sqrt-pow1_binary64_778 associate-*r*_binary64_700 associate-*l*_binary64_701 pow1/2_binary64_840 *-commutative_binary64_691
Counts
4 → 62
Calls

4 calls:

16.0ms
(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.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))))) 2)))))
10.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.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))))) 2)))
1.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))

series470.0ms (5.4%)

Counts
4 → 12
Calls

4 calls:

174.0ms
(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.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))))) 2)))))
145.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.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))))) 2)))
76.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))
74.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify48.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
050321767

prune157.0ms (1.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New73174
Fresh077
Picked011
Done022
Total731184

Merged error: 14.4b

Counts
84 → 11
Compiler

Compiled 2949 to 2417 computations (18% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b
(cbrt.f64 (cos.f64 (/.f64 K 2)))
8.3b
(*.f64 (*.f64 (*.f64 (*.f64 J -2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.8b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite45.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
30×pow1_binary64_821
29×add-exp-log_binary64_798
20×add-cbrt-cube_binary64_796
19×prod-exp_binary64_809 cbrt-unprod_binary64_793 pow-prod-down_binary64_831
13×*-un-lft-identity_binary64_760
10×add-sqr-sqrt_binary64_782
9×add-cube-cbrt_binary64_795
8×sqrt-prod_binary64_776
7×associate-*r*_binary64_700
6×cbrt-prod_binary64_791
4×add-log-exp_binary64_799 sqrt-div_binary64_777
2×pow1/3_binary64_842 distribute-lft-out_binary64_711 flip3-+_binary64_763 flip-+_binary64_734 associate-*r/_binary64_702
1×rem-sqrt-square_binary64_773 sqrt-pow1_binary64_778 associate-*l*_binary64_701 pow1/2_binary64_840 *-commutative_binary64_691
Counts
4 → 74
Calls

4 calls:

25.0ms
(*.f64 (*.f64 (*.f64 (*.f64 J -2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))

series481.0ms (5.6%)

Counts
4 → 12
Calls

4 calls:

189.0ms
(*.f64 (*.f64 (*.f64 (*.f64 J -2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
150.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
74.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))
68.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify80.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049592191
149592191

prune180.0ms (2.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New83386
Fresh077
Picked101
Done033
Total841397

Merged error: 14.4b

Counts
97 → 13
Compiler

Compiled 3206 to 2610 computations (18.6% saved)

regimes327.0ms (3.8%)

Compiler

Compiled 3848 to 3468 computations (9.9% saved)

bsearch2.0ms (0%)

Compiler

Compiled 24 to 22 computations (8.3% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
047179
147179

end0.0ms (0%)

sample3.2s (36.6%)

Algorithm
1×intervals
Results
1.1s2011×body1024valid
523.0ms4475×body128valid
409.0ms1029×body512valid
123.0ms479×body256valid
5.0ms6×body2048valid
0.0ms2×body128invalid
Compiler

Compiled 771 to 684 computations (11.3% saved)

Profiling

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