Details

Time bar (total: 10.7s)

analyze1.9s (17.8%)

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)

sample88.0ms (0.8%)

Algorithm
1×intervals
Results
45.0ms71×body1024valid
16.0ms142×body128valid
13.0ms33×body512valid
3.0ms10×body256valid
Compiler

Compiled 49 to 48 computations (2% saved)

simplify185.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (86.0ms)

IterNodesCost
0487137
1487137

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
18.2b
Counts
2 → 1
Compiler

Compiled 48 to 44 computations (8.3% saved)

localize18.0ms (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)
6.4b
(*.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))))
10.6b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite45.0ms (0.4%)

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:

16.0ms
(*.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)))

series486.0ms (4.6%)

Counts
4 → 12
Calls

4 calls:

183.0ms
(*.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))))
152.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
115.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
37.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify63.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
052572394

prune409.0ms (3.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New91798
Fresh000
Picked011
Done000
Total91899
Error
11.0b
Counts
99 → 8
Compiler

Compiled 3164 to 2543 computations (19.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b
(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
1.4b
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
16.0b
(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
16.0b
(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite46.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
15×*-un-lft-identity_binary64_760
14×pow1_binary64_821
13×add-exp-log_binary64_798 add-cbrt-cube_binary64_796 cbrt-prod_binary64_791
11×add-sqr-sqrt_binary64_782
9×add-cube-cbrt_binary64_795
7×sqrt-prod_binary64_776
6×prod-exp_binary64_809 cbrt-div_binary64_792 cbrt-unprod_binary64_793 pow-prod-down_binary64_831
4×add-log-exp_binary64_799
3×pow1/3_binary64_842 distribute-lft-out_binary64_711 flip3-+_binary64_763 flip-+_binary64_734 associate-*l*_binary64_701
2×rem-sqrt-square_binary64_773 sqrt-pow1_binary64_778 sqrt-div_binary64_777
1×associate-*r*_binary64_700 pow1/2_binary64_840 *-commutative_binary64_691
Counts
4 → 70
Calls

4 calls:

13.0ms
(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms
(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms
(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))

series1.1s (10.4%)

Counts
4 → 12
Calls

4 calls:

306.0ms
(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
303.0ms
(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
303.0ms
(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
196.0ms
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))

simplify76.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049442739
149442739

prune247.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New82082
Fresh066
Picked011
Done011
Total82890
Error
11.0b
Counts
90 → 8
Compiler

Compiled 4326 to 3540 computations (18.2% 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)))
6.4b
(*.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))))
10.6b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite50.0ms (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:

26.0ms
(*.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)))

series490.0ms (4.6%)

Counts
4 → 12
Calls

4 calls:

186.0ms
(*.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))))
154.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
81.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))
68.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify78.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049592191
149592191

prune192.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New83386
Fresh055
Picked101
Done022
Total841094
Error
11.0b
Counts
94 → 10
Compiler

Compiled 3488 to 2861 computations (18% saved)

localize25.0ms (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)))
6.4b
(*.f64 (*.f64 (*.f64 (*.f64 J -2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (log.f64 (exp.f64 (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))))
10.6b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite48.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
30×pow1_binary64_821
29×add-exp-log_binary64_798
25×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:

27.0ms
(*.f64 (*.f64 (*.f64 (*.f64 J -2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (log.f64 (exp.f64 (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)))

series855.0ms (8%)

Counts
4 → 12
Calls

4 calls:

551.0ms
(*.f64 (*.f64 (*.f64 (*.f64 J -2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (log.f64 (exp.f64 (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))))
149.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
78.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))
77.0ms
(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify78.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
050182235

prune191.0ms (1.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New83386
Fresh167
Picked011
Done022
Total841296
Error
11.0b
Counts
96 → 12
Compiler

Compiled 3332 to 2732 computations (18% saved)

regimes460.0ms (4.3%)

Accuracy

Total 0.8b remaining (5.9%)

Threshold costs 0.8b (5.9%)

Compiler

Compiled 5570 to 4980 computations (10.6% saved)

bsearch2.0ms (0%)

Compiler

Compiled 24 to 22 computations (8.3% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046152
146152

end0.0ms (0%)

sample3.5s (32.8%)

Algorithm
1×intervals
Results
1.2s2015×body1024valid
523.0ms4449×body128valid
421.0ms1003×body512valid
146.0ms531×body256valid
2.0ms2×body2048valid
0.0ms1×body512invalid
0.0ms3×body128invalid
Compiler

Compiled 1040 to 923 computations (11.3% saved)

Profiling

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