Details

analyze2.4s (10.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5366	148
0	3	3
1	3	3

Search

True	Other	False	Iter
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)

sample114.0ms (0.5%)

Algorithm

1×

intervals

Results

47.0ms	68×	body	1024	valid
25.0ms	137×	body	128	valid
19.0ms	39×	body	512	valid
4.0ms	12×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify111.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

18.2b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.3b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
8.5b	(sqrt.f64 (+.f64 1 (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))))

rewrite260.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

18.1b

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×	`pow-prod-down_binary64_831` `cbrt-unprod_binary64_793`
8×	`sqrt-prod_binary64_776`
7×	`unpow-prod-down_binary64_839`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777` `pow-exp_binary64_828`
3×	`times-frac_binary64_766` `pow-unpow_binary64_837` `div-exp_binary64_811`
2×	`flip3-+_binary64_763` `associate-r/_binary64_702` `flip-+_binary64_734` `associate-l_binary64_701` `distribute-lft-out_binary64_711` `-commutative_binary64_691`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `div-inv_binary64_757` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `unpow2_binary64_825` `sqr-pow_binary64_732`

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))))
10.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
8.0ms	(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)))

Compiler

Compiled 3141 to 2524 computations (19.6% saved)

series2.1s (9.4%)

Error

0.1b

Counts

4 → 61

Calls

4 calls:

825.0ms	(.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))))
669.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
396.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
118.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4671 to 3991 computations (14.6% saved)

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5298	3997

prune308.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	141	6	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	6	148

Error

0.0b

Counts

148 → 6

Compiler

Compiled 4510 to 3441 computations (23.7% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
2.3b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))))
15.0b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
15.0b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))

rewrite305.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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×	`cbrt-div_binary64_792` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
4×	`add-log-exp_binary64_799`
3×	`pow1/3_binary64_842` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-r_binary64_700`
2×	`sqrt-pow1_binary64_778` `sqrt-div_binary64_777` `rem-sqrt-square_binary64_773`
1×	`associate-l_binary64_701` `*-commutative_binary64_691` `pow1/2_binary64_840`

Counts

4 → 70

Calls

4 calls:

9.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))))
9.0ms	(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 J 2) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 4097 to 3350 computations (18.2% saved)

series4.0s (17.6%)

Error

0.0b

Counts

4 → 67

Calls

4 calls:

1.1s	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))
1.0s	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
976.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
609.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))))

Compiler

Compiled 10305 to 8881 computations (13.8% saved)

simplify111.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4969	5700
1	4969	5700

prune585.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	137	6	143

Error

0.0b

Counts

143 → 6

Compiler

Compiled 7553 to 5902 computations (21.9% saved)

localize20.0ms (0.1%)

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)))
8.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.5b	(.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)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

rewrite343.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`pow1_binary64_821`
29×	`add-exp-log_binary64_798`
20×	`add-cbrt-cube_binary64_796`
19×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
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×	`flip3-+_binary64_763` `associate-*r/_binary64_702` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `pow1/3_binary64_842`
1×	`associate-l_binary64_701` `*-commutative_binary64_691` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773`

Counts

4 → 74

Calls

4 calls:

27.0ms	(.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)))) (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)))

Compiler

Compiled 3902 to 3195 computations (18.1% saved)

series2.1s (9.2%)

Error

0.0b

Counts

4 → 52

Calls

4 calls:

1.1s	(.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)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
691.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
99.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
85.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4889 to 4157 computations (15% saved)

simplify107.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4971	3550
1	4971	3550

prune359.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	125	7	132

Error

0.0b

Counts

132 → 7

Compiler

Compiled 4869 to 3848 computations (21% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
0.3b	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
8.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.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))))

rewrite598.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

58×	`pow1_binary64_821`
57×	`add-exp-log_binary64_798`
42×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
39×	`add-cbrt-cube_binary64_796`
13×	`*-un-lft-identity_binary64_760`
10×	`add-sqr-sqrt_binary64_782` `cbrt-prod_binary64_791`
9×	`add-cube-cbrt_binary64_795`
8×	`sqrt-prod_binary64_776`
7×	`associate-r_binary64_700`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
2×	`flip3-+_binary64_763` `associate-*r/_binary64_702` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `pow1/3_binary64_842`
1×	`associate-l_binary64_701` `*-commutative_binary64_691` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773`

Counts

4 → 90

Calls

4 calls:

42.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.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)))
7.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
2.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))

Compiler

Compiled 6410 to 5304 computations (17.3% saved)

series2.0s (9.1%)

Error

0.0b

Counts

4 → 52

Calls

4 calls:

915.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.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))))
733.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
128.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
126.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))

Compiler

Compiled 5917 to 5038 computations (14.9% saved)

simplify149.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4930	4234
1	4930	4234

prune430.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	142	7	149

Error

0.0b

Counts

149 → 7

Compiler

Compiled 6113 to 4893 computations (20% saved)

regimes1.1s (4.9%)

Accuracy

Total 9.0b remaining (99.7%)

Threshold costs 0b (0%)

Compiler

Compiled 8729 to 7748 computations (11.2% saved)

bsearch3.0ms (0%)

Compiler: Compiled 24 to 22 computations (8.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	123
1	35	123

end0.0ms (0%)

sample4.8s (21.4%)

Algorithm

1×

intervals

Results

1.4s	1970×	body	1024	valid
628.0ms	4484×	body	128	valid
488.0ms	1014×	body	512	valid
172.0ms	531×	body	256	valid
1.0ms	1×	body	2048	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 1528 to 1351 computations (11.6% saved)

Details

analyze2.4s (10.8%)

sample114.0ms (0.5%)

simplify111.0ms (0.5%)

prune4.0ms (0%)

localize20.0ms (0.1%)

rewrite260.0ms (1.2%)

series2.1s (9.4%)

simplify91.0ms (0.4%)

prune308.0ms (1.4%)

localize24.0ms (0.1%)

rewrite305.0ms (1.4%)

series4.0s (17.6%)

simplify111.0ms (0.5%)

prune585.0ms (2.6%)

localize20.0ms (0.1%)

rewrite343.0ms (1.5%)

series2.1s (9.2%)

simplify107.0ms (0.5%)

prune359.0ms (1.6%)

localize24.0ms (0.1%)

rewrite598.0ms (2.7%)

series2.0s (9.1%)

simplify149.0ms (0.7%)

prune430.0ms (1.9%)

regimes1.1s (4.9%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.8s (21.4%)

Profiling