Details

analyze2.0s (10.5%)

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

Symmetry

Compiler

Compiled 25 to 23 computations (8% saved)

sample82.0ms (0.4%)

Algorithm

1×

intervals

Results

37.0ms	69×	body	1024	valid
14.0ms	135×	body	128	valid
12.0ms	31×	body	512	valid
5.0ms	21×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

prune3.0ms (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

19.9b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize19.0ms (0.1%)

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)
8.8b	(.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))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite223.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

19.9b

Rules

28×	`add-exp-log_binary64_1139`
20×	`pow1_binary64_1162`
18×	`add-cbrt-cube_binary64_1137`
15×	`*-un-lft-identity_binary64_1101`
12×	`add-sqr-sqrt_binary64_1123` `prod-exp_binary64_1150`
11×	`add-cube-cbrt_binary64_1136`
10×	`associate-r_binary64_1041`
9×	`pow-prod-down_binary64_1172` `cbrt-unprod_binary64_1134`
8×	`sqrt-prod_binary64_1117`
7×	`unpow-prod-down_binary64_1180`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `pow-exp_binary64_1169`
3×	`times-frac_binary64_1107` `pow-unpow_binary64_1178` `div-exp_binary64_1152`
2×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `distribute-lft-out_binary64_1052` `associate-r/_binary64_1043` `associate-l_binary64_1042` `-commutative_binary64_1032`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `div-inv_binary64_1098` `pow-pow_binary64_1173` `pow-to-exp_binary64_1170` `unpow2_binary64_1166` `sqr-pow_binary64_1073`

Counts

4 → 86

Calls

4 calls:

15.0ms	(.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)))

Compiler

Compiled 3141 to 2524 computations (19.6% saved)

series1.9s (10.1%)

Error

0.1b

Counts

4 → 61

Calls

4 calls:

856.0ms	(.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))))
485.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
341.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
112.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4988 to 4248 computations (14.8% saved)

simplify102.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4954	4248
1	4954	4248

prune270.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	140	8	148

Error

0.0b

Counts

148 → 8

Compiler

Compiled 4682 to 3503 computations (25.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.4b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
8.8b	(.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))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite260.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`pow1_binary64_1162`
29×	`add-exp-log_binary64_1139`
20×	`add-cbrt-cube_binary64_1137`
19×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
13×	`*-un-lft-identity_binary64_1101`
10×	`add-sqr-sqrt_binary64_1123`
9×	`add-cube-cbrt_binary64_1136`
8×	`sqrt-prod_binary64_1117`
7×	`associate-r_binary64_1041`
6×	`cbrt-prod_binary64_1132`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
2×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `distribute-lft-out_binary64_1052` `associate-*r/_binary64_1043` `pow1/3_binary64_1183`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-l_binary64_1042` `*-commutative_binary64_1032`

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)))

Compiler

Compiled 3902 to 3195 computations (18.1% saved)

series1.6s (8.7%)

Error

0.0b

Counts

4 → 52

Calls

4 calls:

870.0ms	(.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))))
504.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
86.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
84.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 5111 to 4338 computations (15.1% saved)

simplify65.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4972	3865
1	4972	3865

prune288.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	124	10	134

Error

0.0b

Counts

134 → 10

Compiler

Compiled 5142 to 3991 computations (22.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.4b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
8.8b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (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))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite606.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

91×	`pow1_binary64_1162`
90×	`add-exp-log_binary64_1139`
70×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
58×	`add-cbrt-cube_binary64_1137`
13×	`*-un-lft-identity_binary64_1101`
10×	`add-sqr-sqrt_binary64_1123`
9×	`add-cube-cbrt_binary64_1136`
8×	`sqrt-prod_binary64_1117`
7×	`associate-r_binary64_1041`
6×	`cbrt-prod_binary64_1132`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
2×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `distribute-lft-out_binary64_1052` `associate-*r/_binary64_1043` `pow1/3_binary64_1183`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-l_binary64_1042` `*-commutative_binary64_1032`

Counts

4 → 104

Calls

4 calls:

42.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (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)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 7649 to 6344 computations (17.1% saved)

series1.7s (9%)

Error

0.0b

Counts

4 → 52

Calls

4 calls:

882.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (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))))
514.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
91.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
87.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 6236 to 5313 computations (14.8% saved)

simplify108.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4985	5027
1	4985	5027

prune408.0ms (2.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	156	10	166

Error

0.0b

Counts

166 → 10

Compiler

Compiled 6962 to 5523 computations (20.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
0.6b	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
8.8b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite248.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`pow1_binary64_1162`
13×	`add-exp-log_binary64_1139`
11×	`*-un-lft-identity_binary64_1101`
9×	`add-cbrt-cube_binary64_1137`
8×	`add-sqr-sqrt_binary64_1123` `sqrt-prod_binary64_1117`
7×	`add-cube-cbrt_binary64_1136` `associate-r_binary64_1041`
6×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
2×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `distribute-lft-out_binary64_1052` `associate-*r/_binary64_1043` `pow1/3_binary64_1183` `cbrt-prod_binary64_1132`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-l_binary64_1042` `*-commutative_binary64_1032`

Counts

4 → 61

Calls

4 calls:

26.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (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)))
4.0ms	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
4.0ms	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))

Compiler

Compiled 3766 to 3045 computations (19.1% saved)

series2.3s (12.4%)

Error

0.0b

Counts

4 → 58

Calls

4 calls:

1.1s	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
501.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
328.0ms	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
309.0ms	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))

Compiler

Compiled 7362 to 6288 computations (14.6% saved)

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4944	3750
1	4944	3750

prune324.0ms (1.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	118	11	129

Error

0.0b

Counts

129 → 11

Compiler

Compiled 5303 to 4081 computations (23% saved)

regimes1.5s (8%)

Accuracy

Total 8.8b remaining (99.8%)

Threshold costs 0b (0%)

Compiler

Compiled 13867 to 12040 computations (13.2% saved)

bsearch4.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	147
1	56	147

Removed

()

end0.0ms (0%)

sample4.5s (24%)

Algorithm

1×

intervals

Results

1.1s	2022×	body	1024	valid
500.0ms	4456×	body	128	valid
398.0ms	987×	body	512	valid
136.0ms	534×	body	256	valid
4.0ms	1×	body	2048	valid
2.0ms	3×	body	1024	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 2374 to 2057 computations (13.4% saved)

Details

analyze2.0s (10.5%)

sample82.0ms (0.4%)

simplify88.0ms (0.5%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite223.0ms (1.2%)

series1.9s (10.1%)

simplify102.0ms (0.5%)

prune270.0ms (1.4%)

localize18.0ms (0.1%)

rewrite260.0ms (1.4%)

series1.6s (8.7%)

simplify65.0ms (0.3%)

prune288.0ms (1.5%)

localize22.0ms (0.1%)

rewrite606.0ms (3.2%)

series1.7s (9%)

simplify108.0ms (0.6%)

prune408.0ms (2.2%)

localize18.0ms (0.1%)

rewrite248.0ms (1.3%)

series2.3s (12.4%)

simplify101.0ms (0.5%)

prune324.0ms (1.7%)

regimes1.5s (8%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.5s (24%)

Profiling