Details

analyze4.0s (12.6%)

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)

sample166.0ms (0.5%)

Algorithm

1×

intervals

Results

80.0ms	72×	body	1024	valid
29.0ms	138×	body	128	valid
18.0ms	24×	body	512	valid
11.0ms	22×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify234.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (222.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

prune8.0ms (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

17.9b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize42.0ms (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)
8.3b	(.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))))
8.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite97.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

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×	`cbrt-unprod_binary64_1134` `pow-prod-down_binary64_1172`
8×	`sqrt-prod_binary64_1117`
7×	`unpow-prod-down_binary64_1180`
4×	`pow-exp_binary64_1169` `add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`pow-unpow_binary64_1178` `times-frac_binary64_1107` `div-exp_binary64_1152`
2×	`-commutative_binary64_1032` `distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `associate-r/_binary64_1043` `flip-+_binary64_1075` `associate-l_binary64_1042`
1×	`rem-sqrt-square_binary64_1114` `pow-pow_binary64_1173` `sqrt-pow1_binary64_1119` `div-inv_binary64_1098` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170` `unpow2_binary64_1166` `pow1/2_binary64_1181`

Counts

4 → 86

Calls

4 calls:

34.0ms	(.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))))
18.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
15.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
12.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

series3.0s (9.7%)

Counts

4 → 53

Calls

4 calls:

1.3s	(.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))))
903.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
591.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
240.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2677 to 2385 computations (10.9% saved)

simplify213.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	5055	3879

prune663.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	131	8	139
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	9	140

Error

0.0b

Counts

140 → 9

Compiler

Compiled 4465 to 3412 computations (23.6% saved)

localize48.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
1.1b	(.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)))
15.9b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
15.9b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite91.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1101`
14×	`pow1_binary64_1162`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `cbrt-prod_binary64_1132`
11×	`add-sqr-sqrt_binary64_1123`
9×	`add-cube-cbrt_binary64_1136`
7×	`sqrt-prod_binary64_1117`
6×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172` `cbrt-div_binary64_1133`
4×	`add-log-exp_binary64_1140`
3×	`pow1/3_binary64_1183` `distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-l_binary64_1042`
2×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `sqrt-div_binary64_1118`
1×	`-commutative_binary64_1032` `associate-r*_binary64_1041` `pow1/2_binary64_1181`

Counts

4 → 70

Calls

4 calls:

19.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
18.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
18.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
16.0ms	(.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)))

series5.1s (16.2%)

Counts

4 → 54

Calls

4 calls:

1.4s	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.3s	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
1.3s	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.0s	(.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)))

Compiler

Compiled 5358 to 4731 computations (11.7% saved)

simplify171.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4992	4459
1	4992	4459

prune1.3s (4.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	124	9	133

Error

0.0b

Counts

133 → 9

Compiler

Compiled 6510 to 5136 computations (21.1% saved)

localize44.0ms (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)))
8.3b	(.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))))
8.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite109.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_1162`
29×	`add-exp-log_binary64_1139`
20×	`add-cbrt-cube_binary64_1137`
19×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
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×	`pow1/3_binary64_1183` `distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `associate-*r/_binary64_1043` `flip-+_binary64_1075`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `associate-l*_binary64_1042` `pow1/2_binary64_1181`

Counts

4 → 74

Calls

4 calls:

63.0ms	(.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))))
18.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
3.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
3.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

series2.6s (8.4%)

Counts

4 → 47

Calls

4 calls:

1.3s	(.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))))
958.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
191.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
177.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2800 to 2459 computations (12.2% saved)

simplify277.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (203.0ms)

Iter	Nodes	Cost
0	4955	3661
1	4955	3661

prune725.0ms (2.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	120	10	130

Error

0.0b

Counts

130 → 10

Compiler

Compiled 4938 to 3849 computations (22.1% saved)

localize58.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite141.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`pow1_binary64_1162`
57×	`add-exp-log_binary64_1139`
42×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
39×	`add-cbrt-cube_binary64_1137`
12×	`*-un-lft-identity_binary64_1101`
9×	`add-sqr-sqrt_binary64_1123`
8×	`sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
7×	`associate-r_binary64_1041`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `cbrt-prod_binary64_1132`
2×	`pow1/3_binary64_1183` `distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `associate-*r/_binary64_1043` `flip-+_binary64_1075`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `associate-l*_binary64_1042` `pow1/2_binary64_1181`

Counts

4 → 87

Calls

4 calls:

68.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.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))))
19.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
3.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

series2.8s (9%)

Counts

4 → 47

Calls

4 calls:

1.4s	(.f64 (.f64 (.f64 (.f64 J -2) (.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))))
1.0s	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
225.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
177.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3354 to 2935 computations (12.5% saved)

simplify262.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	4999	5669
1	4999	5669

prune919.0ms (2.9%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	134	10	144

Error

0.0b

Counts

144 → 10

Compiler

Compiled 6749 to 5399 computations (20% saved)

regimes1.4s (4.4%)

Accuracy

Total 9.3b remaining (99.7%)

Threshold costs 0b (0%)

Compiler

Compiled 5414 to 4836 computations (10.7% saved)

bsearch5.0ms (0%)

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

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	125
1	39	125

end0.0ms (0%)

sample6.9s (21.9%)

Algorithm

1×

intervals

Results

2.4s	1971×	body	1024	valid
1.0s	4559×	body	128	valid
813.0ms	974×	body	512	valid
265.0ms	494×	body	256	valid
4.0ms	2×	body	2048	valid
2.0ms	8×	body	128	invalid
1.0ms	1×	body	512	invalid

Compiler

Compiled 997 to 885 computations (11.2% saved)

Details

analyze4.0s (12.6%)

sample166.0ms (0.5%)

simplify234.0ms (0.7%)

prune8.0ms (0%)

localize42.0ms (0.1%)

rewrite97.0ms (0.3%)

series3.0s (9.7%)

simplify213.0ms (0.7%)

prune663.0ms (2.1%)

localize48.0ms (0.2%)

rewrite91.0ms (0.3%)

series5.1s (16.2%)

simplify171.0ms (0.5%)

prune1.3s (4.3%)

localize44.0ms (0.1%)

rewrite109.0ms (0.3%)

series2.6s (8.4%)

simplify277.0ms (0.9%)

prune725.0ms (2.3%)

localize58.0ms (0.2%)

rewrite141.0ms (0.4%)

series2.8s (9%)

simplify262.0ms (0.8%)

prune919.0ms (2.9%)

regimes1.4s (4.4%)

bsearch5.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample6.9s (21.9%)

Profiling