Details

analyze2.0s (11.1%)

Algorithm

1×

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)

sample87.0ms (0.5%)

Algorithm

1×

intervals

Results

44.0ms	74×	body	1024	valid
15.0ms	137×	body	128	valid
12.0ms	32×	body	512	valid
3.0ms	13×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify181.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

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

17.5b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.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)
6.7b	(.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))))
9.6b	(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

17.4b

Rules

28×	`add-exp-log_binary64_798`
20×	`pow1_binary64_821`
18×	`add-cbrt-cube_binary64_796`
15×	`*-un-lft-identity_binary64_760`
12×	`add-sqr-sqrt_binary64_782` `prod-exp_binary64_809`
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` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-r/_binary64_702` `associate-l_binary64_701` `-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:

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)

series1.7s (9.6%)

Error

0.1b

Counts

4 → 55

Calls

4 calls:

712.0ms	(.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))))
466.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
322.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
121.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4590 to 3930 computations (14.4% saved)

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4947	4063
1	4947	4063

prune269.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	134	8	142

Error

0.1b

Counts

142 → 8

Compiler

Compiled 4630 to 3512 computations (24.1% saved)

localize23.0ms (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)))
6.7b	(.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))))
9.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite265.0ms (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` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-*r/_binary64_702` `pow1/3_binary64_842`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

4 → 74

Calls

4 calls:

24.0ms	(.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)

series1.5s (8.4%)

Error

0.1b

Counts

4 → 49

Calls

4 calls:

725.0ms	(.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))))
488.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
89.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
88.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4972 to 4232 computations (14.9% saved)

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5373	3739

prune281.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	120	11	131

Error

0.0b

Counts

131 → 11

Compiler

Compiled 5240 to 4095 computations (21.9% saved)

localize23.0ms (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)))
6.7b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (log.f64 (exp.f64 (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))))
9.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite279.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`pow1_binary64_821`
29×	`add-exp-log_binary64_798`
22×	`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` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-*r/_binary64_702` `pow1/3_binary64_842`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

4 → 74

Calls

4 calls:

28.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (log.f64 (exp.f64 (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 4110 to 3399 computations (17.3% saved)

series2.3s (13%)

Error

0.0b

Counts

4 → 49

Calls

4 calls:

1.5s	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (log.f64 (exp.f64 (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))))
500.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
97.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
88.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 6049 to 5234 computations (13.5% saved)

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4972	4126
1	4972	4126

prune325.0ms (1.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	123	11	134

Error

0.0b

Counts

134 → 11

Compiler

Compiled 5553 to 4392 computations (20.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
0.3b	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
6.7b	(.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))))
9.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite589.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

91×	`pow1_binary64_821`
90×	`add-exp-log_binary64_798`
70×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
58×	`add-cbrt-cube_binary64_796`
18×	`cbrt-prod_binary64_791`
15×	`*-un-lft-identity_binary64_760`
12×	`add-sqr-sqrt_binary64_782`
11×	`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` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-*r/_binary64_702` `pow1/3_binary64_842`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

4 → 110

Calls

4 calls:

39.0ms	(.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))))
10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
2.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
2.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))

Compiler

Compiled 8033 to 6668 computations (17% saved)

series1.5s (8.5%)

Error

0.0b

Counts

4 → 49

Calls

4 calls:

722.0ms	(.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))))
504.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
88.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
85.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))

Compiler

Compiled 6069 to 5179 computations (14.7% saved)

simplify109.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4939	5081
1	4939	5081

prune481.0ms (2.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	159	11	170

Error

0.0b

Counts

170 → 11

Compiler

Compiled 7000 to 5590 computations (20.1% saved)

regimes1.1s (6.1%)

Accuracy

Total 8.7b remaining (99.8%)

Threshold costs 0b (0%)

Compiler

Compiled 12397 to 10828 computations (12.7% saved)

bsearch4.0ms (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	39	125
1	39	125

end0.0ms (0%)

sample4.3s (24.1%)

Algorithm

1×

intervals

Results

1.1s	1999×	body	1024	valid
493.0ms	4510×	body	128	valid
374.0ms	960×	body	512	valid
132.0ms	529×	body	256	valid
2.0ms	2×	body	2048	valid
0.0ms	1×	body	512	invalid
0.0ms	2×	body	128	invalid

Compiler

Compiled 2115 to 1844 computations (12.8% saved)

Details

analyze2.0s (11.1%)

sample87.0ms (0.5%)

simplify181.0ms (1%)

prune4.0ms (0%)

localize20.0ms (0.1%)

rewrite223.0ms (1.2%)

series1.7s (9.6%)

simplify101.0ms (0.6%)

prune269.0ms (1.5%)

localize23.0ms (0.1%)

rewrite265.0ms (1.5%)

series1.5s (8.4%)

simplify66.0ms (0.4%)

prune281.0ms (1.6%)

localize23.0ms (0.1%)

rewrite279.0ms (1.6%)

series2.3s (13%)

simplify89.0ms (0.5%)

prune325.0ms (1.8%)

localize24.0ms (0.1%)

rewrite589.0ms (3.3%)

series1.5s (8.5%)

simplify109.0ms (0.6%)

prune481.0ms (2.7%)

regimes1.1s (6.1%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.3s (24.1%)

Profiling