Details

analyze2.2s (17.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample46.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	252×	body	128	valid
1.0ms	4×	body	512	invalid
1.0ms	3×	body	512	valid
1.0ms	10×	body	128	invalid
1.0ms	1×	body	1024	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify141.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5097	43

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

12.9b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize20.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(*.f64 K (+.f64 m n))
0.0b	(/.f64 (*.f64 K (+.f64 m n)) 2)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
29.8b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_759`
15×	`*-un-lft-identity_binary64_737`
12×	`add-exp-log_binary64_775`
11×	`add-cbrt-cube_binary64_773` `add-cube-cbrt_binary64_772`
7×	`pow1_binary64_798`
6×	`unpow-prod-down_binary64_816`
4×	`add-log-exp_binary64_776` `cos-sum_binary64_871` `associate-r_binary64_677` `associate-*r/_binary64_679` `times-frac_binary64_743`
3×	`associate-/r_binary64_681` `pow-unpow_binary64_814` `cancel-sign-sub-inv_binary64_703` `associate-l*_binary64_678`
2×	`flip3-+_binary64_740` `cbrt-unprod_binary64_770` `prod-exp_binary64_786` `cbrt-undiv_binary64_771` `flip-+_binary64_711` `div-exp_binary64_788` `associate-/l/_binary64_684` `difference-of-squares_binary64_706`
1×	`unswap-sqr_binary64_705` `distribute-lft-in_binary64_686` `cos-diff_binary64_874` `frac-2neg_binary64_748` `clear-num_binary64_736` `pow-exp_binary64_805` `associate-/l_binary64_682` `distribute-lft-out--_binary64_689` `sub-neg_binary64_730` `div-inv_binary64_734` `pow-pow_binary64_809` `pow-to-exp_binary64_806` `unpow2_binary64_802` `distribute-rgt-in_binary64_687` `distribute-lft-out_binary64_688` `pow-prod-down_binary64_808` `-commutative_binary64_668` `sqr-pow_binary64_709`

Counts

4 → 79

Calls

8 calls:

15.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
6.0ms	(*.f64 K (+.f64 m n))
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series648.0ms (5.2%)

Counts

4 → 69

Calls

4 calls:

291.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
138.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
118.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
100.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 3587 to 2871 computations (20% saved)

simplify67.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5054	2094

prune263.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	143	5	148
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	5	149

Error

0.8b

Counts

149 → 5

Compiler

Compiled 4856 to 2330 computations (52% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_737`
20×	`add-sqr-sqrt_binary64_759`
13×	`add-log-exp_binary64_776`
8×	`add-cube-cbrt_binary64_772`
7×	`cancel-sign-sub-inv_binary64_703`
6×	`unpow-prod-down_binary64_816`
5×	`add-exp-log_binary64_775` `pow1_binary64_798` `difference-of-squares_binary64_706`
4×	`add-cbrt-cube_binary64_773` `distribute-lft-out--_binary64_689`
3×	`diff-log_binary64_829` `pow-unpow_binary64_814` `distribute-lft-out_binary64_688`
2×	`sub-neg_binary64_730` `flip3--_binary64_741` `flip--_binary64_712` `sum-log_binary64_828` `times-frac_binary64_743`
1×	`flip3-+_binary64_740` `pow-exp_binary64_805` `flip-+_binary64_711` `pow-pow_binary64_809` `+-commutative_binary64_667` `pow-to-exp_binary64_806` `unpow2_binary64_802` `associate--r+_binary64_673` `sqr-pow_binary64_709`

Counts

4 → 70

Calls

8 calls:

19.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
14.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series1.7s (13.3%)

Counts

4 → 111

Calls

4 calls:

643.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
603.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
279.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
134.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

Compiler

Compiled 4434 to 3753 computations (15.4% saved)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5089	3882

prune221.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	181	5	186

Error

0.8b

Counts

186 → 5

Compiler

Compiled 4620 to 2107 computations (54.4% saved)

localize30.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) M)
0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
15.4b	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
15.4b	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
15.4b	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
29.9b	(cos.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) M))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`cbrt-prod_binary64_768`
11×	`add-cube-cbrt_binary64_772` `add-sqr-sqrt_binary64_759` `*-un-lft-identity_binary64_737`
9×	`times-frac_binary64_743`
4×	`add-cbrt-cube_binary64_773` `add-log-exp_binary64_776` `cos-sum_binary64_871` `add-exp-log_binary64_775` `pow1_binary64_798`
3×	`pow1/3_binary64_819` `cbrt-div_binary64_769` `div-inv_binary64_734` `cancel-sign-sub-inv_binary64_703`
1×	`cos-diff_binary64_874` `sub-neg_binary64_730`

Counts

4 → 60

Calls

8 calls:

14.0ms	(cos.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) M))
5.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
5.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
5.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series1.0s (8.2%)

Counts

4 → 42

Calls

4 calls:

359.0ms	(cos.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) M))
225.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
224.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
211.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))

Compiler

Compiled 4325 to 3318 computations (23.3% saved)

simplify113.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5104	1737

prune189.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	102	5	107

Error

0.8b

Counts

107 → 5

Compiler

Compiled 4847 to 2398 computations (50.5% saved)

localize31.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.4b	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
29.8b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
29.8b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
29.8b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cos-sum_binary64_871`
9×	`cancel-sign-sub-inv_binary64_703`
8×	`add-cube-cbrt_binary64_772` `add-sqr-sqrt_binary64_759` `*-un-lft-identity_binary64_737`
4×	`add-cbrt-cube_binary64_773` `add-log-exp_binary64_776` `add-exp-log_binary64_775` `pow1_binary64_798`
3×	`cos-diff_binary64_874` `cbrt-prod_binary64_768` `sub-neg_binary64_730`
1×	`pow1/3_binary64_819`

Counts

4 → 47

Calls

8 calls:

10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
2.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series990.0ms (8%)

Counts

4 → 48

Calls

4 calls:

591.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
133.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
133.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
132.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 5627 to 3935 computations (30.1% saved)

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4808	1780
1	4808	1780

prune205.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	95	5	100

Error

0.8b

Counts

100 → 5

Compiler

Compiled 5370 to 2665 computations (50.4% saved)

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	1289	1195
1	1289	1195

regimes336.0ms (2.7%)

Accuracy

Total 0.2b remaining (15.8%)

Threshold costs 0.2b (15.8%)

Compiler

Compiled 3875 to 3260 computations (15.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	31
1	62	31

end0.0ms (0%)

sample3.8s (30.8%)

Algorithm

1×

intervals

Results

812.0ms	7845×	body	128	valid
32.0ms	77×	body	1024	invalid
31.0ms	295×	body	128	invalid
28.0ms	56×	body	1024	valid
26.0ms	87×	body	512	invalid
19.0ms	60×	body	512	valid
10.0ms	18×	body	2048	invalid
9.0ms	39×	body	256	valid
8.0ms	41×	body	256	invalid

Compiler

Compiled 2349 to 1955 computations (16.8% saved)

Pareto

0.166064147843901

Details

analyze2.2s (17.4%)

sample46.0ms (0.4%)

simplify141.0ms (1.1%)

prune8.0ms (0.1%)

localize20.0ms (0.2%)

rewrite47.0ms (0.4%)

series648.0ms (5.2%)

simplify67.0ms (0.5%)

prune263.0ms (2.1%)

localize14.0ms (0.1%)

rewrite62.0ms (0.5%)

series1.7s (13.3%)

simplify85.0ms (0.7%)

prune221.0ms (1.8%)

localize30.0ms (0.2%)

rewrite37.0ms (0.3%)

series1.0s (8.2%)

simplify113.0ms (0.9%)

prune189.0ms (1.5%)

localize31.0ms (0.2%)

rewrite39.0ms (0.3%)

series990.0ms (8%)

simplify110.0ms (0.9%)

prune205.0ms (1.6%)

simplify55.0ms (0.4%)

regimes336.0ms (2.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.8s (30.8%)

Profiling