Details

analyze665.0ms (5.5%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample162.0ms (1.3%)

Algorithm

1×

intervals

Results

48.0ms	29×	body	4096	valid
39.0ms	177×	body	128	valid
36.0ms	24×	body	2048	valid
12.0ms	13×	body	1024	valid
6.0ms	9×	body	512	valid
2.0ms	4×	body	256	valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

652×	`div-sub_binary64`
554×	`fma-neg_binary64`
550×	`hypot-def_binary64`
431×	`fma-def_binary64`
378×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	36
1	44	25
2	96	25
3	264	25
4	706	25
5	2223	25
6	4175	25
7	4825	25
8	4983	25

prune9.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

12.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	30.1b	(.f64 180 (/.f64 (atan.f64 (.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) PI.f64))
▶	12.3b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) PI.f64))

Status

Error

Program

30.1b

(*.f64 180 (/.f64 (atan.f64 (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) PI.f64))

▶

12.3b

(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) PI.f64))

Compiler

Compiled 132 to 91 computations (31.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))
✓	0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) PI.f64)
✓	0.0b	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
✓	1.1b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

rewrite74.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
40×	`add-cube-cbrt_binary64`
27×	`times-frac_binary64`
24×	`prod-diff_binary64`

Counts

4 → 136

Calls

4 calls:

23.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
14.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
12.0ms	(atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))
7.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) PI.f64)

series339.0ms (2.8%)

Counts

4 → 144

Calls

4 calls:

139.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
107.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
80.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) PI.f64)
11.0ms	(atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))

simplify389.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-def_binary64`
336×	`associate-/l*_binary64`
232×	`times-frac_binary64`
204×	`sub-neg_binary64`
193×	`associate-/r*_binary64`

Counts

280 → 465

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	637	9182
1	1859	8041
2	4894	8039
3	4987	8039

prune524.0ms (4.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	457	8	465
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	459	8	467

Error

0.2b

Counts

467 → 8

Alt Table

Status	Error	Program
	12.7b	(.f64 180 (/.f64 (atan.f64 (/.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (.f64 (cbrt.f64 B) (cbrt.f64 B))) (cbrt.f64 B))) PI.f64))
	54.3b	(.f64 180 (/.f64 (atan.f64 (fma.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (+.f64 (/.f64 B A) (/.f64 (.f64 B (.f64 C C)) (pow.f64 A 3)))) (*.f64 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) -1/8))) PI.f64))
	19.5b	(*.f64 180 (/.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 C A)) B))) PI.f64))
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 B B) C) (.f64 A A)) (/.f64 (.f64 B B) A))) B)) PI.f64))
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) PI.f64))
▶	12.3b	(*.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))))
	47.3b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) PI.f64))
	47.0b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) PI.f64))

Compiler

Compiled 11897 to 5025 computations (57.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))
✓	0.0b	(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))))
	0.0b	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
	1.1b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

1 → 78

Calls

1 calls:

8.0ms

(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))))

series82.0ms (0.7%)

Counts

1 → 36

Calls

1 calls:

82.0ms

(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))))

simplify633.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

994×	`fma-def_binary64`
946×	`fabs-mul_binary64`
831×	`fma-neg_binary64`
459×	`unswap-sqr_binary64`
331×	`pow-sqr_binary64`

Counts

114 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	3954
1	190	3661
2	455	3634
3	953	3634
4	1340	3634
5	1718	3634
6	2194	3634
7	2712	3634
8	3217	3634
9	4342	3634
10	4910	3634
11	4546	3634
12	4746	3634
13	4973	3634

prune622.0ms (5.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	558	3	561
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	560	9	569

Error

0.2b

Counts

569 → 9

Alt Table

Status	Error	Program
	19.5b	(*.f64 180 (/.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 C A)) B))) PI.f64))
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 B B) C) (.f64 A A)) (/.f64 (.f64 B B) A))) B)) PI.f64))
✓	12.3b	(*.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))))
▶	12.7b	(.f64 180 (/.f64 (atan.f64 (/.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (.f64 (cbrt.f64 B) (cbrt.f64 B))) (cbrt.f64 B))) PI.f64))
	48.4b	(.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (*.f64 B B) C)) B)))))
	47.3b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) PI.f64))
	47.0b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) PI.f64))
	47.4b	(.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (.f64 1/2 (/.f64 B A))))))
	54.3b	(.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (fma.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (+.f64 (/.f64 B A) (/.f64 (.f64 B (.f64 C C)) (pow.f64 A 3)))) (*.f64 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) -1/8))))))

Compiler

Compiled 14762 to 6196 computations (58% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 B)
	0.6b	(cbrt.f64 B)
✓	0.6b	(cbrt.f64 B)
	1.1b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(cbrt.f64 B)

series440.0ms (3.7%)

Counts

1 → 12

Calls

1 calls:

439.0ms

(cbrt.f64 B)

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l/_binary64`
374×	`log-prod_binary64`
316×	`distribute-rgt-neg-in_binary64`
314×	`distribute-lft-neg-in_binary64`
287×	`*-commutative_binary64`

Counts

25 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	141
1	38	137
2	86	137
3	208	137
4	626	133
5	1904	133
6	2565	133
7	3552	133
8	4861	133

prune319.0ms (2.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	500	2	502
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	501	10	511

Error

0.2b

Counts

511 → 10

Alt Table

Status	Error	Program
	19.5b	(*.f64 180 (/.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 C A)) B))) PI.f64))
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 B B) C) (.f64 A A)) (/.f64 (.f64 B B) A))) B)) PI.f64))
✓	12.3b	(*.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))))
	48.4b	(.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (*.f64 B B) C)) B)))))
	47.3b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) PI.f64))
	47.0b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) PI.f64))
	47.4b	(.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (.f64 1/2 (/.f64 B A))))))
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) (*.f64 (cbrt.f64 B) (cbrt.f64 B))) (cbrt.f64 B))) PI.f64))
▶	12.8b	(.f64 180 (/.f64 (atan.f64 (/.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 B)) (cbrt.f64 (cbrt.f64 B))) (cbrt.f64 (cbrt.f64 B))) (cbrt.f64 B))) (cbrt.f64 B))) PI.f64))
	54.3b	(.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (fma.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (+.f64 (/.f64 B A) (/.f64 (.f64 B (.f64 C C)) (pow.f64 A 3)))) (*.f64 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) -1/8))))))

Compiler

Compiled 7931 to 3287 computations (58.6% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 B)
	0.6b	(cbrt.f64 B)
	0.6b	(cbrt.f64 B)
	1.1b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune347.0ms (2.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	1844	0	1844
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	1844	10	1854

Error

0.2b

Counts

1854 → 10

Alt Table

Status	Error	Program
	19.5b	(*.f64 180 (/.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 C A)) B))) PI.f64))
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 B B) C) (.f64 A A)) (/.f64 (.f64 B B) A))) B)) PI.f64))
✓	12.3b	(*.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))))
	48.4b	(.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (*.f64 B B) C)) B)))))
	47.3b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) PI.f64))
	47.0b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) PI.f64))
	47.4b	(.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (.f64 1/2 (/.f64 B A))))))
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) (*.f64 (cbrt.f64 B) (cbrt.f64 B))) (cbrt.f64 B))) PI.f64))
✓	12.8b	(.f64 180 (/.f64 (atan.f64 (/.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 B)) (cbrt.f64 (cbrt.f64 B))) (cbrt.f64 (cbrt.f64 B))) (cbrt.f64 B))) (cbrt.f64 B))) PI.f64))
	54.3b	(.f64 180 (/.f64 1 (/.f64 PI.f64 (atan.f64 (fma.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (+.f64 (/.f64 B A) (/.f64 (.f64 B (.f64 C C)) (pow.f64 A 3)))) (*.f64 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) -1/8))))))

Compiler

Compiled 9423 to 3295 computations (65% saved)

regimes1.6s (13.1%)

Accuracy

Total 10.9b remaining (96.5%)

Threshold costs 0b (0%)

Compiler

Compiled 16067 to 11566 computations (28% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
8×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	155
1	57	155
2	70	155
3	78	155
4	82	155
5	81	155

end3.0ms (0%)

Compiler: Compiled 103 to 54 computations (47.6% saved)

sample5.5s (45.3%)

Algorithm

1×

intervals

Results

1.5s	860×	body	4096	valid
1.3s	5422×	body	128	valid
1.1s	852×	body	2048	valid
497.0ms	493×	body	1024	valid
191.0ms	253×	body	512	valid
59.0ms	120×	body	256	valid

Compiler

Compiled 363 to 237 computations (34.7% saved)

Details

analyze665.0ms (5.5%)

sample162.0ms (1.3%)

simplify81.0ms (0.7%)

prune9.0ms (0.1%)

localize20.0ms (0.2%)

rewrite74.0ms (0.6%)

series339.0ms (2.8%)

simplify389.0ms (3.2%)

prune524.0ms (4.4%)

localize21.0ms (0.2%)

rewrite22.0ms (0.2%)

series82.0ms (0.7%)

simplify633.0ms (5.3%)

prune622.0ms (5.2%)

localize26.0ms (0.2%)

rewrite2.0ms (0%)

series440.0ms (3.7%)

simplify110.0ms (0.9%)

prune319.0ms (2.6%)

localize34.0ms (0.3%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify51.0ms (0.4%)

prune347.0ms (2.9%)

regimes1.6s (13.1%)

bsearch8.0ms (0.1%)

simplify14.0ms (0.1%)

end3.0ms (0%)

sample5.5s (45.3%)

Profiling