Details

analyze315.0ms (3.3%)

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)

sample4.0s (42.6%)

Results

1.2s	5629×	body	128	valid
1.1s	878×	body	4096	valid
1.0s	875×	body	2048	valid
414.0ms	503×	body	1024	valid
146.0ms	251×	body	512	valid
55.0ms	120×	body	256	valid

Compiler

Compiled 80 to 62 computations (22.5% saved)

simplify62.0ms (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

prune5.0ms (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

13.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.2b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
	29.3b	(.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)))

Status

Error

Program

▶

13.2b

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

29.3b

(*.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)))

Compiler

Compiled 132 to 91 computations (31.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)
✓	0.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
✓	0.5b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series163.0ms (1.7%)

Counts

4 → 144

Calls

4 calls:

56.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
44.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
36.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
26.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64`
37×	`times-frac_binary64`
24×	`prod-diff_binary64`

Counts

4 → 161

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
8.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
7.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
4.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

simplify152.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-def_binary64`
355×	`associate-/l*_binary64`
238×	`times-frac_binary64`
205×	`sub-neg_binary64`
198×	`associate-/r*_binary64`

Counts

305 → 377

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	674	10323
1	1950	9081
2	4971	9081

prune407.0ms (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	370	7	377
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	372	7	379

Error

0.2b

Counts

379 → 7

Alt Table

Status	Error	Program
	15.5b	(.f64 180 (/.f64 (atan.f64 (/.f64 (+.f64 C (-.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 A)) (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	50.1b	(.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)))
	44.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
▶	13.2b	(*.f64 180 (/.f64 1 (/.f64 (PI.f64) (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))))
	54.6b	(.f64 180 (/.f64 (atan.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 B 3) (pow.f64 C 3))) (.f64 1/2 (+.f64 (/.f64 B C) (+.f64 (/.f64 A (/.f64 (.f64 C C) B)) (/.f64 (.f64 (.f64 A A) B) (pow.f64 C 3))))))) (PI.f64)))
	47.4b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	48.8b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))

Compiler

Compiled 13394 to 5268 computations (60.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
✓	0.0b	(*.f64 180 (/.f64 1 (/.f64 (PI.f64) (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))))
	0.5b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series65.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

38.0ms	(*.f64 180 (/.f64 1 (/.f64 (PI.f64) (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))))
27.0ms	(/.f64 1 (/.f64 (PI.f64) (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

147×	`times-frac_binary64`
94×	`add-sqr-sqrt_binary64`
82×	`*-un-lft-identity_binary64`
80×	`add-cube-cbrt_binary64`
44×	`associate-r_binary64`

Counts

2 → 153

Calls

2 calls:

14.0ms	(*.f64 180 (/.f64 1 (/.f64 (PI.f64) (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))))
5.0ms	(/.f64 1 (/.f64 (PI.f64) (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))))

simplify332.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-neg_binary64`
615×	`fma-def_binary64`
407×	`associate-/l/_binary64`
397×	`*-commutative_binary64`
328×	`sqr-pow_binary64`

Counts

225 → 240

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	7180
1	300	6638
2	718	6611
3	1791	6611
4	2511	6611
5	3000	6611
6	3743	6611
7	4456	6611
8	4632	6611
9	5142	6611

prune391.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	502	0	502
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	502	7	509

Error

0.2b

Counts

509 → 7

Alt Table

Status	Error	Program
▶	15.5b	(.f64 180 (/.f64 (atan.f64 (/.f64 (+.f64 C (-.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 A)) (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	50.1b	(.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)))
	44.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
✓	13.2b	(*.f64 180 (/.f64 1 (/.f64 (PI.f64) (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))))
	54.6b	(.f64 180 (/.f64 (atan.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 B 3) (pow.f64 C 3))) (.f64 1/2 (+.f64 (/.f64 B C) (+.f64 (/.f64 A (/.f64 (.f64 C C) B)) (/.f64 (.f64 (.f64 A A) B) (pow.f64 C 3))))))) (PI.f64)))
	47.4b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	48.8b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))

Compiler

Compiled 18803 to 7085 computations (62.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 A) (cbrt.f64 A))
✓	0.6b	(cbrt.f64 A)
✓	0.9b	(+.f64 C (-.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 A)) (hypot.f64 B (-.f64 C A))))
✓	6.9b	(-.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 A)) (hypot.f64 B (-.f64 C A)))

series165.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

49.0ms	(+.f64 C (-.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 A)) (hypot.f64 B (-.f64 C A))))
42.0ms	(-.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 A)) (hypot.f64 B (-.f64 C A)))
37.0ms	(*.f64 (cbrt.f64 A) (cbrt.f64 A))
36.0ms	(cbrt.f64 A)

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
19×	`cbrt-prod_binary64`
18×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 101

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 A) (cbrt.f64 A))
6.0ms	(+.f64 C (-.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 A)) (hypot.f64 B (-.f64 C A))))
4.0ms	(-.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 A)) (hypot.f64 B (-.f64 C A)))
1.0ms	(cbrt.f64 A)

simplify116.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

659×	`fma-neg_binary64`
441×	`fma-def_binary64`
255×	`associate-l_binary64`
248×	`associate-r_binary64`
232×	`associate--r+_binary64`

Counts

197 → 265

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	433	4840
1	1254	4303
2	4898	4302
3	5458	4302

prune256.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	297	7	304

Error

0.2b

Counts

304 → 7

Alt Table

Status	Error	Program
✓	15.5b	(.f64 180 (/.f64 (atan.f64 (/.f64 (+.f64 C (-.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 A)) (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	50.1b	(.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)))
▶	44.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
✓	13.2b	(*.f64 180 (/.f64 1 (/.f64 (PI.f64) (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))))
	54.6b	(.f64 180 (/.f64 (atan.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 B 3) (pow.f64 C 3))) (.f64 1/2 (+.f64 (/.f64 B C) (+.f64 (/.f64 A (/.f64 (.f64 C C) B)) (/.f64 (.f64 (.f64 A A) B) (pow.f64 C 3))))))) (PI.f64)))
	47.4b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	48.8b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))

Compiler

Compiled 10947 to 5204 computations (52.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (/.f64 B A)))) (PI.f64))
✓	4.9b	(+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))
✓	6.7b	(/.f64 (*.f64 A A) B)
✓	7.9b	(/.f64 C (/.f64 (*.f64 A A) B))

series144.0ms (1.5%)

Counts

4 → 132

Calls

4 calls:

49.0ms	(/.f64 C (/.f64 (*.f64 A A) B))
45.0ms	(+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))
38.0ms	(/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (/.f64 B A)))) (PI.f64))
11.0ms	(/.f64 (*.f64 A A) B)

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
44×	`add-cube-cbrt_binary64`
26×	`fma-def_binary64`

Counts

4 → 144

Calls

4 calls:

19.0ms	(+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))
7.0ms	(/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (/.f64 B A)))) (PI.f64))
6.0ms	(/.f64 C (/.f64 (*.f64 A A) B))
4.0ms	(/.f64 (*.f64 A A) B)

simplify150.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

678×	`times-frac_binary64`
485×	`associate-/l*_binary64`
440×	`associate-/l/_binary64`
432×	`associate-*l/_binary64`
429×	`associate-/r/_binary64`

Counts

276 → 217

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	212	4620
1	453	4188
2	1287	4043
3	4538	4040
4	4973	4040
5	4957	4040

prune147.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	214	3	217
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	215	9	224

Error

0.2b

Counts

224 → 9

Alt Table

Status	Error	Program
	54.6b	(.f64 180 (/.f64 (atan.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 B 3) (pow.f64 C 3))) (.f64 1/2 (+.f64 (/.f64 B C) (+.f64 (/.f64 A (/.f64 (.f64 C C) B)) (/.f64 (.f64 (.f64 A A) B) (pow.f64 C 3))))))) (PI.f64)))
	48.1b	(.f64 180 (cbrt.f64 (pow.f64 (/.f64 (atan.f64 (.f64 (*.f64 (/.f64 B A) (+.f64 (/.f64 C A) 1)) 1/2)) (PI.f64)) 3)))
✓	15.5b	(.f64 180 (/.f64 (atan.f64 (/.f64 (+.f64 C (-.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 A)) (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	50.1b	(.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)))
	44.0b	(.f64 180 (.f64 (/.f64 (.f64 (cbrt.f64 (atan.f64 (.f64 (.f64 (/.f64 B A) (+.f64 (/.f64 C A) 1)) 1/2))) (cbrt.f64 (atan.f64 (.f64 (.f64 (/.f64 B A) (+.f64 (/.f64 C A) 1)) 1/2)))) (sqrt.f64 (PI.f64))) (/.f64 (cbrt.f64 (atan.f64 (.f64 (*.f64 (/.f64 B A) (+.f64 (/.f64 C A) 1)) 1/2))) (sqrt.f64 (PI.f64)))))
✓	13.2b	(*.f64 180 (/.f64 1 (/.f64 (PI.f64) (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))))
	44.1b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (*.f64 (+.f64 (/.f64 C (pow.f64 A 2)) (/.f64 1 A)) B))) (PI.f64)))
	47.4b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	48.8b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))

Compiler

Compiled 5878 to 2513 computations (57.2% saved)

regimes2.1s (22.2%)

Accuracy

Total 11.3b remaining (97%)

Threshold costs 0b (0%)

Counts

237 → 2

Compiler

Compiled 37319 to 26056 computations (30.2% saved)

bsearch82.0ms (0.9%)

Steps

Iters	Range		Point
6	-8.315152306477164e+139	-1.7599491337010797e+139	-3.205797192814889e+139

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	59
1	38	59
2	45	59
3	49	59
4	51	59
5	50	59

end161.0ms (1.7%)

Compiler: Compiled 323 to 223 computations (31% saved)

Details

analyze315.0ms (3.3%)

sample4.0s (42.6%)

simplify62.0ms (0.7%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

series163.0ms (1.7%)

rewrite43.0ms (0.5%)

simplify152.0ms (1.6%)

prune407.0ms (4.3%)

localize13.0ms (0.1%)

series65.0ms (0.7%)

rewrite42.0ms (0.4%)

simplify332.0ms (3.5%)

prune391.0ms (4.1%)

localize15.0ms (0.2%)

series165.0ms (1.7%)

rewrite24.0ms (0.3%)

simplify116.0ms (1.2%)

prune256.0ms (2.7%)

localize11.0ms (0.1%)

series144.0ms (1.5%)

rewrite44.0ms (0.5%)

simplify150.0ms (1.6%)

prune147.0ms (1.6%)

regimes2.1s (22.2%)

bsearch82.0ms (0.9%)

simplify3.0ms (0%)

end161.0ms (1.7%)

Profiling