Details

analyze331.0ms (4.1%)

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
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)

sample3.9s (49.3%)

Results

1.2s	5649×	body	128	valid
1.2s	887×	body	4096	valid
871.0ms	847×	body	2048	valid
419.0ms	516×	body	1024	valid
145.0ms	236×	body	512	valid
50.0ms	121×	body	256	valid

Compiler

Compiled 80 to 62 computations (22.5% saved)

simplify65.0ms (0.8%)

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

15.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	29.1b	(.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)))
▶	15.5b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))

Status

Error

Program

29.1b

(*.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)))

▶

15.5b

(*.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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series227.0ms (2.8%)

Counts

4 → 144

Calls

4 calls:

81.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
64.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
52.0ms	(hypot.f64 B (-.f64 C A))
29.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

rewrite34.0ms (0.4%)

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 → 137

Calls

4 calls:

9.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
7.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
5.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))
0.0ms	(hypot.f64 B (-.f64 C A))

simplify297.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-def_binary64`
373×	`associate-/l*_binary64`
264×	`sub-neg_binary64`
257×	`times-frac_binary64`
190×	`+-commutative_binary64`

Counts

281 → 387

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	740	10235
1	2203	8926
2	5210	8926

prune412.0ms (5.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	379	8	387
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	381	8	389

Error

0.6b

Counts

389 → 8

Alt Table

Status	Error	Program
	41.7b	(.f64 180 (/.f64 (atan.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 C B) (pow.f64 A 2))) (.f64 1/2 (/.f64 B A)))) (PI.f64)))
	46.0b	(.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)))
	51.7b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	49.9b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
	41.5b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
	19.3b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	46.8b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
▶	15.7b	(*.f64 180 (expm1.f64 (log1p.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))

Compiler

Compiled 14918 to 6922 computations (53.6% saved)

localize14.0ms (0.2%)

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 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))
✓	0.1b	(expm1.f64 (log1p.f64 (/.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)))

series31.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

30.0ms

(expm1.f64 (log1p.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))))

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

900×	`times-frac_binary64`
866×	`unswap-sqr_binary64`
581×	`fma-def_binary64`
565×	`associate-/l*_binary64`
562×	`fma-neg_binary64`

Counts

47 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	1106
1	53	1061
2	116	1061
3	245	1061
4	445	1061
5	797	1061
6	1242	1061
7	1759	1061
8	4328	1061
9	5183	1061

prune285.0ms (3.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	336	8	344

Error

0.6b

Counts

344 → 8

Alt Table

Status	Error	Program
	41.7b	(.f64 180 (/.f64 (atan.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 C B) (pow.f64 A 2))) (.f64 1/2 (/.f64 B A)))) (PI.f64)))
	46.0b	(.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)))
	51.7b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	49.9b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
	41.5b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
▶	19.3b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	46.8b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
✓	15.7b	(*.f64 180 (expm1.f64 (log1p.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))

Compiler

Compiled 12722 to 5654 computations (55.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64))
✓	0.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
✓	0.3b	(-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A))))
✓	1.1b	(+.f64 A (hypot.f64 B (-.f64 C A)))

series240.0ms (3%)

Counts

4 → 80

Calls

4 calls:

102.0ms	(+.f64 A (hypot.f64 B (-.f64 C A)))
65.0ms	(-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A))))
43.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
29.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
13×	`associate-r_binary64`

Counts

4 → 117

Calls

4 calls:

6.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
5.0ms	(-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A))))
5.0ms	(+.f64 A (hypot.f64 B (-.f64 C A)))
4.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64))

simplify151.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-neg_binary64`
352×	`fma-def_binary64`
209×	`associate--l+_binary64`
199×	`associate--r+_binary64`
188×	`associate-+r+_binary64`

Counts

197 → 260

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	454	7027
1	1351	6040
2	4861	6039
3	5378	6039

prune225.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	260	8	268

Error

0.6b

Counts

268 → 8

Alt Table

Status	Error	Program
	41.7b	(.f64 180 (/.f64 (atan.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 C B) (pow.f64 A 2))) (.f64 1/2 (/.f64 B A)))) (PI.f64)))
	46.0b	(.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)))
	49.9b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
	44.7b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (sqrt.f64 C) (sqrt.f64 C) (neg.f64 (+.f64 A (hypot.f64 B (-.f64 C A))))) B)) (PI.f64)))
▶	41.5b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
✓	19.3b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	46.8b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
✓	15.7b	(*.f64 180 (expm1.f64 (log1p.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))

Compiler

Compiled 9608 to 4366 computations (54.6% saved)

localize13.0ms (0.2%)

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))
✓	2.4b	(+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))
✓	7.5b	(/.f64 (*.f64 A A) B)
✓	8.6b	(/.f64 C (/.f64 (*.f64 A A) B))

series178.0ms (2.2%)

Counts

4 → 132

Calls

4 calls:

65.0ms	(/.f64 C (/.f64 (*.f64 A A) B))
57.0ms	(+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))
43.0ms	(/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (/.f64 B A)))) (PI.f64))
13.0ms	(/.f64 (*.f64 A A) B)

rewrite45.0ms (0.6%)

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:

20.0ms	(+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))
6.0ms	(/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (/.f64 B A)))) (PI.f64))
5.0ms	(/.f64 C (/.f64 (*.f64 A A) B))
4.0ms	(/.f64 (*.f64 A A) B)

simplify203.0ms (2.5%)

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

prune140.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	213	4	217
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	216	9	225

Error

0.6b

Counts

225 → 9

Alt Table

Status	Error	Program
	51.3b	(.f64 180 (exp.f64 (log.f64 (/.f64 (atan.f64 (.f64 (*.f64 (/.f64 B A) (+.f64 (/.f64 C A) 1)) 1/2)) (PI.f64)))))
	44.7b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (sqrt.f64 C) (sqrt.f64 C) (neg.f64 (+.f64 A (hypot.f64 B (-.f64 C A))))) B)) (PI.f64)))
	40.6b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (*.f64 (+.f64 (/.f64 C (pow.f64 A 2)) (/.f64 1 A)) B))) (PI.f64)))
	49.9b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
	40.5b	(.f64 180 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (atan.f64 (.f64 (.f64 (/.f64 B A) (+.f64 (/.f64 C A) 1)) 1/2)) (sqrt.f64 (PI.f64)))))
	40.7b	(.f64 180 (/.f64 1 (/.f64 (PI.f64) (atan.f64 (.f64 (*.f64 (/.f64 B A) (+.f64 (/.f64 C A) 1)) 1/2)))))
✓	19.3b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	46.8b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
✓	15.7b	(*.f64 180 (expm1.f64 (log1p.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))

Compiler

Compiled 5818 to 2479 computations (57.4% saved)

regimes761.0ms (9.5%)

Accuracy

Total 11.1b remaining (96.8%)

Threshold costs 0b (0%)

Counts

91 → 2

Compiler

Compiled 12553 to 9501 computations (24.3% saved)

bsearch95.0ms (1.2%)

Steps

Iters	Range		Point
8	-8.816800925899894e+91	-3.7326781509700612e+87	-2.28422592167895e+91

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

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	26	57
1	33	57
2	41	57
3	45	57
4	47	57
5	47	57

end157.0ms (2%)

Compiler: Compiled 261 to 187 computations (28.4% saved)

Details

analyze331.0ms (4.1%)

sample3.9s (49.3%)

simplify65.0ms (0.8%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

series227.0ms (2.8%)

rewrite34.0ms (0.4%)

simplify297.0ms (3.7%)

prune412.0ms (5.1%)

localize14.0ms (0.2%)

series31.0ms (0.4%)

rewrite1.0ms (0%)

simplify98.0ms (1.2%)

prune285.0ms (3.6%)

localize12.0ms (0.2%)

series240.0ms (3%)

rewrite28.0ms (0.3%)

simplify151.0ms (1.9%)

prune225.0ms (2.8%)

localize13.0ms (0.2%)

series178.0ms (2.2%)

rewrite45.0ms (0.6%)

simplify203.0ms (2.5%)

prune140.0ms (1.7%)

regimes761.0ms (9.5%)

bsearch95.0ms (1.2%)

simplify4.0ms (0.1%)

end157.0ms (2%)

Profiling