Details

analyze630.0ms (6.7%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.4s (25.6%)

Results

721.0ms	5325×	body	128	valid
616.0ms	1153×	body	2048	valid
313.0ms	758×	body	1024	valid
260.0ms	403×	body	4096	valid
140.0ms	1110×	body	128	invalid
127.0ms	404×	body	512	valid
47.0ms	213×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify147.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

2079×	`fma-neg_binary64`
1006×	`fma-def_binary64`
919×	`div-sub_binary64`
626×	`distribute-rgt-in_binary64`
435×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	95	24
3	227	22
4	357	22
5	614	22
6	1103	22
7	1373	22
8	1636	22
9	2330	22
10	3187	22
11	2880	22
12	2827	22
13	2896	22
14	2922	22
15	3797	22
16	4824	22
17	5240	22

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

36.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	36.2b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))

Compiler

Compiled 71 to 46 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	0.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	24.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series165.0ms (1.8%)

Counts

3 → 60

Calls

3 calls:

73.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
51.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
41.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
5×	`distribute-lft-out_binary64`

Counts

3 → 67

Calls

3 calls:

4.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
539×	`associate-/l*_binary64`
458×	`fma-def_binary64`
246×	`fma-neg_binary64`
189×	`cancel-sign-sub-inv_binary64`

Counts

127 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	3311
1	510	3170
2	1534	3008
3	4840	3008
4	4954	3008

prune141.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	158	11	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Error

6.2b

Counts

170 → 11

Alt Table

Status	Error	Program
	38.2b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	36.6b	(.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))))
	36.5b	(.f64 -1/2 (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) (cbrt.f64 a))))
	49.6b	(.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a) 3)))
	56.0b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
	36.1b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)))
	48.8b	(.f64 -1/2 (exp.f64 (log.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))))
	46.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	36.1b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
▶	36.0b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))
	46.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))

Compiler

Compiled 4780 to 2902 computations (39.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))
✓	0.0b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	0.1b	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)
✓	14.6b	(sqrt.f64 (.f64 a (.f64 c -4)))

series453.0ms (4.8%)

Counts

4 → 42

Calls

4 calls:

196.0ms	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)
131.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
108.0ms	(hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))
18.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
10×	`pow1_binary64`

Counts

4 → 76

Calls

4 calls:

4.0ms	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)
3.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))
2.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
0.0ms	(hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Rules

750×	`associate-/l*_binary64`
718×	`fma-def_binary64`
617×	`associate-/r*_binary64`
201×	`cancel-sign-sub-inv_binary64`
199×	`associate-*l/_binary64`

Counts

118 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	2952
1	513	2787
2	1472	2716
3	4742	2712
4	5026	2712

prune142.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	182	3	185
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	184	12	196

Error

3.1b

Counts

196 → 12

Alt Table

Status	Error	Program
	38.2b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	36.6b	(.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))))
	36.5b	(.f64 -1/2 (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) (cbrt.f64 a))))
	49.6b	(.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a) 3)))
	36.1b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)))
	48.8b	(.f64 -1/2 (exp.f64 (log.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))))
▶	36.1b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	47.4b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))) a))
	38.8b	(*.f64 -1/2 (/.f64 2 (/.f64 b (/.f64 c 1))))
	46.1b	(*.f64 -1/2 (fma.f64 (/.f64 b a) 2 (/.f64 -2 (/.f64 b (/.f64 c 1)))))
✓	36.0b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))
	46.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))

Compiler

Compiled 5236 to 3363 computations (35.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	0.1b	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
✓	0.1b	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
	14.6b	(sqrt.f64 (.f64 a (.f64 c -4)))

series541.0ms (5.8%)

Counts

2 → 28

Calls

2 calls:

354.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
187.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
94×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
62×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

2 → 133

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
3.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))

simplify111.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

704×	`associate-/l*_binary64`
646×	`associate-/r*_binary64`
360×	`fma-def_binary64`
321×	`associate-/r/_binary64`
167×	`cancel-sign-sub-inv_binary64`

Counts

161 → 224

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	5545
1	542	5019
2	1711	4960
3	5020	4960

prune238.0ms (2.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	290	3	293
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	292	13	305

Error

3.1b

Counts

305 → 13

Alt Table

Status	Error	Program
	38.2b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	36.6b	(.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))))
▶	36.1b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))))
	47.4b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))) a))
	36.1b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)))
	48.8b	(.f64 -1/2 (exp.f64 (log.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))))
	46.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	47.4b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 -4 c))))))))
	44.6b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 (.f64 b a) (.f64 -4 (*.f64 a c))) -2))))
	49.6b	(.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a) 3)))
	38.8b	(*.f64 -1/2 (/.f64 2 (/.f64 b (/.f64 c 1))))
	46.1b	(*.f64 -1/2 (fma.f64 (/.f64 b a) 2 (/.f64 -2 (/.f64 b (/.f64 c 1)))))
✓	36.0b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))

Compiler

Compiled 9275 to 6108 computations (34.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
✓	0.1b	(/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
✓	0.1b	(.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
	14.6b	(sqrt.f64 (.f64 a (.f64 c -4)))

series858.0ms (9.2%)

Counts

3 → 42

Calls

3 calls:

348.0ms

(*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))

315.0ms

(/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))

194.0ms

(/.f64 1 (*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-exp-log_binary64`
38×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`

Counts

3 → 124

Calls

3 calls:

7.0ms

(*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))

6.0ms

(/.f64 1 (*.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))

4.0ms

(/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))

simplify127.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

445×	`fma-neg_binary64`
422×	`fma-def_binary64`
396×	`associate-*l/_binary64`
341×	`associate-*r/_binary64`
234×	`cancel-sign-sub-inv_binary64`

Counts

166 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	237	4541
1	633	3918
2	2142	3888
3	4609	3882
4	4957	3882

prune205.0ms (2.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	256	13	269

Error

3.1b

Counts

269 → 13

Alt Table

Status	Error	Program
	38.2b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	36.6b	(.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))))
✓	36.1b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))))
	47.4b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))) a))
	43.3b	(.f64 -1/2 (/.f64 1 (.f64 a (fma.f64 -2 (/.f64 b (.f64 -4 (.f64 a c))) (/.f64 -1/2 b)))))
	36.1b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)))
	48.8b	(.f64 -1/2 (exp.f64 (log.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))))
	46.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	47.4b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 -4 c))))))))
	49.6b	(.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a) 3)))
	38.8b	(*.f64 -1/2 (/.f64 2 (/.f64 b (/.f64 c 1))))
	46.1b	(*.f64 -1/2 (fma.f64 (/.f64 b a) 2 (/.f64 -2 (/.f64 b (/.f64 c 1)))))
✓	36.0b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))

Compiler

Compiled 7638 to 5266 computations (31.1% saved)

regimes2.6s (27.8%)

Accuracy

Total 7.8b remaining (71.7%)

Threshold costs 0b (0%)

Counts

156 → 3

Compiler

Compiled 14984 to 10510 computations (29.9% saved)

bsearch80.0ms (0.9%)

Steps

Iters	Range		Point
8	1.5379008350198317e+75	6.255524633154715e+77	5.864249003435115e+77
9	-4.6005944062657114e-126	-4.2261503208602204e-134	-4.5237376809518334e-126

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	60
1	37	60
2	44	60
3	48	60
4	51	60
5	52	60
6	52	60

end184.0ms (2%)

Compiler: Compiled 336 to 238 computations (29.2% saved)

Details

analyze630.0ms (6.7%)

sample2.4s (25.6%)

simplify147.0ms (1.6%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series165.0ms (1.8%)

rewrite12.0ms (0.1%)

simplify103.0ms (1.1%)

prune141.0ms (1.5%)

localize12.0ms (0.1%)

series453.0ms (4.8%)

rewrite13.0ms (0.1%)

simplify97.0ms (1%)

prune142.0ms (1.5%)

localize11.0ms (0.1%)

series541.0ms (5.8%)

rewrite25.0ms (0.3%)

simplify111.0ms (1.2%)

prune238.0ms (2.5%)

localize11.0ms (0.1%)

series858.0ms (9.2%)

rewrite28.0ms (0.3%)

simplify127.0ms (1.4%)

prune205.0ms (2.2%)

regimes2.6s (27.8%)

bsearch80.0ms (0.9%)

simplify4.0ms (0%)

end184.0ms (2%)

Profiling