Details

analyze596.0ms (7.8%)

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)

sample204.0ms (2.7%)

Algorithm

1×

intervals

Results

13.0ms	43×	body	2048	valid
11.0ms	166×	body	128	valid
7.0ms	27×	body	1024	valid
3.0ms	7×	body	4096	valid
2.0ms	8×	body	128	invalid
2.0ms	10×	body	512	valid
1.0ms	19×	body	128	nan
0.0ms	3×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify148.0ms (1.9%)

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

33.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	33.0b	(.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)

localize10.0ms (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)
✓	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	21.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series509.0ms (6.7%)

Counts

3 → 60

Calls

3 calls:

386.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
72.0ms	(/.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))))

rewrite14.0ms (0.2%)

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:

5.0ms	(/.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 (1.3%)

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

prune191.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	159	10	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	10	170

Error

4.3b

Counts

170 → 10

Alt Table

Status	Error	Program
	32.6b	(.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)))
	45.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	44.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	34.5b	(.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a))
	57.0b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
	39.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
▶	32.5b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))
	33.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	44.5b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
	46.9b	(.f64 -1/2 (.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))

Compiler

Compiled 4744 to 2870 computations (39.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)
✓	0.3b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	12.6b	(sqrt.f64 (.f64 a (.f64 c -4)))

series371.0ms (4.8%)

Counts

3 → 28

Calls

3 calls:

205.0ms	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)
144.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
21.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
9×	`pow1_binary64`

Counts

3 → 66

Calls

3 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)))
3.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))

simplify98.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

722×	`associate-/l*_binary64`
598×	`associate-/r*_binary64`
368×	`associate-l_binary64`
333×	`fma-def_binary64`
192×	`associate-*l/_binary64`

Counts

94 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2413
1	440	2262
2	1293	2199
3	4963	2199
4	4997	2199

prune118.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	145	10	155

Error

3.1b

Counts

155 → 10

Alt Table

Status	Error	Program
	32.6b	(.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)))
	45.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	44.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
▶	32.5b	(.f64 -1/2 (.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (/.f64 1 a)))
	46.9b	(.f64 -1/2 (.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	39.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
✓	32.5b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))
	45.1b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))) a))
	34.5b	(.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a))
	44.5b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))

Compiler

Compiled 4151 to 2647 computations (36.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) (/.f64 1 a))
	0.3b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
	12.6b	(sqrt.f64 (.f64 a (.f64 c -4)))

series217.0ms (2.8%)

Counts

1 → 14

Calls

1 calls:

216.0ms

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

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 43

Calls

1 calls:

8.0ms

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

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

585×	`times-frac_binary64`
373×	`associate-r_binary64`
361×	`associate-l_binary64`
338×	`associate-/l*_binary64`
277×	`associate-/r*_binary64`

Counts

57 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	1680
1	367	1510
2	1099	1477
3	4614	1475
4	4947	1475

prune126.0ms (1.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	159	10	169

Error

3.1b

Counts

169 → 10

Alt Table

Status	Error	Program
▶	32.6b	(.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)))
	45.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	44.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
✓	32.5b	(.f64 -1/2 (.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (/.f64 1 a)))
	46.9b	(.f64 -1/2 (.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	39.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
✓	32.5b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))
	45.1b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))) a))
	34.5b	(.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a))
	44.5b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))

Compiler

Compiled 4655 to 3046 computations (34.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)
✓	0.2b	(.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))
	0.3b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
	12.6b	(sqrt.f64 (.f64 a (.f64 c -4)))

series715.0ms (9.3%)

Counts

2 → 20

Calls

2 calls:

474.0ms

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

241.0ms

(*.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))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
50×	`add-sqr-sqrt_binary64`
46×	`times-frac_binary64`
37×	`sqrt-prod_binary64`
34×	`add-cube-cbrt_binary64`

Counts

2 → 105

Calls

2 calls:

16.0ms

(*.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))

5.0ms

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

simplify137.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

775×	`times-frac_binary64`
668×	`fma-def_binary64`
654×	`associate-/l*_binary64`
366×	`associate-/r*_binary64`
214×	`associate-/l/_binary64`

Counts

125 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	4809
1	505	4260
2	1490	4114
3	4783	4114
4	5305	4114

prune292.0ms (3.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	316	10	326

Error

3.1b

Counts

326 → 10

Alt Table

Status	Error	Program
✓	32.6b	(.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)))
	45.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	44.7b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
✓	32.5b	(.f64 -1/2 (.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (/.f64 1 a)))
	46.9b	(.f64 -1/2 (.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	39.9b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
✓	32.5b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))
	45.1b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))) a))
	34.5b	(.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a))
	44.5b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))

Compiler

Compiled 12499 to 8131 computations (34.9% saved)

regimes1.7s (22.8%)

Accuracy

Total 7.5b remaining (72.5%)

Threshold costs 0b (0%)

Counts

111 → 6

Compiler

Compiled 10112 to 7014 computations (30.6% saved)

bsearch147.0ms (1.9%)

Steps

Iters	Range		Point
9	5.89436712264605e+54	3.9447224865212797e+62	3.892507664467116e+62
7	4.223826937588207e-185	1.2832745259139112e-183	1.2651552890294784e-183
7	-5.23600730124732e-135	-2.7678995838009516e-136	-5.1898591130371494e-135
8	-5.1506693407233705e-109	-7.0835872038617945e-112	-1.094625315287698e-111
6	-8.979613940424115e-51	-1.1973829779341131e-51	-2.5960673063938545e-51

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
5×	`+-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	48	134
1	64	134
2	70	134
3	74	134
4	77	134
5	78	134
6	77	134

end2.0ms (0%)

Compiler: Compiled 94 to 61 computations (35.1% saved)

sample1.7s (22.6%)

Algorithm

1×

intervals

Results

382.0ms	5226×	body	128	valid
368.0ms	1114×	body	2048	valid
188.0ms	731×	body	1024	valid
165.0ms	392×	body	4096	valid
72.0ms	354×	body	512	valid
42.0ms	670×	body	128	nan
25.0ms	388×	body	128	invalid
23.0ms	183×	body	256	valid

Compiler

Compiled 315 to 214 computations (32.1% saved)

Details

analyze596.0ms (7.8%)

sample204.0ms (2.7%)

simplify148.0ms (1.9%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series509.0ms (6.7%)

rewrite14.0ms (0.2%)

simplify103.0ms (1.3%)

prune191.0ms (2.5%)

localize9.0ms (0.1%)

series371.0ms (4.8%)

rewrite14.0ms (0.2%)

simplify98.0ms (1.3%)

prune118.0ms (1.5%)

localize10.0ms (0.1%)

series217.0ms (2.8%)

rewrite12.0ms (0.2%)

simplify81.0ms (1.1%)

prune126.0ms (1.6%)

localize11.0ms (0.1%)

series715.0ms (9.3%)

rewrite34.0ms (0.4%)

simplify137.0ms (1.8%)

prune292.0ms (3.8%)

regimes1.7s (22.8%)

bsearch147.0ms (1.9%)

simplify7.0ms (0.1%)

end2.0ms (0%)

sample1.7s (22.6%)

Profiling