Details

analyze630.0ms (7.2%)

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)

sample2.7s (31.1%)

Results

1.0s	1169×	body	2048	valid
697.0ms	5364×	body	128	valid
317.0ms	775×	body	1024	valid
251.0ms	414×	body	4096	valid
123.0ms	1010×	body	128	invalid
104.0ms	341×	body	512	valid
41.0ms	193×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify143.0ms (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

32.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.9b	(.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 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	21.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series161.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

66.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
45.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
40.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
9.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 77

Calls

4 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)))
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Rules

834×	`times-frac_binary64`
539×	`associate-/l*_binary64`
468×	`fma-def_binary64`
198×	`cancel-sign-sub-inv_binary64`
125×	`associate-/r/_binary64`

Counts

173 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	3876
1	521	3658
2	1578	3494
3	5011	3494

prune159.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	183	10	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	183	11	194

Error

4.5b

Counts

194 → 11

Alt Table

Status	Error	Program
	33.3b	(.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))))))))
	33.3b	(.f64 -1/2 (.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) (/.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) a)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
▶	33.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
✓	32.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	57.4b	(.f64 -1/2 (log.f64 (exp.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4))))) a))))
	50.6b	(.f64 -1/2 (exp.f64 (-.f64 (log.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (log.f64 a))))
	46.8b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	43.6b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) a))
	47.6b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))

Compiler

Compiled 5277 to 3195 computations (39.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
✓	0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	21.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series264.0ms (3%)

Counts

2 → 40

Calls

2 calls:

195.0ms	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
69.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))

rewrite26.0ms (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 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
4.0ms	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))

simplify111.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

712×	`associate-/l*_binary64`
631×	`associate-/r*_binary64`
411×	`fma-def_binary64`
324×	`associate-/r/_binary64`
172×	`cancel-sign-sub-inv_binary64`

Counts

173 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	5780
1	538	5307
2	1750	5032
3	5356	5032

prune239.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	310	4	314
Fresh	5	4	9
Picked	1	0	1
Done	0	1	1
Total	316	9	325

Error

4.3b

Counts

325 → 9

Alt Table

Status	Error	Program
	43.6b	(.f64 -1/2 (.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) a) (/.f64 1 (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
✓	32.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	57.4b	(.f64 -1/2 (log.f64 (exp.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4))))) a))))
	50.6b	(.f64 -1/2 (exp.f64 (-.f64 (log.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (log.f64 a))))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
▶	33.0b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))))
	38.2b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b)))))
	46.9b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (/.f64 a b))))

Compiler

Compiled 9686 to 5998 computations (38.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
✓	0.2b	(/.f64 1 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	21.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series253.0ms (2.9%)

Counts

2 → 40

Calls

2 calls:

188.0ms	(.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
64.0ms	(/.f64 1 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
18×	`div-exp_binary64`

Counts

2 → 85

Calls

2 calls:

8.0ms	(.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
7.0ms	(/.f64 1 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

494×	`fma-neg_binary64`
330×	`fma-def_binary64`
281×	`associate-*l/_binary64`
239×	`*-commutative_binary64`
223×	`associate-*r/_binary64`

Counts

125 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	3287
1	518	2853
2	1783	2723
3	4102	2723
4	4980	2723

prune181.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	250	10	260

Error

4.3b

Counts

260 → 10

Alt Table

Status	Error	Program
▶	38.2b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b)))))
	46.9b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b b)))))
	43.6b	(.f64 -1/2 (.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) a) (/.f64 1 (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
✓	32.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	57.4b	(.f64 -1/2 (log.f64 (exp.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4))))) a))))
	50.6b	(.f64 -1/2 (exp.f64 (-.f64 (log.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (log.f64 a))))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
✓	33.0b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))))
	46.9b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (/.f64 a b))))

Compiler

Compiled 7442 to 4861 computations (34.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 b c) (/.f64 a b))
✓	0.0b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b)))))
✓	0.7b	(/.f64 1 (*.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))))

series86.0ms (1%)

Counts

3 → 81

Calls

3 calls:

34.0ms	(-.f64 (/.f64 b c) (/.f64 a b))
29.0ms	(/.f64 1 (*.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))))
22.0ms	(.f64 -1/2 (/.f64 1 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b)))))

rewrite75.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

264×	`times-frac_binary64`
218×	`add-sqr-sqrt_binary64`
210×	`*-un-lft-identity_binary64`
204×	`add-cube-cbrt_binary64`
169×	`prod-diff_binary64`

Counts

3 → 285

Calls

3 calls:

15.0ms	(.f64 -1/2 (/.f64 1 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b)))))
14.0ms	(-.f64 (/.f64 b c) (/.f64 a b))
11.0ms	(/.f64 1 (*.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))))

simplify263.0ms (3%)

Algorithm

1×	egg-herbie

Rules

878×	`times-frac_binary64`
213×	`fma-neg_binary64`
175×	`exp-prod_binary64`
164×	`fma-udef_binary64`
163×	`unsub-neg_binary64`

Counts

366 → 367

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	444	11769
1	1037	7716
2	2643	6432
3	4529	6406
4	4902	6406
5	4861	6406

prune227.0ms (2.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	363	4	367
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	364	13	377

Error

4.3b

Counts

377 → 13

Alt Table

Status	Error	Program
	57.4b	(.f64 -1/2 (log.f64 (exp.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4))))) a))))
	54.7b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (log.f64 (exp.f64 (-.f64 (/.f64 b c) (/.f64 a b)))))))
✓	38.2b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b)))))
	46.9b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b b)))))
	50.9b	(exp.f64 (log.f64 (/.f64 -1 (-.f64 (/.f64 b c) (/.f64 a b)))))
	38.7b	(neg.f64 (/.f64 c b))
	43.6b	(.f64 -1/2 (.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) a) (/.f64 1 (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
✓	32.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	50.6b	(.f64 -1/2 (exp.f64 (-.f64 (log.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (log.f64 a))))
	38.9b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (cbrt.f64 b) (cbrt.f64 c)) (neg.f64 (.f64 (cbrt.f64 (/.f64 a b)) (.f64 (cbrt.f64 (/.f64 a b)) (cbrt.f64 (/.f64 a b)))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 a b))) (.f64 (cbrt.f64 (/.f64 a b)) (cbrt.f64 (/.f64 a b))) (.f64 (cbrt.f64 (/.f64 a b)) (*.f64 (cbrt.f64 (/.f64 a b)) (cbrt.f64 (/.f64 a b)))))))))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
✓	33.0b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))))
	46.9b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (/.f64 a b))))

Compiler

Compiled 13193 to 4681 computations (64.5% saved)

regimes2.7s (31.2%)

Accuracy

Total 5.3b remaining (49.2%)

Threshold costs 0b (0%)

Counts

199 → 3

Compiler

Compiled 21792 to 13738 computations (37% saved)

bsearch51.0ms (0.6%)

Steps

Iters	Range		Point
6	3.8657611513446867e+90	2.928767619032365e+91	2.818024375880192e+91
5	-1.1401732337828577e-138	-2.8577058786826562e-139	-1.1192253259106201e-138

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
2×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	59
1	40	57
2	48	57
3	53	57
4	57	57
5	58	57
6	56	57

end168.0ms (1.9%)

Compiler: Compiled 362 to 227 computations (37.3% saved)

Details

analyze630.0ms (7.2%)

sample2.7s (31.1%)

simplify143.0ms (1.6%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series161.0ms (1.8%)

rewrite15.0ms (0.2%)

simplify83.0ms (1%)

prune159.0ms (1.8%)

localize11.0ms (0.1%)

series264.0ms (3%)

rewrite26.0ms (0.3%)

simplify111.0ms (1.3%)

prune239.0ms (2.7%)

localize11.0ms (0.1%)

series253.0ms (2.9%)

rewrite23.0ms (0.3%)

simplify95.0ms (1.1%)

prune181.0ms (2.1%)

localize8.0ms (0.1%)

series86.0ms (1%)

rewrite75.0ms (0.9%)

simplify263.0ms (3%)

prune227.0ms (2.6%)

regimes2.7s (31.2%)

bsearch51.0ms (0.6%)

simplify4.0ms (0%)

end168.0ms (1.9%)

Profiling