Details

analyze343.0ms (5.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample1.4s (22.7%)

Results

1.1s	7918×	body	128	valid
122.0ms	893×	body	128	invalid
89.0ms	338×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify258.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1743×	`fma-neg_binary64`
1393×	`fma-def_binary64`
800×	`div-sub_binary64`
619×	`times-frac_binary64`
473×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	22
2	67	22
3	138	22
4	204	22
5	338	22
6	558	22
7	924	22
8	1388	22
9	1604	22
10	2375	22
11	2742	22
12	2533	22
13	2621	22
14	3171	22
15	3313	22
16	3873	22
17	3679	22
18	4029	22
19	4317	22
20	4485	22
21	4561	22
22	4805	22
23	4793	22
24	4797	22
25	4797	22
26	4948	22

prune4.0ms (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

28.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	28.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
✓	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	28.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

series187.0ms (3%)

Counts

4 → 96

Calls

4 calls:

83.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
52.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
41.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
10.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b 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))

simplify188.0ms (3%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
338×	`distribute-rgt-in_binary64`
273×	`cancel-sign-sub-inv_binary64`
155×	`associate-l_binary64`
153×	`associate-r_binary64`

Counts

205 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	5424
1	673	4468
2	2524	4293
3	4550	4293
4	4991	4293
5	4994	4293
6	4884	4293

prune144.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	220	6	226
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	222	6	228

Error

0.1b

Counts

228 → 6

Alt Table

Status	Error	Program
	28.8b	(.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (.f64 b b))) b) (/.f64 1/2 a))
	4.7b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
▶	0.4b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	28.9b	(cbrt.f64 (.f64 (.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a)) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1/2 a))) (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))))
	29.6b	(.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b))) (/.f64 1/2 a))
	4.9b	(.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 10 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (/.f64 1/2 a))

Compiler

Compiled 6311 to 3674 computations (41.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
✓	0.2b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	0.3b	(.f64 (+.f64 (.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

series362.0ms (5.7%)

Counts

3 → 64

Calls

3 calls:

309.0ms

(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

49.0ms

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

3.0ms

(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

rewrite257.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
15×	`add-cube-cbrt_binary64`

Counts

3 → 92

Calls

3 calls:

240.0ms

(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

8.0ms

(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

3.0ms

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

simplify111.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-neg_binary64`
248×	`associate-l_binary64`
225×	`associate-/l*_binary64`
220×	`associate-r_binary64`
176×	`div-sub_binary64`

Counts

156 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3787
1	708	3244
2	3132	3157
3	4613	3157
4	4932	3157

prune273.0ms (4.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	207	8	215
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	212	9	221

Error

Counts

221 → 9

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) (/.f64 1/2 a)) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (-.f64 (.f64 c (.f64 a -4)) 0)))
▶	0.3b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.5b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) 1) (/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	0.5b	(/.f64 (/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) (/.f64 1/2 a)) (-.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	4.7b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	0.4b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) 1/2) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) a))
	0.5b	(.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	0.5b	(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 (+.f64 (.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))))
	0.5b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)) 3))) b))

Compiler

Compiled 7370 to 4662 computations (36.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.2b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

series265.0ms (4.2%)

Counts

1 → 20

Calls

1 calls:

265.0ms

(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`associate-/r*_binary64`
4×	`times-frac_binary64`

Counts

1 → 27

Calls

1 calls:

5.0ms

(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Rules

769×	`times-frac_binary64`
615×	`associate-/l*_binary64`
357×	`associate-/r*_binary64`
352×	`fma-neg_binary64`
235×	`fma-def_binary64`

Counts

47 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	1488
1	366	1333
2	1180	1254
3	4844	1254
4	5078	1254

prune158.0ms (2.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	176	4	180
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	182	7	189

Error

Counts

189 → 7

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) 1/2) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) a))
	0.3b	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))
	0.3b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)) 3))) b))
	0.5b	(/.f64 (/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) (/.f64 1/2 a)) (-.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.6b	(/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) (/.f64 1/2 a)) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (-.f64 (.f64 c (.f64 a -4)) 0)))
▶	0.3b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
	4.7b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))

Compiler

Compiled 4850 to 2936 computations (39.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
✓	0.2b	(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) b)

series343.0ms (5.4%)

Counts

2 → 72

Calls

2 calls:

232.0ms

(/.f64 (*.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b))

111.0ms

(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

3.0ms

(/.f64 (*.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b))

0.0ms

(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b)

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

615×	`times-frac_binary64`
500×	`associate-/l*_binary64`
461×	`associate-/r*_binary64`
265×	`fma-def_binary64`
159×	`*-commutative_binary64`

Counts

105 → 170

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	465	6615
1	1628	6286
2	5309	6286

prune374.0ms (5.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	296	0	296
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	296	7	303

Error

Counts

303 → 7

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) 1/2) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) a))
	0.3b	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))
	0.3b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)) 3))) b))
	0.5b	(/.f64 (/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) (/.f64 1/2 a)) (-.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.6b	(/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) (/.f64 1/2 a)) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (-.f64 (.f64 c (.f64 a -4)) 0)))
✓	0.3b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
	4.7b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))

Compiler

Compiled 13742 to 9207 computations (33% saved)

regimes1.2s (19.6%)

Accuracy

Total 0.2b remaining (87.5%)

Threshold costs 0.2b (87.5%)

Counts

240 → 1

Compiler

Compiled 29276 to 19462 computations (33.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	19	24
2	19	24

end146.0ms (2.3%)

Compiler: Compiled 258 to 178 computations (31% saved)

Details

analyze343.0ms (5.4%)

sample1.4s (22.7%)

simplify258.0ms (4.1%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series187.0ms (3%)

rewrite21.0ms (0.3%)

simplify188.0ms (3%)

prune144.0ms (2.3%)

localize13.0ms (0.2%)

series362.0ms (5.7%)

rewrite257.0ms (4.1%)

simplify111.0ms (1.8%)

prune273.0ms (4.3%)

localize9.0ms (0.1%)

series265.0ms (4.2%)

rewrite7.0ms (0.1%)

simplify63.0ms (1%)

prune158.0ms (2.5%)

localize11.0ms (0.2%)

series343.0ms (5.4%)

rewrite6.0ms (0.1%)

simplify100.0ms (1.6%)

prune374.0ms (5.9%)

regimes1.2s (19.6%)

simplify2.0ms (0%)

end146.0ms (2.3%)

Profiling