Details

analyze342.0ms (5.9%)

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 (25.2%)

Results

1.1s	7943×	body	128	valid
123.0ms	912×	body	128	invalid
79.0ms	313×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify256.0ms (4.4%)

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

29.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	29.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	29.9b	(/.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)

localize9.0ms (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)))
✓	0.3b	(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))
✓	29.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

series121.0ms (2.1%)

Counts

4 → 96

Calls

4 calls:

53.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
32.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
26.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
9.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite22.0ms (0.4%)

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:

10.0ms	(.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))

simplify182.0ms (3.2%)

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

prune226.0ms (3.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	217	9	226
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	219	9	228

Error

0.1b

Counts

228 → 9

Alt Table

Status	Error	Program
	29.9b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)) (/.f64 (cbrt.f64 1/2) a))
	29.9b	(.f64 (/.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.f64 b b)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)) (/.f64 1/2 a))
	5.4b	(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))))))
	31.4b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (neg.f64 (.f64 (cbrt.f64 b) (.f64 (cbrt.f64 b) (cbrt.f64 b))))) (fma.f64 (neg.f64 (cbrt.f64 b)) (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (*.f64 (cbrt.f64 b) (cbrt.f64 b))))) (/.f64 1/2 a))
	5.6b	(.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/2 a))
	29.9b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/2 (cbrt.f64 a)))
	29.9b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
▶	0.5b	(/.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))
	7.4b	(.f64 (fma.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3))) (.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -4)) (/.f64 1/2 a))

Compiler

Compiled 6591 to 3842 computations (41.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series160.0ms (2.8%)

Counts

3 → 64

Calls

3 calls:

126.0ms

(/.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))

31.0ms

(+.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))

rewrite30.0ms (0.5%)

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:

11.0ms

(/.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))

10.0ms

(*.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)

simplify110.0ms (1.9%)

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

prune499.0ms (8.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	209	6	215
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	217	7	224

Error

0.0b

Counts

224 → 7

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 (-.f64 (.f64 (.f64 c (.f64 a -4)) (.f64 c (.f64 a -4))) (.f64 0 0)) 1/2) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 (-.f64 (.f64 c (*.f64 a -4)) 0) a)))
	0.7b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (.f64 c (.f64 a -4)) 0)) (/.f64 (.f64 (.f64 1/2 1/2) 1/2) (.f64 (.f64 a a) a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
▶	0.3b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	5.4b	(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))))))
	0.9b	(/.f64 (.f64 (.f64 c (.f64 (.f64 a -4) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) a)) (+.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)))
	1.3b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))) (/.f64 (/.f64 1/2 a) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))))

Compiler

Compiled 7328 to 4624 computations (36.9% 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	(/.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)
	0.3b	(fma.f64 a (.f64 c -4) (.f64 b b))

series187.0ms (3.3%)

Counts

1 → 20

Calls

1 calls:

187.0ms

(/.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:

6.0ms

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

simplify60.0ms (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

prune154.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	6	180
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	180	7	187

Error

Counts

187 → 7

Alt Table

Status	Error	Program
	5.4b	(-.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))))
▶	0.3b	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.4b	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))
	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))
	0.5b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (sqrt.f64 (cbrt.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)))
	0.6b	(.f64 (/.f64 -2 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 c (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))

Compiler

Compiled 4822 to 2900 computations (39.9% saved)

localize9.0ms (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	(/.f64 (.f64 c -2) (+.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	(fma.f64 a (.f64 c -4) (.f64 b b))

series127.0ms (2.2%)

Counts

1 → 20

Calls

1 calls:

127.0ms

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

rewrite8.0ms (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:

6.0ms

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

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

786×	`times-frac_binary64`
650×	`associate-/l*_binary64`
352×	`associate-/r*_binary64`
343×	`fma-neg_binary64`
235×	`fma-def_binary64`

Counts

47 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	1488
1	368	1333
2	1210	1254
3	4762	1254
4	4982	1254

prune183.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	180	7	187

Error

Counts

187 → 7

Alt Table

Status	Error	Program
	5.4b	(-.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))))
✓	0.3b	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.4b	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))
	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))
	0.5b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (sqrt.f64 (cbrt.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)))
	0.6b	(.f64 (/.f64 -2 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 c (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))

Compiler

Compiled 4616 to 2766 computations (40.1% saved)

regimes1.4s (23.9%)

Accuracy

Total 0.3b remaining (91.6%)

Threshold costs 0.3b (91.6%)

Counts

270 → 1

Compiler

Compiled 31824 to 21166 computations (33.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	16	22
2	16	22

end140.0ms (2.4%)

Compiler: Compiled 242 to 158 computations (34.7% saved)

Details

analyze342.0ms (5.9%)

sample1.4s (25.2%)

simplify256.0ms (4.4%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series121.0ms (2.1%)

rewrite22.0ms (0.4%)

simplify182.0ms (3.2%)

prune226.0ms (3.9%)

localize15.0ms (0.3%)

series160.0ms (2.8%)

rewrite30.0ms (0.5%)

simplify110.0ms (1.9%)

prune499.0ms (8.7%)

localize10.0ms (0.2%)

series187.0ms (3.3%)

rewrite7.0ms (0.1%)

simplify60.0ms (1%)

prune154.0ms (2.7%)

localize9.0ms (0.2%)

series127.0ms (2.2%)

rewrite8.0ms (0.1%)

simplify62.0ms (1.1%)

prune183.0ms (3.2%)

regimes1.4s (23.9%)

simplify2.0ms (0%)

end140.0ms (2.4%)

Profiling