Details

analyze382.0ms (5.2%)

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)

sample2.8s (37.5%)

Results

1.2s	3907×	body	256	valid
877.0ms	1529×	body	512	valid
454.0ms	2820×	body	128	valid
136.0ms	845×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify261.0ms (3.5%)

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

50.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	50.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	50.7b	(/.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 (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
✓	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	25.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

series127.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

54.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
35.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
27.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
10.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite23.0ms (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))

simplify212.0ms (2.9%)

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

prune148.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	221	5	226
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	222	6	228

Error

0.0b

Counts

228 → 6

Alt Table

Status	Error	Program
	2.6b	(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))))))
✓	50.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	50.7b	(.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)) (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
▶	0.3b	(/.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))
	50.7b	(/.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)) 1/2) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) a))
	2.9b	(.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))

Compiler

Compiled 6299 to 3674 computations (41.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	0.1b	(/.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))
	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.3b	(.f64 (+.f64 (.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

series189.0ms (2.5%)

Counts

3 → 64

Calls

3 calls:

153.0ms

(/.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))

32.0ms

(+.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))

rewrite33.0ms (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))

11.0ms

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

5.0ms

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

simplify114.0ms (1.5%)

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 → 198

Iterations

Useful iterations: 2 (0.0ms)

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

prune215.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	211	6	217
Fresh	3	1	4
Picked	1	0	1
Done	1	0	1
Total	216	7	223

Error

Counts

223 → 7

Alt Table

Status	Error	Program
	2.6b	(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))))))
	0.6b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (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)))
	2.5b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))
▶	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))
	0.9b	(/.f64 (.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	0.6b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 (/.f64 1/2 a) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))

Compiler

Compiled 7328 to 4618 computations (37% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) a)
	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.3b	(/.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))

series174.0ms (2.3%)

Counts

2 → 40

Calls

2 calls:

130.0ms	(/.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))
43.0ms	(.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) a)

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
6×	`associate-*l/_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

2 → 50

Calls

2 calls:

11.0ms	(/.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))
7.0ms	(.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) a)

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-def_binary64`
396×	`distribute-rgt-in_binary64`
253×	`times-frac_binary64`
190×	`associate-/l*_binary64`
174×	`associate-l_binary64`

Counts

90 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	3124
1	615	2625
2	2709	2495
3	4948	2495

prune178.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	199	7	206

Error

Counts

206 → 7

Alt Table

Status	Error	Program
	2.6b	(-.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))))
	0.6b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (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)))
	2.5b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))
✓	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))
	0.9b	(/.f64 (.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	0.6b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 (/.f64 1/2 a) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))

Compiler

Compiled 6850 to 4329 computations (36.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.3b	(/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
✓	0.4b	(.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)))

series264.0ms (3.6%)

Counts

2 → 40

Calls

2 calls:

133.0ms

(*.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)))

131.0ms

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

rewrite67.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

209×	`times-frac_binary64`
157×	`*-un-lft-identity_binary64`
130×	`add-sqr-sqrt_binary64`
100×	`add-cube-cbrt_binary64`
58×	`associate-r_binary64`

Counts

2 → 197

Calls

2 calls:

27.0ms

(*.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)))

8.0ms

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

simplify254.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

345×	`associate-l_binary64`
326×	`associate-r_binary64`
299×	`associate-/l*_binary64`
280×	`associate-*l/_binary64`
257×	`*-commutative_binary64`

Counts

237 → 345

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	9096
1	987	8324
2	4149	8076
3	4601	8076
4	4977	8076
5	4830	8076

prune389.0ms (5.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	414	2	416
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	417	6	423

Error

Counts

423 → 6

Alt Table

Status	Error	Program
	2.6b	(-.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))))
	0.6b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (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))
	0.3b	(.f64 (/.f64 (.f64 (.f64 c a) -2) a) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	0.6b	(.f64 (/.f64 (.f64 c (.f64 a -4)) (sqrt.f64 a)) (/.f64 (/.f64 1/2 (sqrt.f64 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
✓	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))
	0.9b	(/.f64 (.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))

Compiler

Compiled 16281 to 10620 computations (34.8% saved)

regimes1.3s (17.7%)

Accuracy

Total 0.1b remaining (86.5%)

Threshold costs 0.1b (86.5%)

Counts

256 → 1

Compiler

Compiled 33556 to 23302 computations (30.6% 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

end130.0ms (1.8%)

Compiler: Compiled 237 to 158 computations (33.3% saved)

Details

analyze382.0ms (5.2%)

sample2.8s (37.5%)

simplify261.0ms (3.5%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series127.0ms (1.7%)

rewrite23.0ms (0.3%)

simplify212.0ms (2.9%)

prune148.0ms (2%)

localize15.0ms (0.2%)

series189.0ms (2.5%)

rewrite33.0ms (0.5%)

simplify114.0ms (1.5%)

prune215.0ms (2.9%)

localize15.0ms (0.2%)

series174.0ms (2.3%)

rewrite22.0ms (0.3%)

simplify74.0ms (1%)

prune178.0ms (2.4%)

localize16.0ms (0.2%)

series264.0ms (3.6%)

rewrite67.0ms (0.9%)

simplify254.0ms (3.4%)

prune389.0ms (5.3%)

regimes1.3s (17.7%)

simplify2.0ms (0%)

end130.0ms (1.8%)

Profiling