Details

analyze705.0ms (13.3%)

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
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample1.7s (32%)

Results

1.5s	8256×	body	128	valid
177.0ms	1056×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1122×	`fma-def_binary64`
776×	`fma-neg_binary64`
260×	`associate-/l*_binary64`
249×	`cancel-sign-sub-inv_binary64`
205×	`div-sub_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	47	52
2	123	52
3	304	50
4	546	50
5	993	50
6	2057	50
7	3568	50
8	4834	50

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

19.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	19.7b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	19.8b	(if (>=.f64 b 0) (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (/.f64 -1/2 a)) (.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) b))))

Status

Error

Program

▶

19.7b

(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

19.8b

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

Compiler

Compiled 231 to 147 computations (36.4% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	24.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series106.0ms (2%)

Counts

4 → 96

Calls

4 calls:

35.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
29.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite71.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`
167×	`egg-rr`
147×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	68
1	301	56
2	4302	56

Stop Event

1×	node limit

Counts

4 → 167

Calls

4 calls:

67.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
67.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
67.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
293×	`fma-def_binary64`
279×	`associate-r_binary64`
278×	`associate-/l*_binary64`
257×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	2213
1	296	2123
2	973	2035

Stop Event

1×	node limit

Counts

263 → 226

prune460.0ms (8.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	329	5	334
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	330	6	336

Error

4.5b

Counts

336 → 6

Alt Table

Status	Error	Program
	21.8b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	29.8b	(if (>=.f64 b 0) (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	28.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (-.f64 (pow.f64 b 4) (pow.f64 (.f64 4 (.f64 a c)) 2)) (/.f64 1 (fma.f64 b b (.f64 4 (.f64 a c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	21.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
▶	17.4b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (.f64 -1 b))))
	19.8b	(if (>=.f64 b 0) (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (/.f64 -1/2 a)) (.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) b))))

Compiler

Compiled 16387 to 9730 computations (40.6% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 4 a) c)
	0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	24.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(*.f64 (*.f64 4 a) c)

rewrite29.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
377×	`unpow-prod-down_binary64`
295×	`log-prod_binary64`
153×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	122	7
2	1410	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

1 calls:

28.0ms

(*.f64 (*.f64 4 a) c)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	10	168
2	17	168
3	19	168

Stop Event

1×

saturated

Counts

41 → 19

prune255.0ms (4.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	196	5	201

Error

4.5b

Counts

201 → 5

Alt Table

Status	Error	Program
	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
	29.8b	(if (>=.f64 b 0) (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	28.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (-.f64 (pow.f64 b 4) (pow.f64 (.f64 4 (.f64 a c)) 2)) (/.f64 1 (fma.f64 b b (.f64 4 (.f64 a c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
▶	19.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
	19.8b	(if (>=.f64 b 0) (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (/.f64 -1/2 a)) (.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) b))))

Compiler

Compiled 8230 to 5113 computations (37.9% saved)

localize21.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 a (/.f64 c b)) b)
✓	3.8b	(/.f64 (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b)) (*.f64 2 a))
✓	5.9b	(*.f64 a (/.f64 c b))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series35.0ms (0.7%)

Counts

3 → 108

Calls

3 calls:

13.0ms	(*.f64 a (/.f64 c b))
13.0ms	(/.f64 (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b)) (*.f64 2 a))
8.0ms	(-.f64 (*.f64 a (/.f64 c b)) b)

rewrite74.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

742×	`prod-diff_binary64`
202×	`egg-rr`
128×	`add-sqr-sqrt_binary64`
121×	`log1p-expm1-u_binary64`
121×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	251	30
2	3750	30

Stop Event

1×	node limit

Counts

3 → 202

Calls

3 calls:

69.0ms	(-.f64 (*.f64 a (/.f64 c b)) b)
69.0ms	(/.f64 (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b)) (*.f64 2 a))
69.0ms	(*.f64 a (/.f64 c b))

simplify102.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
601×	`fma-neg_binary64`
345×	`div-sub_binary64`
262×	`times-frac_binary64`
218×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	883
1	22	883
2	34	883
3	55	883
4	87	883
5	162	883
6	334	883
7	538	883
8	896	883
9	1454	883
10	2228	883
11	3161	883
12	3982	883
13	4232	883
14	4262	883
15	4288	883
16	4288	883
17	4288	883

Stop Event

1×

saturated

Counts

310 → 212

prune237.0ms (4.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	212	5	217

Error

4.5b

Counts

217 → 5

Alt Table

Status	Error	Program
▶	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
	29.8b	(if (>=.f64 b 0) (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	28.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (-.f64 (pow.f64 b 4) (pow.f64 (.f64 4 (.f64 a c)) 2)) (/.f64 1 (fma.f64 b b (.f64 4 (.f64 a c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
✓	19.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
	19.8b	(if (>=.f64 b 0) (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (/.f64 -1/2 a)) (.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) b))))

Compiler

Compiled 7706 to 3949 computations (48.8% saved)

localize15.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 (neg.f64 b) b) (*.f64 2 a))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series6.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(/.f64 (-.f64 (neg.f64 b) b) (*.f64 2 a))

rewrite40.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

849×	`log1p-expm1-u_binary64`
849×	`expm1-log1p-u_binary64`
95×	`add-sqr-sqrt_binary64`
90×	`add-cbrt-cube_binary64`
88×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	184	10
2	2916	10

Stop Event

1×	node limit

Counts

1 → 42

Calls

1 calls:

39.0ms

(/.f64 (-.f64 (neg.f64 b) b) (*.f64 2 a))

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
8×	`sub-neg_binary64`
4×	`+-commutative_binary64`
4×	`fma-neg_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	144
1	10	144
2	17	144
3	23	144
4	29	144
5	37	144
6	45	144
7	55	144
8	63	144
9	77	144

Stop Event

1×

saturated

Counts

66 → 44

prune47.0ms (0.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	44	5	49

Error

4.5b

Counts

49 → 5

Alt Table

Status	Error	Program
✓	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
	29.8b	(if (>=.f64 b 0) (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	28.9b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (-.f64 (pow.f64 b 4) (pow.f64 (.f64 4 (.f64 a c)) 2)) (/.f64 1 (fma.f64 b b (.f64 4 (.f64 a c))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
✓	19.4b	(if (>=.f64 b 0) (/.f64 (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
	19.8b	(if (>=.f64 b 0) (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (/.f64 -1/2 a)) (.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) b))))

Compiler

Compiled 1339 to 806 computations (39.8% saved)

regimes976.0ms (18.4%)

Accuracy

Total 1.3b remaining (18.1%)

Threshold costs 0b (0%)

Counts

85 → 5

Compiler

Compiled 12166 to 8294 computations (31.8% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 41 to 26 computations (36.6% saved)

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
17×	`*-commutative_binary64`
15×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	487
1	72	473
2	98	473
3	122	473
4	138	473
5	146	473
6	148	473

Stop Event

1×

saturated

end231.0ms (4.4%)

Compiler: Compiled 828 to 502 computations (39.4% saved)

Details

analyze705.0ms (13.3%)

sample1.7s (32%)

simplify37.0ms (0.7%)

prune5.0ms (0.1%)

localize21.0ms (0.4%)

series106.0ms (2%)

rewrite71.0ms (1.3%)

simplify44.0ms (0.8%)

prune460.0ms (8.7%)

localize20.0ms (0.4%)

series4.0ms (0.1%)

rewrite29.0ms (0.5%)

simplify9.0ms (0.2%)

prune255.0ms (4.8%)

localize21.0ms (0.4%)

series35.0ms (0.7%)

rewrite74.0ms (1.4%)

simplify102.0ms (1.9%)

prune237.0ms (4.5%)

localize15.0ms (0.3%)

series6.0ms (0.1%)

rewrite40.0ms (0.8%)

simplify16.0ms (0.3%)

prune47.0ms (0.9%)

regimes976.0ms (18.4%)

bsearch5.0ms (0.1%)

simplify34.0ms (0.6%)

end231.0ms (4.4%)

Profiling