Details

analyze672.0ms (9.6%)

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)

sample2.4s (33.9%)

Alt Table

Status	Error	Program
▶	33.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Results

731.0ms	5356×	body	128	valid
600.0ms	1127×	body	2048	valid
342.0ms	743×	body	1024	valid
256.0ms	402×	body	4096	valid
138.0ms	1061×	body	128	invalid
138.0ms	412×	body	512	valid
60.0ms	216×	body	256	valid

Compiler

Compiled 102 to 72 computations (29.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.4b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	23.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series185.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

80.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
51.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
42.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
11.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite127.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

507×	`fma-neg_binary64`
277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
178×	`egg-rr`
166×	`add-sqr-sqrt_binary64`

Counts

4 → 178

Calls

4 calls:

122.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
122.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
122.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	338	62
2	4153	62
3	4979	62
4	5349	62
0	0	0
1	0	0

prune208.0ms (3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	261	13	274
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	262	13	275

Error

8.0b

Counts

275 → 13

Alt Table

Status	Error	Program
	44.2b	(*.f64 -1 (/.f64 b a))
	47.8b	(pow.f64 (cbrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 3)
	57.1b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	47.8b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 a 2)) 2)) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (cbrt.f64 (*.f64 a 2))))
	47.6b	(neg.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (*.f64 a -2)))
	47.6b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) -1)
	44.2b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.2b	(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
	41.7b	(*.f64 -1 (/.f64 c b))
	44.9b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
▶	33.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (.f64 a c)))))) (.f64 2 a))
	57.2b	(exp.f64 (log.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))))
	47.8b	(.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) 2) (.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (/.f64 1/2 a)))

Compiler

Compiled 7140 to 4180 computations (41.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(fma.f64 b b (.f64 (.f64 a c) -4))
✓	1.4b	(+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (*.f64 a c))))))
✓	23.1b	(sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (*.f64 a c)))))
✓	54.3b	(fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (*.f64 a c)))

series115.0ms (1.6%)

Counts

4 → 100

Calls

4 calls:

52.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (*.f64 a c))))))
42.0ms	(sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (*.f64 a c)))))
11.0ms	(fma.f64 b b (.f64 (.f64 a c) -4))
9.0ms	(fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (*.f64 a c)))

rewrite82.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

387×	`fma-neg_binary64`
273×	`expm1-udef_binary64`
273×	`log1p-udef_binary64`
180×	`add-sqr-sqrt_binary64`
173×	`log1p-expm1-u_binary64`

Counts

4 → 117

Calls

4 calls:

78.0ms	(fma.f64 b b (.f64 (.f64 a c) -4))
78.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (*.f64 a c))))))
78.0ms	(sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (*.f64 a c)))))
78.0ms	(fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (*.f64 a c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	94
1	367	86
2	3910	86
3	4937	86
0	0	0
1	0	0

prune158.0ms (2.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	217	13	230

Error

8.0b

Counts

230 → 13

Alt Table

Status	Error	Program
	44.2b	(*.f64 -1 (/.f64 b a))
	47.8b	(pow.f64 (cbrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 3)
	57.1b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	47.8b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 a 2)) 2)) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (cbrt.f64 (*.f64 a 2))))
▶	33.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0))) (*.f64 2 a))
✓	33.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (.f64 a c)))))) (.f64 2 a))
	47.6b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) -1)
	44.2b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.2b	(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
	41.7b	(*.f64 -1 (/.f64 c b))
	44.9b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	57.2b	(exp.f64 (log.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))))
	47.8b	(.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) 2) (.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (/.f64 1/2 a)))

Compiler

Compiled 7360 to 4478 computations (39.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0))) (*.f64 2 a))
✓	1.2b	(fma.f64 b b (.f64 (.f64 a c) -4))
✓	1.4b	(+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0)))
✓	23.1b	(sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0))

series184.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

81.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0))) (*.f64 2 a))
51.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0)))
42.0ms	(sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0))
9.0ms	(fma.f64 b b (.f64 (.f64 a c) -4))

rewrite89.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

382×	`fma-def_binary64`
280×	`fma-neg_binary64`
253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
162×	`egg-rr`

Counts

4 → 162

Calls

4 calls:

85.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0))) (*.f64 2 a))
85.0ms	(fma.f64 b b (.f64 (.f64 a c) -4))
85.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0)))
85.0ms	(sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	66
1	330	59
2	3732	59
3	4958	59
0	0	0
1	0	0

prune191.0ms (2.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	253	5	258
Fresh	5	6	11
Picked	0	1	1
Done	0	1	1
Total	258	13	271

Error

8.0b

Counts

271 → 13

Alt Table

Status	Error	Program
	44.2b	(*.f64 -1 (/.f64 b a))
	47.9b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 a 2)) 2)) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (.f64 a c) -4)))) (cbrt.f64 (*.f64 a 2))))
✓	33.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0))) (*.f64 2 a))
	47.9b	(.f64 (pow.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (.f64 a c) -4))))) 2) (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (.f64 a c) -4))))) (/.f64 1/2 a)))
✓	33.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (.f64 a c)))))) (.f64 2 a))
	44.2b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.2b	(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
▶	41.7b	(*.f64 -1 (/.f64 c b))
	57.2b	(exp.f64 (log.f64 (.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))))
	44.9b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	57.1b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	47.7b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (*.f64 a c) -4))))) -1)
	47.9b	(pow.f64 (cbrt.f64 (.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 3)

Compiler

Compiled 6371 to 3932 computations (38.3% saved)

localize3.0ms (0%)

prune9.0ms (0.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	10	10
Picked	1	1
Done	2	2
Total	13	13

Error

8.0b

Counts

13 → 13

Alt Table

Status	Error	Program
	44.2b	(*.f64 -1 (/.f64 b a))
	47.9b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 a 2)) 2)) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (.f64 a c) -4)))) (cbrt.f64 (*.f64 a 2))))
✓	33.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 0))) (*.f64 2 a))
	47.9b	(.f64 (pow.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (.f64 a c) -4))))) 2) (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (.f64 a c) -4))))) (/.f64 1/2 a)))
✓	33.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (fma.f64 (neg.f64 c) (.f64 4 a) (.f64 4 (.f64 a c)))))) (.f64 2 a))
	44.2b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.2b	(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
✓	41.7b	(*.f64 -1 (/.f64 c b))
	57.2b	(exp.f64 (log.f64 (.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))))
	44.9b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	57.1b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	47.7b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (*.f64 a c) -4))))) -1)
	47.9b	(pow.f64 (cbrt.f64 (.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 3)

Compiler

Compiled 254 to 177 computations (30.3% saved)

regimes2.3s (32.8%)

Accuracy

Total 5.0b remaining (46.7%)

Threshold costs 0b (0%)

Counts

163 → 3

Compiler

Compiled 14416 to 10054 computations (30.3% saved)

bsearch48.0ms (0.7%)

Steps

Iters	Range		Point
7	1.1087141635383997e-135	1.768822076151751e-133	1.4079437542076584e-134
1	-3.5130526354900675e+110	-3.4815467862880304e+102	-3.4155395926676587e+106

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	55
1	40	53
2	50	53
3	56	53
4	60	53
5	61	53
6	61	53

end212.0ms (3%)

Compiler: Compiled 332 to 225 computations (32.2% saved)

Details

analyze672.0ms (9.6%)

sample2.4s (33.9%)

localize10.0ms (0.1%)

series185.0ms (2.6%)

rewrite127.0ms (1.8%)

prune208.0ms (3%)

localize17.0ms (0.2%)

series115.0ms (1.6%)

rewrite82.0ms (1.2%)

prune158.0ms (2.3%)

localize11.0ms (0.2%)

series184.0ms (2.6%)

rewrite89.0ms (1.3%)

prune191.0ms (2.7%)

localize3.0ms (0%)

prune9.0ms (0.1%)

regimes2.3s (32.8%)

bsearch48.0ms (0.7%)

simplify4.0ms (0.1%)

end212.0ms (3%)

Profiling