Details

analyze1.4s (20.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.1%	87.7%	0.2%	13
21.4%	78.3%	0.4%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.8s (26.2%)

Results

1.1s	6914×	body	128	valid
189.0ms	501×	body	512	valid
173.0ms	1272×	body	128	invalid
154.0ms	405×	body	1024	valid
75.0ms	370×	body	256	valid
31.0ms	66×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

836×	`unsub-neg_binary64`
769×	`fma-def_binary64`
696×	`div-sub_binary64`
646×	`sub-neg_binary64`
478×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	21	19
2	52	17
3	144	17
4	421	17
5	1092	17
6	2657	17
7	3901	17
8	4408	17
9	4807	17
10	4881	17

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

10.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

Compiler

Compiled 100 to 55 computations (45% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	14.4b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series87.0ms (1.3%)

Counts

2 → 108

Calls

2 calls:

61.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
25.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite71.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

514×	`fma-def_binary64`
264×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`

Counts

2 → 76

Calls

2 calls:

69.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
69.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	257	27
2	3776	27
3	5340	27
0	0	0
1	0	0

simplify142.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

512×	`cancel-sign-sub-inv_binary64`
445×	`sub-neg_binary64`
351×	`associate-+r+_binary64`
288×	`distribute-neg-in_binary64`
271×	`+-commutative_binary64`

Counts

184 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	5085
1	820	5085
2	3265	5049
3	4994	5049

prune114.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	135	9	144
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	136	10	146

Error

0.3b

Counts

146 → 10

Alt Table

Status	Error	Program
▶	14.8b	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) (-.f64 t x)) -1) x)
	40.7b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
	34.3b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	38.5b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	28.7b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	42.0b	(fma.f64 (-.f64 y z) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 t x)) 2) (sqrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 t x)) (sqrt.f64 (-.f64 a z)))) x)
	42.2b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	34.4b	(fma.f64 (-.f64 y z) (.f64 (/.f64 (-.f64 t x) (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 z a)) x)
	36.5b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)

Compiler

Compiled 5025 to 1640 computations (67.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
✓	0.3b	(pow.f64 (/.f64 (-.f64 a z) (-.f64 t x)) -1)
✓	14.4b	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) (-.f64 t x)) -1) x)

series392.0ms (5.8%)

Counts

3 → 156

Calls

3 calls:

282.0ms	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) (-.f64 t x)) -1) x)
87.0ms	(pow.f64 (/.f64 (-.f64 a z) (-.f64 t x)) -1)
23.0ms	(/.f64 (-.f64 a z) (-.f64 t x))

rewrite71.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

281×	`expm1-udef_binary64`
281×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`

Counts

3 → 110

Calls

3 calls:

69.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
69.0ms	(pow.f64 (/.f64 (-.f64 a z) (-.f64 t x)) -1)
69.0ms	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) (-.f64 t x)) -1) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	299	37
2	4147	37
3	4951	37
0	0	0
1	0	0

simplify258.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

432×	`fma-def_binary64`
357×	`+-commutative_binary64`
300×	`associate-+r+_binary64`
232×	`associate-*r/_binary64`
232×	`associate-*l/_binary64`

Counts

266 → 235

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	820	17082
1	3118	16566
2	5194	16566

prune272.0ms (4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	235	10	245

Error

0.3b

Counts

245 → 10

Alt Table

Status	Error	Program
✓	14.8b	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) (-.f64 t x)) -1) x)
	40.7b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
	34.3b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	38.5b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	28.7b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	42.0b	(fma.f64 (-.f64 y z) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 t x)) 2) (sqrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 t x)) (sqrt.f64 (-.f64 a z)))) x)
	42.2b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
▶	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	34.4b	(fma.f64 (-.f64 y z) (.f64 (/.f64 (-.f64 t x) (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 z a)) x)
	36.5b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)

Compiler

Compiled 16177 to 6893 computations (57.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 t x))
✓	2.4b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
✓	20.6b	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

series155.0ms (2.3%)

Counts

3 → 168

Calls

3 calls:

88.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
55.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
12.0ms	(*.f64 (-.f64 y z) (-.f64 t x))

rewrite89.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

280×	`expm1-udef_binary64`
280×	`log1p-udef_binary64`
152×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`

Counts

3 → 119

Calls

3 calls:

86.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
86.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
86.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	284	45
2	4296	45
3	5151	45
0	0	0
1	0	0

simplify145.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

636×	`cancel-sign-sub-inv_binary64`
589×	`sub-neg_binary64`
563×	`associate-+r+_binary64`
422×	`associate-+l+_binary64`
367×	`+-commutative_binary64`

Counts

287 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	8080
1	1041	8080
2	3970	7438
3	5528	7438

prune174.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	221	9	230

Error

0.3b

Counts

230 → 9

Alt Table

Status	Error	Program
✓	14.8b	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) (-.f64 t x)) -1) x)
	40.7b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
	34.3b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	38.5b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	42.2b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
✓	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	34.4b	(fma.f64 (-.f64 y z) (.f64 (/.f64 (-.f64 t x) (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 z a)) x)
	36.5b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
▶	10.7b	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)))

Compiler

Compiled 7934 to 2451 computations (69.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
✓	1.7b	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x))
✓	2.4b	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)))

series154.0ms (2.3%)

Counts

3 → 156

Calls

3 calls:

82.0ms	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)))
55.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x))
17.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

rewrite84.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

284×	`expm1-udef_binary64`
284×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Counts

3 → 117

Calls

3 calls:

81.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
81.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x))
81.0ms	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	287	43
2	4402	43
3	5271	43
0	0	0
1	0	0

simplify143.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

537×	`associate-+r+_binary64`
426×	`associate-+l+_binary64`
394×	`+-commutative_binary64`
308×	`associate--l+_binary64`
292×	`associate--r+_binary64`

Counts

273 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	383	8465
1	1119	8456
2	4600	7736
3	5008	7736

prune186.0ms (2.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	240	1	241
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	241	9	250

Error

0.3b

Counts

250 → 9

Alt Table

Status	Error	Program
✓	14.8b	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) (-.f64 t x)) -1) x)
	40.7b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
	34.3b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	38.5b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	42.2b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
✓	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	11.1b	(+.f64 x (*.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 y z) (-.f64 a z))) 3) (-.f64 t x)))
	36.5b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
✓	10.7b	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)))

Compiler

Compiled 8496 to 2704 computations (68.2% saved)

regimes749.0ms (11%)

Accuracy

Total 9.2b remaining (89.8%)

Threshold costs 0b (0%)

Counts

85 → 3

Compiler

Compiled 9900 to 6030 computations (39.1% saved)

bsearch61.0ms (0.9%)

Steps

Iters	Range		Point
7	3.3708438386564876e-148	5.61998870189387e-146	1.3731471589482035e-146
7	-5.736309353566996e-168	-2.5147471920297757e-169	-5.662532019002217e-168

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
14×	`*-commutative_binary64`
14×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	85
1	48	85
2	64	85
3	80	85
4	102	85
5	114	85
6	122	85
7	125	85
8	125	85

end146.0ms (2.1%)

Compiler: Compiled 359 to 202 computations (43.7% saved)

Details

analyze1.4s (20.5%)

sample1.8s (26.2%)

simplify89.0ms (1.3%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series87.0ms (1.3%)

rewrite71.0ms (1%)

simplify142.0ms (2.1%)

prune114.0ms (1.7%)

localize9.0ms (0.1%)

series392.0ms (5.8%)

rewrite71.0ms (1%)

simplify258.0ms (3.8%)

prune272.0ms (4%)

localize9.0ms (0.1%)

series155.0ms (2.3%)

rewrite89.0ms (1.3%)

simplify145.0ms (2.1%)

prune174.0ms (2.5%)

localize9.0ms (0.1%)

series154.0ms (2.3%)

rewrite84.0ms (1.2%)

simplify143.0ms (2.1%)

prune186.0ms (2.7%)

regimes749.0ms (11%)

bsearch61.0ms (0.9%)

simplify6.0ms (0.1%)

end146.0ms (2.1%)

Profiling