Details

analyze1.1s (8.2%)

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
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample2.1s (16.3%)

Results

1.3s	8256×	body	128	valid
567.0ms	3139×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	72	17
3	227	17
4	512	17
5	1044	17
6	1436	17
7	1492	17
8	1573	17
9	1615	17
10	1631	17
11	1631	17
12	1550	17

prune3.0ms (0%)

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

5.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.9b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
▶	5.9b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))

Compiler

Compiled 95 to 57 computations (40% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 z z) t)
✓	0.0b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
✓	5.5b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

series63.0ms (0.5%)

Counts

3 → 108

Calls

3 calls:

30.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
29.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
4.0ms	(-.f64 (*.f64 z z) t)

rewrite117.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

532×	`fma-def_binary64`
258×	`egg-rr`
238×	`expm1-udef_binary64`
238×	`log1p-udef_binary64`
234×	`fma-neg_binary64`

Counts

3 → 258

Calls

3 calls:

110.0ms	(-.f64 (*.f64 z z) t)
110.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
110.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	269	37
2	3365	37
3	4943	37

simplify355.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

735×	`distribute-rgt-neg-in_binary64`
690×	`fma-neg_binary64`
678×	`cube-prod_binary64`
666×	`fma-def_binary64`
547×	`sqr-pow_binary64`

Counts

366 → 285

Iterations

Useful iterations: 11 (0.0ms)

Iter	Nodes	Cost
0	33	1537
1	99	1382
2	236	1310
3	515	1310
4	1141	1310
5	2104	1310
6	2615	1310
7	3195	1310
8	3235	1310
9	3447	1310
10	3617	1310
11	3802	1172
12	3408	1172
13	3979	1172
14	4669	1172
15	4943	1172

prune325.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	277	8	285
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	279	8	287

Error

3.2b

Counts

287 → 8

Alt Table

Status	Error	Program
▶	5.9b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) (fma.f64 z z (neg.f64 t))))
	36.3b	(.f64 y (.f64 4 t))
	30.9b	(fma.f64 (.f64 (.f64 y -4) (hypot.f64 z (sqrt.f64 (neg.f64 t)))) (hypot.f64 z (sqrt.f64 (neg.f64 t))) (*.f64 x x))
	61.8b	(log.f64 (/.f64 (+.f64 1 (expm1.f64 (.f64 x x))) (pow.f64 (pow.f64 (exp.f64 y) 4) (-.f64 (.f64 z z) t))))
	41.6b	(pow.f64 x 2)
	6.5b	(-.f64 (.f64 x x) (pow.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) 3))
	6.0b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (fma.f64 (.f64 z (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (neg.f64 t))))
	6.0b	(fma.f64 x x (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))))

Compiler

Compiled 7905 to 3278 computations (58.5% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) (fma.f64 z z (neg.f64 t))))
✓	5.5b	(.f64 (.f64 y 4) (fma.f64 z z (neg.f64 t)))

series54.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) (fma.f64 z z (neg.f64 t))))
23.0ms	(.f64 (.f64 y 4) (fma.f64 z z (neg.f64 t)))

rewrite101.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

602×	`log-prod_binary64`
402×	`fma-def_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
187×	`log-pow_binary64`

Counts

2 → 182

Calls

2 calls:

95.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) (fma.f64 z z (neg.f64 t))))
95.0ms	(.f64 (.f64 y 4) (fma.f64 z z (neg.f64 t)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	261	26
2	2974	26
3	5479	26

simplify239.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

735×	`distribute-rgt-neg-in_binary64`
690×	`fma-neg_binary64`
678×	`cube-prod_binary64`
665×	`fma-def_binary64`
547×	`sqr-pow_binary64`

Counts

266 → 204

Iterations

Useful iterations: 11 (0.0ms)

Iter	Nodes	Cost
0	32	1390
1	97	1235
2	235	1163
3	513	1163
4	1139	1163
5	2102	1163
6	2614	1163
7	3194	1163
8	3234	1163
9	3446	1163
10	3616	1163
11	3801	1025
12	3407	1025
13	3978	1025
14	4668	1025
15	4942	1025

prune178.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	207	5	212

Error

0.0b

Counts

212 → 5

Alt Table

Status	Error	Program
	6.5b	(-.f64 (.f64 x x) (pow.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) 3))
▶	6.0b	(fma.f64 x x (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))))
✓	5.9b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) (fma.f64 z z (neg.f64 t))))
	30.9b	(fma.f64 (.f64 (.f64 y -4) (hypot.f64 z (sqrt.f64 (neg.f64 t)))) (hypot.f64 z (sqrt.f64 (neg.f64 t))) (*.f64 x x))
	45.2b	(fma.f64 (.f64 (.f64 y -4) (hypot.f64 z (sqrt.f64 t))) (hypot.f64 z (sqrt.f64 t)) (*.f64 x x))

Compiler

Compiled 5785 to 2565 computations (55.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))))
✓	5.5b	(fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))))
	5.5b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
✓	55.4b	(fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))

series142.0ms (1.1%)

Counts

3 → 120

Calls

3 calls:

58.0ms

(fma.f64 x x (fma.f64 (-.f64 (*.f64 z z) t) (*.f64 y -4) (fma.f64 (-.f64 (*.f64 z z) t) (*.f64 y -4) (*.f64 (*.f64 y 4) (-.f64 (*.f64 z z) t)))))

44.0ms

(fma.f64 (-.f64 (*.f64 z z) t) (*.f64 y -4) (*.f64 (*.f64 y 4) (-.f64 (*.f64 z z) t)))

39.0ms

(fma.f64 (-.f64 (*.f64 z z) t) (*.f64 y -4) (fma.f64 (-.f64 (*.f64 z z) t) (*.f64 y -4) (*.f64 (*.f64 y 4) (-.f64 (*.f64 z z) t))))

rewrite80.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

375×	`fma-def_binary64`
256×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`
226×	`log-pow_binary64`
216×	`fma-neg_binary64`

Counts

3 → 83

Calls

3 calls:

77.0ms

(fma.f64 x x (fma.f64 (-.f64 (*.f64 z z) t) (*.f64 y -4) (fma.f64 (-.f64 (*.f64 z z) t) (*.f64 y -4) (*.f64 (*.f64 y 4) (-.f64 (*.f64 z z) t)))))

77.0ms

(fma.f64 (-.f64 (*.f64 z z) t) (*.f64 y -4) (fma.f64 (-.f64 (*.f64 z z) t) (*.f64 y -4) (*.f64 (*.f64 y 4) (-.f64 (*.f64 z z) t))))

77.0ms

(fma.f64 (-.f64 (*.f64 z z) t) (*.f64 y -4) (*.f64 (*.f64 y 4) (-.f64 (*.f64 z z) t)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	108
1	313	87
2	3405	81
3	5025	81

simplify244.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

708×	`distribute-rgt-neg-in_binary64`
678×	`cube-prod_binary64`
657×	`fma-def_binary64`
600×	`fma-neg_binary64`
547×	`sqr-pow_binary64`

Counts

203 → 99

Iterations

Useful iterations: 11 (0.0ms)

Iter	Nodes	Cost
0	28	1516
1	82	1271
2	192	1199
3	465	1199
4	1047	1199
5	1855	1199
6	2608	1199
7	3162	1199
8	3174	1199
9	3372	1199
10	3536	1199
11	3721	1061
12	3351	1061
13	3922	1061
14	4612	1061
15	4874	1061

prune114.0ms (0.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	128	5	133

Error

0.0b

Counts

133 → 5

Alt Table

Status	Error	Program
▶	6.5b	(-.f64 (.f64 x x) (pow.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) 3))
✓	6.0b	(fma.f64 x x (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))))
✓	5.9b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) (fma.f64 z z (neg.f64 t))))
	30.9b	(fma.f64 (.f64 (.f64 y -4) (hypot.f64 z (sqrt.f64 (neg.f64 t)))) (hypot.f64 z (sqrt.f64 (neg.f64 t))) (*.f64 x x))
	45.2b	(fma.f64 (.f64 (.f64 y -4) (hypot.f64 z (sqrt.f64 t))) (hypot.f64 z (sqrt.f64 t)) (*.f64 x x))

Compiler

Compiled 4004 to 1758 computations (56.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x x) (pow.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) 3))
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))) 3)
	5.5b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
✓	6.2b	(cbrt.f64 (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))

series2.0s (15.9%)

Counts

3 → 120

Calls

3 calls:

1.5s	(pow.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))) 3)
482.0ms	(cbrt.f64 (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))
82.0ms	(-.f64 (.f64 x x) (pow.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) 3))

rewrite92.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

433×	`fma-def_binary64`
258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
196×	`fma-neg_binary64`
167×	`egg-rr`

Counts

3 → 167

Calls

3 calls:

87.0ms	(-.f64 (.f64 x x) (pow.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) 3))
87.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))) 3)
87.0ms	(cbrt.f64 (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	310	47
2	3634	47
3	4918	47

simplify129.0ms (1%)

Algorithm

1×	egg-herbie

Rules

644×	`fma-def_binary64`
355×	`cancel-sign-sub-inv_binary64`
331×	`fma-neg_binary64`
278×	`distribute-rgt-neg-in_binary64`
233×	`associate-r_binary64`

Counts

287 → 265

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	4109
1	820	3844
2	2613	3598
3	4900	3598
4	4964	3598

prune284.0ms (2.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	294	5	299

Error

0.0b

Counts

299 → 5

Alt Table

Status	Error	Program
✓	6.5b	(-.f64 (.f64 x x) (pow.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) 3))
✓	6.0b	(fma.f64 x x (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (fma.f64 (-.f64 (.f64 z z) t) (.f64 y -4) (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))))
✓	5.9b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) (fma.f64 z z (neg.f64 t))))
	30.9b	(fma.f64 (.f64 (.f64 y -4) (hypot.f64 z (sqrt.f64 (neg.f64 t)))) (hypot.f64 z (sqrt.f64 (neg.f64 t))) (*.f64 x x))
	45.2b	(fma.f64 (.f64 (.f64 y -4) (hypot.f64 z (sqrt.f64 t))) (hypot.f64 z (sqrt.f64 t)) (*.f64 x x))

Compiler

Compiled 8166 to 4371 computations (46.5% saved)

regimes4.8s (37.4%)

Accuracy

Total 3.2b remaining (98.7%)

Threshold costs 0b (0%)

Counts

214 → 3

Compiler

Compiled 56204 to 36419 computations (35.2% saved)

bsearch96.0ms (0.7%)

Steps

Iters	Range		Point
7	3.437368832179221e+152	2.3359749995903315e+154	1.3453380665676873e+154
11	-1.581048118976614e+141	-1.697392565653608e+121	-1.55634019542455e+141

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	83
1	39	83
2	47	83
3	57	83
4	64	83
5	69	83
6	71	83
7	70	83

end114.0ms (0.9%)

Compiler: Compiled 233 to 126 computations (45.9% saved)

Details

analyze1.1s (8.2%)

sample2.1s (16.3%)

simplify65.0ms (0.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series63.0ms (0.5%)

rewrite117.0ms (0.9%)

simplify355.0ms (2.8%)

prune325.0ms (2.5%)

localize11.0ms (0.1%)

series54.0ms (0.4%)

rewrite101.0ms (0.8%)

simplify239.0ms (1.9%)

prune178.0ms (1.4%)

localize15.0ms (0.1%)

series142.0ms (1.1%)

rewrite80.0ms (0.6%)

simplify244.0ms (1.9%)

prune114.0ms (0.9%)

localize11.0ms (0.1%)

series2.0s (15.9%)

rewrite92.0ms (0.7%)

simplify129.0ms (1%)

prune284.0ms (2.2%)

regimes4.8s (37.4%)

bsearch96.0ms (0.7%)

simplify5.0ms (0%)

end114.0ms (0.9%)

Profiling