Details

analyze975.0ms (12.2%)

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
9.4%	90.4%	0.2%	10
23.4%	74.9%	1.8%	11
27.3%	69%	3.7%	12
36.6%	56.5%	6.8%	13
40.5%	52%	7.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.3s (16.7%)

Symmetry

(sort y t)

Results

930.0ms	8256×	body	128	valid
250.0ms	2030×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

998×	`fma-def_binary64`
304×	`fma-neg_binary64`
112×	`distribute-rgt-in_binary64`
90×	`associate-l_binary64`
87×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.7b	(.f64 y (.f64 t (-.f64 x z)))
	7.1b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 t (-.f64 x z))
✓	6.4b	(.f64 y (.f64 t (-.f64 x z)))

series21.0ms (0.3%)

Counts

2 → 84

Calls

2 calls:

15.0ms	(.f64 y (.f64 t (-.f64 x z)))
6.0ms	(*.f64 t (-.f64 x z))

rewrite56.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

874×	`log1p-expm1-u_binary64`
874×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
82×	`add-log-exp_binary64`

Counts

2 → 42

Calls

2 calls:

55.0ms	(*.f64 t (-.f64 x z))
55.0ms	(.f64 y (.f64 t (-.f64 x z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	170	17
2	2202	17
3	6056	17
0	0	0
1	0	0

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-def_binary64`
384×	`fma-neg_binary64`
134×	`cancel-sign-sub-inv_binary64`
108×	`distribute-rgt-in_binary64`
86×	`distribute-lft-in_binary64`

Counts

126 → 56

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	708
1	64	708
2	107	708
3	158	708
4	266	708
5	396	708
6	613	708
7	816	708
8	863	708
9	935	708
10	947	708
11	947	708
12	884	708

prune40.0ms (0.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	49	9	58

Error

0.0b

Counts

58 → 9

Alt Table

Status	Error	Program
	29.0b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
▶	6.7b	(.f64 (-.f64 (.f64 t x) (*.f64 t z)) y)
	7.6b	(pow.f64 (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))) 3)
	47.7b	(pow.f64 (pow.f64 (.f64 y (.f64 t (-.f64 x z))) 3) 1/3)
	7.1b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	7.3b	(.f64 (-.f64 x z) (.f64 y t))
	7.6b	(.f64 y (pow.f64 (cbrt.f64 (.f64 t (-.f64 x z))) 3))
	36.3b	(cbrt.f64 (pow.f64 (.f64 y (.f64 t (-.f64 x z))) 3))
	31.3b	(pow.f64 (sqrt.f64 (.f64 y (.f64 t (-.f64 x z)))) 2)

Compiler

Compiled 817 to 367 computations (55.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (.f64 t x) (.f64 t z))
✓	6.4b	(.f64 (-.f64 (.f64 t x) (*.f64 t z)) y)

series21.0ms (0.3%)

Counts

2 → 54

Calls

2 calls:

14.0ms	(.f64 (-.f64 (.f64 t x) (*.f64 t z)) y)
6.0ms	(-.f64 (.f64 t x) (.f64 t z))

rewrite82.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

557×	`log-prod_binary64`
498×	`fma-def_binary64`
261×	`egg-rr`
216×	`fma-neg_binary64`
186×	`expm1-udef_binary64`

Counts

2 → 261

Calls

2 calls:

74.0ms	(-.f64 (.f64 t x) (.f64 t z))
74.0ms	(.f64 (-.f64 (.f64 t x) (*.f64 t z)) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	197	17
2	2586	17
3	5166	17
0	0	0
1	0	0

simplify61.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

773×	`fma-def_binary64`
335×	`fma-neg_binary64`
104×	`cancel-sign-sub-inv_binary64`
93×	`distribute-rgt-in_binary64`
90×	`unsub-neg_binary64`

Counts

315 → 275

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	462
1	74	462
2	162	462
3	288	462
4	445	462
5	729	462
6	871	462
7	951	462
8	959	462
9	959	462
10	896	462

prune212.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	269	6	275
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	275	9	284

Error

0.0b

Counts

284 → 9

Alt Table

Status	Error	Program
▶	6.7b	(fma.f64 (.f64 t (-.f64 x z)) y (.f64 (fma.f64 t (neg.f64 z) (*.f64 t z)) y))
	19.3b	(.f64 (fma.f64 (cbrt.f64 (.f64 t t)) (.f64 (cbrt.f64 t) x) (neg.f64 (.f64 t z))) y)
	36.8b	(.f64 (fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) t) (neg.f64 (*.f64 t z))) y)
	22.9b	(.f64 (fma.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) x) (neg.f64 (*.f64 t z))) y)
	7.1b	(.f64 (fma.f64 (cbrt.f64 (.f64 t x)) (pow.f64 (cbrt.f64 (.f64 t x)) 2) (neg.f64 (.f64 t z))) y)
	7.1b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	8.1b	(pow.f64 (cbrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 3)
	7.3b	(.f64 (-.f64 x z) (.f64 y t))
	36.3b	(cbrt.f64 (pow.f64 (.f64 y (.f64 t (-.f64 x z))) 3))

Compiler

Compiled 5420 to 1280 computations (76.4% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 t (-.f64 x z))
✓	6.4b	(fma.f64 (.f64 t (-.f64 x z)) y (.f64 (fma.f64 t (neg.f64 z) (*.f64 t z)) y))
✓	50.0b	(fma.f64 t (neg.f64 z) (*.f64 t z))

series31.0ms (0.4%)

Counts

2 → 72

Calls

2 calls:

23.0ms	(fma.f64 (.f64 t (-.f64 x z)) y (.f64 (fma.f64 t (neg.f64 z) (*.f64 t z)) y))
7.0ms	(fma.f64 t (neg.f64 z) (*.f64 t z))

rewrite67.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

607×	`log-prod_binary64`
255×	`fma-def_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
193×	`log-pow_binary64`

Counts

2 → 63

Calls

2 calls:

65.0ms	(fma.f64 (.f64 t (-.f64 x z)) y (.f64 (fma.f64 t (neg.f64 z) (*.f64 t z)) y))
65.0ms	(fma.f64 t (neg.f64 z) (*.f64 t z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	252	26
2	2883	24
3	5225	24
0	0	0
1	0	0

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-def_binary64`
291×	`fma-neg_binary64`
124×	`cancel-sign-sub-inv_binary64`
94×	`unsub-neg_binary64`
92×	`distribute-rgt-in_binary64`

Counts

135 → 74

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	492
1	81	492
2	177	492
3	337	492
4	578	492
5	760	492
6	918	492
7	963	492
8	967	492
9	967	492
10	904	492

prune66.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	101	9	110

Error

0.0b

Counts

110 → 9

Alt Table

Status	Error	Program
✓	6.7b	(fma.f64 (.f64 t (-.f64 x z)) y (.f64 (fma.f64 t (neg.f64 z) (*.f64 t z)) y))
	19.3b	(.f64 (fma.f64 (cbrt.f64 (.f64 t t)) (.f64 (cbrt.f64 t) x) (neg.f64 (.f64 t z))) y)
	36.8b	(.f64 (fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) t) (neg.f64 (*.f64 t z))) y)
	22.9b	(.f64 (fma.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) x) (neg.f64 (*.f64 t z))) y)
▶	7.1b	(.f64 (fma.f64 (cbrt.f64 (.f64 t x)) (pow.f64 (cbrt.f64 (.f64 t x)) 2) (neg.f64 (.f64 t z))) y)
	7.1b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	8.1b	(pow.f64 (cbrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 3)
	7.3b	(.f64 (-.f64 x z) (.f64 y t))
	36.3b	(cbrt.f64 (pow.f64 (.f64 y (.f64 t (-.f64 x z))) 3))

Compiler

Compiled 2167 to 590 computations (72.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (cbrt.f64 (.f64 t x)) (pow.f64 (cbrt.f64 (.f64 t x)) 2) (neg.f64 (*.f64 t z)))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 t x)) 2)
✓	6.4b	(.f64 (fma.f64 (cbrt.f64 (.f64 t x)) (pow.f64 (cbrt.f64 (.f64 t x)) 2) (neg.f64 (.f64 t z))) y)
✓	10.1b	(cbrt.f64 (*.f64 t x))

series2.8s (34.9%)

Counts

4 → 132

Calls

4 calls:

1.3s	(.f64 (fma.f64 (cbrt.f64 (.f64 t x)) (pow.f64 (cbrt.f64 (.f64 t x)) 2) (neg.f64 (.f64 t z))) y)
566.0ms	(cbrt.f64 (*.f64 t x))
500.0ms	(fma.f64 (cbrt.f64 (.f64 t x)) (pow.f64 (cbrt.f64 (.f64 t x)) 2) (neg.f64 (*.f64 t z)))
437.0ms	(pow.f64 (cbrt.f64 (*.f64 t x)) 2)

rewrite91.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

607×	`log-prod_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
192×	`pow3_binary64`
191×	`log-pow_binary64`

Counts

4 → 116

Calls

4 calls:

89.0ms	(fma.f64 (cbrt.f64 (.f64 t x)) (pow.f64 (cbrt.f64 (.f64 t x)) 2) (neg.f64 (*.f64 t z)))
88.0ms	(pow.f64 (cbrt.f64 (*.f64 t x)) 2)
88.0ms	(.f64 (fma.f64 (cbrt.f64 (.f64 t x)) (pow.f64 (cbrt.f64 (.f64 t x)) 2) (neg.f64 (.f64 t z))) y)
88.0ms	(cbrt.f64 (*.f64 t x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	64
1	265	38
2	2751	34
3	5000	34
4	4913	34
0	0	0
1	0	0

simplify104.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

512×	`fma-neg_binary64`
435×	`fma-def_binary64`
318×	`cancel-sign-sub-inv_binary64`
297×	`unsub-neg_binary64`
282×	`unswap-sqr_binary64`

Counts

248 → 155

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	2688
1	229	2688
2	448	2516
3	1124	1224
4	2672	1208
5	4018	1208
6	4897	1208

prune130.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	191	9	200

Error

0.0b

Counts

200 → 9

Alt Table

Status	Error	Program
✓	6.7b	(fma.f64 (.f64 t (-.f64 x z)) y (.f64 (fma.f64 t (neg.f64 z) (*.f64 t z)) y))
	19.3b	(.f64 (fma.f64 (cbrt.f64 (.f64 t t)) (.f64 (cbrt.f64 t) x) (neg.f64 (.f64 t z))) y)
	36.8b	(.f64 (fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) t) (neg.f64 (*.f64 t z))) y)
	22.9b	(.f64 (fma.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) x) (neg.f64 (*.f64 t z))) y)
✓	7.1b	(.f64 (fma.f64 (cbrt.f64 (.f64 t x)) (pow.f64 (cbrt.f64 (.f64 t x)) 2) (neg.f64 (.f64 t z))) y)
	7.1b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	8.1b	(pow.f64 (cbrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 3)
	7.3b	(.f64 (-.f64 x z) (.f64 y t))
	36.3b	(cbrt.f64 (pow.f64 (.f64 y (.f64 t (-.f64 x z))) 3))

Compiler

Compiled 3549 to 1243 computations (65% saved)

regimes1.4s (17.7%)

Accuracy

Total 0.7b remaining (97.3%)

Threshold costs 0.7b (97.3%)

Counts

109 → 5

Compiler

Compiled 9448 to 6026 computations (36.2% saved)

bsearch3.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	152
1	48	152
2	57	152
3	62	152
4	65	152
5	66	152
6	66	152

end273.0ms (3.4%)

Compiler: Compiled 578 to 206 computations (64.4% saved)

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Iter	Nodes	Cost
0	23	708
1	64	708
2	107	708
3	158	708
4	266	708
5	396	708
6	613	708
7	816	708
8	863	708
9	935	708
10	947	708
11	947	708
12	884	708

Iter	Nodes	Cost
0	26	462
1	74	462
2	162	462
3	288	462
4	445	462
5	729	462
6	871	462
7	951	462
8	959	462
9	959	462
10	896	462

Iter	Nodes	Cost
0	25	492
1	81	492
2	177	492
3	337	492
4	578	492
5	760	492
6	918	492
7	963	492
8	967	492
9	967	492
10	904	492

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Iter	Nodes	Cost
0	23	708
1	64	708
2	107	708
3	158	708
4	266	708
5	396	708
6	613	708
7	816	708
8	863	708
9	935	708
10	947	708
11	947	708
12	884	708

Iter	Nodes	Cost
0	26	462
1	74	462
2	162	462
3	288	462
4	445	462
5	729	462
6	871	462
7	951	462
8	959	462
9	959	462
10	896	462

Iter	Nodes	Cost
0	25	492
1	81	492
2	177	492
3	337	492
4	578	492
5	760	492
6	918	492
7	963	492
8	967	492
9	967	492
10	904	492

Details

analyze975.0ms (12.2%)

sample1.3s (16.7%)

simplify43.0ms (0.5%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series21.0ms (0.3%)

rewrite56.0ms (0.7%)

simplify74.0ms (0.9%)

prune40.0ms (0.5%)

localize8.0ms (0.1%)

series21.0ms (0.3%)

rewrite82.0ms (1%)

simplify61.0ms (0.8%)

prune212.0ms (2.7%)

localize12.0ms (0.1%)

series31.0ms (0.4%)

rewrite67.0ms (0.8%)

simplify59.0ms (0.7%)

prune66.0ms (0.8%)

localize10.0ms (0.1%)

series2.8s (34.9%)

rewrite91.0ms (1.1%)

simplify104.0ms (1.3%)

prune130.0ms (1.6%)

regimes1.4s (17.7%)

bsearch3.0ms (0%)

simplify6.0ms (0.1%)

end273.0ms (3.4%)

Profiling

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Iter	Nodes	Cost
0	23	708
1	64	708
2	107	708
3	158	708
4	266	708
5	396	708
6	613	708
7	816	708
8	863	708
9	935	708
10	947	708
11	947	708
12	884	708

Iter	Nodes	Cost
0	26	462
1	74	462
2	162	462
3	288	462
4	445	462
5	729	462
6	871	462
7	951	462
8	959	462
9	959	462
10	896	462

Iter	Nodes	Cost
0	25	492
1	81	492
2	177	492
3	337	492
4	578	492
5	760	492
6	918	492
7	963	492
8	967	492
9	967	492
10	904	492