Details

analyze1.9s (16.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample2.0s (17.4%)

Symmetry

(sort y z t)

(sort a b)

Results

1.3s	8256×	body	128	valid
438.0ms	3109×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
641×	`fma-def_binary64`
213×	`cancel-sign-sub-inv_binary64`
172×	`distribute-rgt-neg-in_binary64`
157×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	39	23
2	115	21
3	308	21
4	552	21
5	902	21
6	1201	21
7	1433	21
8	1672	21
9	1787	21
10	1791	21
11	1791	21
12	1791	21
13	1674	21

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
	2.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
▶	1.8b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 2 (.f64 (.f64 a 27) b))
✓	0.2b	(.f64 (.f64 a 27) b)
✓	0.3b	(.f64 (.f64 z t) -9)
✓	1.6b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series52.0ms (0.4%)

Counts

4 → 156

Calls

4 calls:

34.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
7.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))
6.0ms	(.f64 (.f64 a 27) b)
5.0ms	(.f64 (.f64 z t) -9)

rewrite67.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

288×	`expm1-udef_binary64`
288×	`log1p-udef_binary64`
258×	`prod-diff_binary64`
161×	`add-sqr-sqrt_binary64`
149×	`add-log-exp_binary64`

Counts

4 → 75

Calls

4 calls:

66.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))
66.0ms	(.f64 (.f64 a 27) b)
66.0ms	(.f64 (.f64 z t) -9)
66.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	46
1	323	46
2	3607	46
3	4924	46
0	0	0
1	0	0

simplify179.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

741×	`fma-def_binary64`
713×	`fma-neg_binary64`
298×	`cancel-sign-sub-inv_binary64`
179×	`distribute-rgt-neg-in_binary64`
119×	`unsub-neg_binary64`

Counts

231 → 89

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	2106
1	54	1992
2	120	1992
3	277	1992
4	478	1992
5	613	1992
6	879	1992
7	1175	1992
8	1476	1992
9	1604	1992
10	1747	1992
11	1781	1992
12	1781	1992
13	1781	1992
14	1666	1992

prune97.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Error

0.0b

Counts

91 → 7

Alt Table

Status	Error	Program
	2.9b	(.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))) 2))
	37.7b	(fma.f64 y (.f64 (.f64 z t) -9) (/.f64 (+.f64 (pow.f64 (.f64 x 2) 3) (pow.f64 (.f64 (.f64 a 27) b) 3)) (+.f64 (.f64 (.f64 x 2) (.f64 x 2)) (-.f64 (pow.f64 (.f64 (.f64 a 27) b) 2) (.f64 (.f64 x 2) (.f64 (.f64 a 27) b))))))
	32.2b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) 2)
	2.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	31.9b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (cbrt.f64 (.f64 (pow.f64 (.f64 a 27) 3) (pow.f64 b 3)))))
▶	1.8b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
✓	1.8b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 2075 to 1297 computations (37.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
✓	0.1b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
✓	0.2b	(.f64 (.f64 y (*.f64 t z)) -9)
✓	5.9b	(.f64 y (.f64 t z))

series62.0ms (0.5%)

Counts

4 → 156

Calls

4 calls:

31.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
13.0ms	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
10.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
8.0ms	(.f64 y (.f64 t z))

rewrite67.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

288×	`expm1-udef_binary64`
288×	`log1p-udef_binary64`
224×	`prod-diff_binary64`
161×	`add-sqr-sqrt_binary64`
149×	`add-log-exp_binary64`

Counts

4 → 75

Calls

4 calls:

65.0ms	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
65.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
65.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
65.0ms	(.f64 y (.f64 t z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
1	323	52
2	3626	52
3	4882	52
0	0	0
1	0	0

simplify193.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
713×	`fma-neg_binary64`
298×	`cancel-sign-sub-inv_binary64`
179×	`distribute-rgt-neg-in_binary64`
119×	`unsub-neg_binary64`

Counts

231 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	2448
1	50	2262
2	113	2262
3	275	2262
4	478	2262
5	613	2262
6	879	2262
7	1175	2262
8	1476	2262
9	1604	2262
10	1747	2262
11	1781	2262
12	1781	2262
13	1781	2262
14	1666	2262

prune81.0ms (0.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	9	93

Error

0.0b

Counts

93 → 9

Alt Table

Status	Error	Program
	32.2b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) 2)
	21.6b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (pow.f64 (sqrt.f64 (.f64 y (.f64 t z))) 2) -9)))
	25.3b	(fma.f64 27 (.f64 a b) (/.f64 (-.f64 (.f64 (.f64 2 x) (.f64 2 x)) (.f64 (pow.f64 (.f64 y (.f64 t z)) 2) 81)) (-.f64 (.f64 2 x) (.f64 (.f64 y (*.f64 t z)) -9))))
▶	2.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.9b	(.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))) 2))
	37.7b	(fma.f64 y (.f64 (.f64 z t) -9) (/.f64 (+.f64 (pow.f64 (.f64 x 2) 3) (pow.f64 (.f64 (.f64 a 27) b) 3)) (+.f64 (.f64 (.f64 x 2) (.f64 x 2)) (-.f64 (pow.f64 (.f64 (.f64 a 27) b) 2) (.f64 (.f64 x 2) (.f64 (.f64 a 27) b))))))
	31.9b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (cbrt.f64 (.f64 (pow.f64 (.f64 a 27) 3) (pow.f64 b 3)))))
✓	1.8b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
✓	1.8b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 2161 to 1185 computations (45.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
	0.2b	(.f64 (.f64 a 27) b)
✓	0.4b	(.f64 (.f64 y 9) z)
✓	6.6b	(.f64 (.f64 (*.f64 y 9) z) t)

series30.0ms (0.3%)

Counts

3 → 108

Calls

3 calls:

14.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
12.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
4.0ms	(.f64 (.f64 y 9) z)

rewrite94.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

688×	`log-prod_binary64`
426×	`fma-def_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
203×	`egg-rr`

Counts

3 → 203

Calls

3 calls:

88.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
88.0ms	(.f64 (.f64 y 9) z)
88.0ms	(.f64 (.f64 (*.f64 y 9) z) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	261	33
2	3190	33
3	5968	33
0	0	0
1	0	0

simplify100.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
290×	`fma-neg_binary64`
132×	`distribute-rgt-neg-in_binary64`
130×	`cancel-sign-sub-inv_binary64`
107×	`associate-l_binary64`

Counts

311 → 210

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	1194
1	35	1122
2	82	1122
3	192	1122
4	307	1122
5	375	1122
6	513	1122
7	648	1122
8	826	1122
9	958	1122
10	1051	1122
11	1081	1122
12	1081	1122
13	992	1122

prune268.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	3	3	6
Picked	1	0	1
Done	1	1	2
Total	227	7	234

Error

0.0b

Counts

234 → 7

Alt Table

Status	Error	Program
	32.2b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) 2)
▶	1.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	31.9b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (cbrt.f64 (.f64 (pow.f64 (.f64 a 27) 3) (pow.f64 b 3)))))
✓	1.8b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	2.9b	(.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))) 2))
	2.0b	(+.f64 (+.f64 (-.f64 (+.f64 x x) (.f64 (.f64 (.f64 y 9) z) t)) (+.f64 (fma.f64 (.f64 (.f64 y 9) z) (neg.f64 t) (.f64 (.f64 (.f64 y 9) z) t)) (fma.f64 (.f64 (.f64 y 9) z) (neg.f64 t) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (*.f64 a 27) b))
	18.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (cbrt.f64 (pow.f64 (.f64 (.f64 a 27) b) 3)))

Compiler

Compiled 7665 to 4579 computations (40.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t))
	0.2b	(.f64 (.f64 a 27) b)
✓	0.2b	(.f64 9 (.f64 y z))
✓	6.6b	(.f64 (.f64 9 (*.f64 y z)) t)

series31.0ms (0.3%)

Counts

3 → 84

Calls

3 calls:

14.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t))
10.0ms	(.f64 (.f64 9 (*.f64 y z)) t)
8.0ms	(.f64 9 (.f64 y z))

rewrite92.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

687×	`log-prod_binary64`
419×	`fma-def_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
201×	`egg-rr`

Counts

3 → 201

Calls

3 calls:

86.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t))
86.0ms	(.f64 9 (.f64 y z))
86.0ms	(.f64 (.f64 9 (*.f64 y z)) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	261	31
2	3189	31
3	5947	31
0	0	0
1	0	0

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
290×	`fma-neg_binary64`
130×	`distribute-rgt-neg-in_binary64`
130×	`cancel-sign-sub-inv_binary64`
109×	`associate-l_binary64`

Counts

285 → 207

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	1026
1	30	954
2	76	954
3	191	954
4	306	954
5	375	954
6	513	954
7	648	954
8	826	954
9	958	954
10	1051	954
11	1081	954
12	1081	954
13	992	954

prune250.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	223	6	229

Error

0.0b

Counts

229 → 6

Alt Table

Status	Error	Program
	32.2b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) 2)
	31.9b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (cbrt.f64 (.f64 (pow.f64 (.f64 a 27) 3) (pow.f64 b 3)))))
✓	1.8b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	2.9b	(.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))) 2))
	18.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (cbrt.f64 (pow.f64 (.f64 (.f64 a 27) b) 3)))
	1.7b	(+.f64 (fma.f64 x 2 (fma.f64 t (.f64 (.f64 y z) -9) (fma.f64 -9 (.f64 (.f64 y z) t) (.f64 (.f64 9 (.f64 y z)) t)))) (.f64 (*.f64 a 27) b))

Compiler

Compiled 7131 to 3506 computations (50.8% saved)

regimes5.0s (43.1%)

Accuracy

Total 0.6b remaining (94%)

Threshold costs 0.6b (94%)

Counts

157 → 2

Compiler

Compiled 63059 to 45105 computations (28.5% saved)

bsearch16.0ms (0.1%)

Steps

Iters	Range		Point
2	1.6045096754022188e-289	1.3562074921142716e-286	8.190218805873687e-289

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	52
1	45	52
2	61	52
3	77	52
4	87	52
5	92	52
6	93	52
7	92	52

end812.0ms (7%)

Compiler: Compiled 426 to 297 computations (30.3% saved)

Details

analyze1.9s (16.1%)

sample2.0s (17.4%)

simplify76.0ms (0.7%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series52.0ms (0.4%)

rewrite67.0ms (0.6%)

simplify179.0ms (1.5%)

prune97.0ms (0.8%)

localize11.0ms (0.1%)

series62.0ms (0.5%)

rewrite67.0ms (0.6%)

simplify193.0ms (1.7%)

prune81.0ms (0.7%)

localize11.0ms (0.1%)

series30.0ms (0.3%)

rewrite94.0ms (0.8%)

simplify100.0ms (0.9%)

prune268.0ms (2.3%)

localize15.0ms (0.1%)

series31.0ms (0.3%)

rewrite92.0ms (0.8%)

simplify94.0ms (0.8%)

prune250.0ms (2.2%)

regimes5.0s (43.1%)

bsearch16.0ms (0.1%)

simplify5.0ms (0%)

end812.0ms (7%)

Profiling