Details

analyze1.4s (20.9%)

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)

sample1.5s (22.2%)

Results

878.0ms	6893×	body	128	valid
157.0ms	390×	body	1024	valid
153.0ms	1270×	body	128	invalid
140.0ms	505×	body	512	valid
88.0ms	401×	body	256	valid
29.0ms	67×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

930×	`fma-def_binary64`
859×	`div-sub_binary64`
817×	`unsub-neg_binary64`
555×	`neg-mul-1_binary64`
380×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	24	17
2	52	17
3	155	17
4	477	17
5	1268	17
6	3213	17
7	4154	17
8	4434	17
9	4965	17
10	4951	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

15.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	15.7b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
▶	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Compiler

Compiled 100 to 54 computations (46% 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))
✓	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series95.0ms (1.4%)

Counts

2 → 108

Calls

2 calls:

64.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
30.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite69.0ms (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 → 74

Calls

2 calls:

67.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
67.0ms	(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

simplify97.0ms (1.4%)

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

182 → 142

Iterations

Useful iterations: 2 (0.0ms)

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

prune144.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	134	10	144

Error

0.6b

Counts

144 → 10

Alt Table

Status	Error	Program
	40.9b	(fma.f64 (-.f64 y z) (.f64 (sqrt.f64 (-.f64 t x)) (.f64 (sqrt.f64 (-.f64 t x)) (/.f64 1 (-.f64 a z)))) x)
	31.9b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
▶	15.7b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
	42.4b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	21.0b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))
	35.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	42.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) 2)
	43.6b	(-.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))))))
	40.4b	(-.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)))
✓	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Compiler

Compiled 4996 to 1632 computations (67.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	3.2b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
✓	5.8b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

series158.0ms (2.3%)

Counts

2 → 120

Calls

2 calls:

93.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
65.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite75.0ms (1.1%)

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

2 → 77

Calls

2 calls:

73.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
73.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	287	33
2	4401	33
3	5270	33
0	0	0
1	0	0

simplify135.0ms (2%)

Algorithm

1×	egg-herbie

Rules

612×	`cancel-sign-sub-inv_binary64`
570×	`sub-neg_binary64`
563×	`associate-+r+_binary64`
422×	`associate-+l+_binary64`
362×	`+-commutative_binary64`

Counts

197 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	7336
1	1017	7336
2	3902	6730
3	5411	6730

prune198.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	233	4	237
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	237	10	247

Error

0.6b

Counts

247 → 10

Alt Table

Status	Error	Program
	21.0b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))
	39.7b	(fma.f64 (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x)
▶	15.8b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
	31.9b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	42.2b	(+.f64 x (/.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (sqrt.f64 (-.f64 a z))) (sqrt.f64 (-.f64 a z))))
	35.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	42.4b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	43.6b	(-.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))))))
	40.4b	(-.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)))
✓	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Compiler

Compiled 8702 to 2769 computations (68.2% 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))
✓	4.1b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
✓	6.1b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

series190.0ms (2.8%)

Counts

3 → 168

Calls

3 calls:

92.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
67.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))
30.0ms	(/.f64 (-.f64 a z) (-.f64 t x))

rewrite91.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

294×	`log1p-udef_binary64`
160×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
149×	`add-log-exp_binary64`

Counts

3 → 122

Calls

3 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	296	43
2	4767	43
3	5265	43
0	0	0
1	0	0

simplify154.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-+r+_binary64`
461×	`associate-+l+_binary64`
408×	`+-commutative_binary64`
333×	`fma-neg_binary64`
293×	`associate--l+_binary64`

Counts

290 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	379	8872
1	1200	8755
2	4639	8149
3	4987	8149

prune179.0ms (2.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	232	10	242

Error

0.6b

Counts

242 → 10

Alt Table

Status	Error	Program
✓	15.8b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
▶	12.0b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
	42.4b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	16.1b	(+.f64 x (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 y z)) 2) (-.f64 a z)) (/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 1 (-.f64 t x)))))
	21.0b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))
	39.7b	(fma.f64 (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	35.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	43.6b	(-.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))))))
	40.4b	(-.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)))
✓	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Compiler

Compiled 8477 to 2688 computations (68.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
✓	3.5b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)

series83.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

61.0ms	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
22.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

rewrite68.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

2 → 74

Calls

2 calls:

66.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
66.0ms	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	257	27
2	3780	27
3	5347	27
0	0	0
1	0	0

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

574×	`cancel-sign-sub-inv_binary64`
500×	`sub-neg_binary64`
341×	`associate-+r+_binary64`
297×	`+-commutative_binary64`
288×	`distribute-neg-in_binary64`

Counts

170 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	4642
1	835	4633
2	3385	4573
3	5205	4573

prune132.0ms (1.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	158	10	168

Error

0.6b

Counts

168 → 10

Alt Table

Status	Error	Program
✓	15.8b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
✓	12.0b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
	42.4b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	12.0b	(fma.f64 (*.f64 (-.f64 y z) (/.f64 1 (-.f64 a z))) (-.f64 t x) x)
	21.0b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))
	39.7b	(fma.f64 (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	35.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	43.6b	(-.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))))))
	40.4b	(-.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)))
✓	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Compiler

Compiled 5218 to 1687 computations (67.7% saved)

regimes1.6s (23.9%)

Accuracy

Total 3.5b remaining (79.7%)

Threshold costs 0b (0%)

Counts

136 → 5

Compiler

Compiled 18372 to 10836 computations (41% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

29×	`+-commutative_binary64`
23×	`*-commutative_binary64`
20×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	237
1	80	237
2	102	237
3	130	237
4	169	237
5	187	237
6	197	237
7	200	237
8	200	237

end165.0ms (2.4%)

Compiler: Compiled 602 to 254 computations (57.8% saved)

Iter	Nodes	Cost
0	54	237
1	80	237
2	102	237
3	130	237
4	169	237
5	187	237
6	197	237
7	200	237
8	200	237

Iter	Nodes	Cost
0	54	237
1	80	237
2	102	237
3	130	237
4	169	237
5	187	237
6	197	237
7	200	237
8	200	237

Details

analyze1.4s (20.9%)

sample1.5s (22.2%)

simplify84.0ms (1.2%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series95.0ms (1.4%)

rewrite69.0ms (1%)

simplify97.0ms (1.4%)

prune144.0ms (2.1%)

localize9.0ms (0.1%)

series158.0ms (2.3%)

rewrite75.0ms (1.1%)

simplify135.0ms (2%)

prune198.0ms (2.9%)

localize9.0ms (0.1%)

series190.0ms (2.8%)

rewrite91.0ms (1.3%)

simplify154.0ms (2.2%)

prune179.0ms (2.6%)

localize9.0ms (0.1%)

series83.0ms (1.2%)

rewrite68.0ms (1%)

simplify93.0ms (1.4%)

prune132.0ms (1.9%)

regimes1.6s (23.9%)

bsearch5.0ms (0.1%)

simplify11.0ms (0.2%)

end165.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	54	237
1	80	237
2	102	237
3	130	237
4	169	237
5	187	237
6	197	237
7	200	237
8	200	237