Details

analyze1.7s (19.7%)

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)

sample1.9s (21.4%)

Results

1.0s	6913×	body	128	valid
284.0ms	1254×	body	128	invalid
185.0ms	373×	body	1024	valid
171.0ms	505×	body	512	valid
90.0ms	390×	body	256	valid
36.0ms	75×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify88.0ms (1%)

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%)

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

10.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.6b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	25.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

Compiler

Compiled 100 to 55 computations (45% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	13.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series99.0ms (1.1%)

Counts

2 → 108

Calls

2 calls:

70.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
29.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite163.0ms (1.9%)

Algorithm

1×	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:

161.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
161.0ms	(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

simplify103.0ms (1.2%)

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

prune126.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	135	9	144

Error

0.7b

Counts

144 → 9

Alt Table

Status	Error	Program
	38.8b	(fma.f64 (-.f64 y z) (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a z))) (/.f64 (-.f64 t x) (sqrt.f64 (-.f64 a z)))) x)
	30.0b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	14.4b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) 3)
	39.4b	(-.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)))
▶	13.7b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
	25.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	37.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	14.4b	(fma.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) 2)) x)
	13.7b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

Compiler

Compiled 4859 to 1558 computations (67.9% 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))
✓	3.5b	(+.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)))

series163.0ms (1.9%)

Counts

2 → 120

Calls

2 calls:

103.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
59.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite84.0ms (1%)

Algorithm

1×	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:

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

Iterations

Useful iterations: 1 (0.0ms)

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

simplify148.0ms (1.7%)

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

prune227.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	233	4	237
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	236	10	246

Error

0.7b

Counts

246 → 10

Alt Table

Status	Error	Program
	14.1b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) 2) (cbrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	13.7b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	14.4b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) 3)
	39.4b	(-.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)))
	13.9b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
▶	13.7b	(+.f64 x (+.f64 (.f64 y (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z)))))
	30.0b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
	37.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.8b	(fma.f64 (-.f64 y z) (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a z))) (/.f64 (-.f64 t x) (sqrt.f64 (-.f64 a z)))) x)
	25.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

Compiler

Compiled 8607 to 2725 computations (68.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z))))
✓	3.2b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
✓	3.5b	(+.f64 x (+.f64 (.f64 y (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z)))))
✓	5.4b	(*.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z)))

series275.0ms (3.1%)

Counts

4 → 228

Calls

4 calls:

101.0ms	(+.f64 x (+.f64 (.f64 y (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z)))))
92.0ms	(+.f64 (.f64 y (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z))))
44.0ms	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
37.0ms	(*.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite102.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

302×	`log1p-udef_binary64`
179×	`add-sqr-sqrt_binary64`
173×	`log1p-expm1-u_binary64`
173×	`expm1-log1p-u_binary64`
165×	`add-cbrt-cube_binary64`

Counts

4 → 137

Calls

4 calls:

98.0ms	(+.f64 (.f64 y (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z))))
98.0ms	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
98.0ms	(+.f64 x (+.f64 (.f64 y (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z)))))
98.0ms	(*.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	67
1	339	59
2	4536	59
3	4991	59

simplify286.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

657×	`associate-+r+_binary64`
542×	`associate-+l+_binary64`
480×	`fma-neg_binary64`
390×	`associate--l+_binary64`
384×	`associate--r+_binary64`

Counts

365 → 279

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	390	11259
1	1305	11259
2	4802	11259
3	5167	11259

prune256.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	279	0	279
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	279	10	289

Error

0.7b

Counts

289 → 10

Alt Table

Status	Error	Program
	14.1b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) 2) (cbrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x)
▶	13.7b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	14.4b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) 3)
	39.4b	(-.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)))
	13.9b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
✓	13.7b	(+.f64 x (+.f64 (.f64 y (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z)))))
	30.0b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
	37.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.8b	(fma.f64 (-.f64 y z) (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a z))) (/.f64 (-.f64 t x) (sqrt.f64 (-.f64 a z)))) x)
	25.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

Compiler

Compiled 11337 to 3269 computations (71.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.2b	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
✓	13.5b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

series96.0ms (1.1%)

Counts

3 → 132

Calls

3 calls:

58.0ms	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
29.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
9.0ms	(/.f64 1 (-.f64 a z))

rewrite75.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`fma-def_binary64`
268×	`expm1-udef_binary64`
268×	`log1p-udef_binary64`
246×	`fma-neg_binary64`
150×	`add-sqr-sqrt_binary64`

Counts

3 → 91

Calls

3 calls:

73.0ms	(/.f64 1 (-.f64 a z))
73.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
73.0ms	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	34
1	290	34
2	3859	34
3	5408	34

simplify118.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

524×	`cancel-sign-sub-inv_binary64`
456×	`sub-neg_binary64`
369×	`associate-+r+_binary64`
309×	`distribute-neg-in_binary64`
288×	`+-commutative_binary64`

Counts

223 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	278	5577
1	870	5559
2	3447	5523
3	5238	5523

prune209.0ms (2.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	173	10	183

Error

0.7b

Counts

183 → 10

Alt Table

Status	Error	Program
	14.1b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) 2) (cbrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x)
✓	13.7b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	38.3b	(fma.f64 (-.f64 y z) (/.f64 (sqrt.f64 (-.f64 t x)) (/.f64 (-.f64 a z) (sqrt.f64 (-.f64 t x)))) x)
	14.4b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) 3)
	39.4b	(-.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)))
	13.9b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
✓	13.7b	(+.f64 x (+.f64 (.f64 y (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (neg.f64 z) (/.f64 (-.f64 t x) (-.f64 a z)))))
	30.0b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
	37.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	25.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

Compiler

Compiled 5264 to 1773 computations (66.3% saved)

regimes2.3s (26.1%)

Accuracy

Total 5.8b remaining (86.4%)

Threshold costs 0b (0%)

Counts

79 → 5

Compiler

Compiled 9174 to 5502 computations (40% saved)

bsearch3.0ms (0%)

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

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

27×	`+-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	268
1	79	268
2	101	268
3	129	268
4	168	268
5	186	268
6	196	268
7	199	268
8	198	268

end209.0ms (2.4%)

Compiler: Compiled 594 to 226 computations (62% saved)

Iter	Nodes	Cost
0	54	268
1	79	268
2	101	268
3	129	268
4	168	268
5	186	268
6	196	268
7	199	268
8	198	268

Iter	Nodes	Cost
0	54	268
1	79	268
2	101	268
3	129	268
4	168	268
5	186	268
6	196	268
7	199	268
8	198	268

Details

analyze1.7s (19.7%)

sample1.9s (21.4%)

simplify88.0ms (1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series99.0ms (1.1%)

rewrite163.0ms (1.9%)

simplify103.0ms (1.2%)

prune126.0ms (1.4%)

localize9.0ms (0.1%)

series163.0ms (1.9%)

rewrite84.0ms (1%)

simplify148.0ms (1.7%)

prune227.0ms (2.6%)

localize11.0ms (0.1%)

series275.0ms (3.1%)

rewrite102.0ms (1.2%)

simplify286.0ms (3.2%)

prune256.0ms (2.9%)

localize9.0ms (0.1%)

series96.0ms (1.1%)

rewrite75.0ms (0.9%)

simplify118.0ms (1.3%)

prune209.0ms (2.4%)

regimes2.3s (26.1%)

bsearch3.0ms (0%)

simplify12.0ms (0.1%)

end209.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	54	268
1	79	268
2	101	268
3	129	268
4	168	268
5	186	268
6	196	268
7	199	268
8	198	268