Details

analyze891.0ms (15.4%)

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
7.8%	92%	0.2%	8
15.6%	84.2%	0.2%	9
23.4%	76.4%	0.2%	10
25%	74.9%	0.2%	11
37.9%	59.6%	2.5%	12
41.4%	55.7%	2.9%	13
46.3%	50.6%	3.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (20.8%)

Results

943.0ms	8256×	body	128	valid
206.0ms	1831×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary64`
547×	`fma-neg_binary64`
454×	`div-sub_binary64`
251×	`distribute-rgt-in_binary64`
229×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	33	16
3	68	16
4	130	16
5	233	16
6	479	16
7	1128	16
8	2572	16

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

5.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.4b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 56 to 35 computations (37.5% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
✓	0.0b	(/.f64 t (-.f64 1 z))
✓	5.2b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series49.0ms (0.9%)

Counts

3 → 78

Calls

3 calls:

29.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
13.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
8.0ms	(/.f64 t (-.f64 1 z))

rewrite78.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

408×	`fma-def_binary64`
234×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
209×	`fma-neg_binary64`
187×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	248	36
2	3758	36

Stop Event

1×	node limit

Counts

3 → 187

Calls

3 calls:

69.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
69.0ms	(/.f64 t (-.f64 1 z))
69.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

396×	`cancel-sign-sub-inv_binary64`
301×	`fma-neg_binary64`
293×	`fma-def_binary64`
233×	`times-frac_binary64`
230×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1328
1	235	1302
2	699	1241
3	2287	1195

Stop Event

1×	node limit

Counts

265 → 237

prune175.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	231	6	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	232	6	238

Error

0.0b

Counts

238 → 6

Alt Table

Status	Error	Program
	6.3b	(*.f64 x (pow.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) 3))
	20.4b	(*.f64 (/.f64 x z) (+.f64 y t))
	22.0b	(.f64 x (/.f64 1 (/.f64 (.f64 z (-.f64 1 z)) (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t)))))
▶	5.3b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	44.4b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3)) x) (fma.f64 (/.f64 t (-.f64 1 z)) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (pow.f64 (/.f64 y z) 2)))
	5.4b	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))

Compiler

Compiled 5167 to 2759 computations (46.6% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	1.7b	(/.f64 (*.f64 t x) (-.f64 1 z))
✓	5.7b	(/.f64 (*.f64 y x) z)

series53.0ms (0.9%)

Counts

3 → 42

Calls

3 calls:

25.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
16.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
11.0ms	(/.f64 (*.f64 y x) z)

rewrite81.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`expm1-udef_binary64`
255×	`log1p-udef_binary64`
145×	`egg-rr`
141×	`add-sqr-sqrt_binary64`
133×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	272	36
2	4341	36

Stop Event

1×	node limit

Counts

3 → 145

Calls

3 calls:

78.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
78.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
78.0ms	(/.f64 (*.f64 y x) z)

simplify37.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

635×	`cancel-sign-sub-inv_binary64`
593×	`fma-neg_binary64`
462×	`times-frac_binary64`
364×	`fma-def_binary64`
153×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	857
1	198	845
2	633	717
3	2372	710

Stop Event

1×	node limit

Counts

187 → 181

prune185.0ms (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	180	7	187

Error

Counts

187 → 7

Alt Table

Status	Error	Program
	20.4b	(*.f64 (/.f64 x z) (+.f64 y t))
▶	5.4b	(-.f64 (/.f64 (.f64 y x) z) (.f64 (*.f64 x t) (/.f64 1 (-.f64 1 z))))
	22.0b	(.f64 x (/.f64 1 (/.f64 (.f64 z (-.f64 1 z)) (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t)))))
	26.8b	(-.f64 (pow.f64 (sqrt.f64 (/.f64 y (/.f64 z x))) 2) (/.f64 (*.f64 t x) (-.f64 1 z)))
	6.9b	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))
	44.4b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3)) x) (fma.f64 (/.f64 t (-.f64 1 z)) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (pow.f64 (/.f64 y z) 2)))
	5.4b	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))

Compiler

Compiled 3946 to 1767 computations (55.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 y x) z) (.f64 (*.f64 x t) (/.f64 1 (-.f64 1 z))))
✓	0.0b	(/.f64 1 (-.f64 1 z))
✓	1.8b	(.f64 (.f64 x t) (/.f64 1 (-.f64 1 z)))
	5.7b	(/.f64 (*.f64 y x) z)

series51.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

28.0ms	(-.f64 (/.f64 (.f64 y x) z) (.f64 (*.f64 x t) (/.f64 1 (-.f64 1 z))))
20.0ms	(.f64 (.f64 x t) (/.f64 1 (-.f64 1 z)))
2.0ms	(/.f64 1 (-.f64 1 z))

rewrite65.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

263×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
149×	`add-sqr-sqrt_binary64`
140×	`add-cbrt-cube_binary64`
140×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	293	36
2	4332	36

Stop Event

1×	node limit

Counts

3 → 94

Calls

3 calls:

63.0ms	(-.f64 (/.f64 (.f64 y x) z) (.f64 (*.f64 x t) (/.f64 1 (-.f64 1 z))))
63.0ms	(/.f64 1 (-.f64 1 z))
63.0ms	(.f64 (.f64 x t) (/.f64 1 (-.f64 1 z)))

simplify47.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

654×	`cancel-sign-sub-inv_binary64`
641×	`fma-neg_binary64`
467×	`times-frac_binary64`
407×	`fma-def_binary64`
179×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1658
1	254	1626
2	804	1411
3	2836	1411

Stop Event

1×	node limit

Counts

190 → 146

prune175.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	189	6	195

Error

Counts

195 → 6

Alt Table

Status	Error	Program
	6.9b	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))
	6.6b	(-.f64 (.f64 y (.f64 x (/.f64 1 z))) (.f64 (.f64 x t) (/.f64 1 (-.f64 1 z))))
	20.4b	(*.f64 (/.f64 x z) (+.f64 y t))
	5.7b	(-.f64 (pow.f64 (/.f64 z (.f64 y x)) -1) (.f64 (*.f64 x t) (/.f64 1 (-.f64 1 z))))
	44.4b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3)) x) (fma.f64 (/.f64 t (-.f64 1 z)) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (pow.f64 (/.f64 y z) 2)))
▶	5.4b	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))

Compiler

Compiled 4025 to 1776 computations (55.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (neg.f64 t) (-.f64 1 z))
✓	0.1b	(fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z)))
✓	5.2b	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))

series73.0ms (1.3%)

Counts

3 → 108

Calls

3 calls:

48.0ms	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))
14.0ms	(fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z)))
10.0ms	(/.f64 (neg.f64 t) (-.f64 1 z))

rewrite99.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

390×	`prod-diff_binary64`
238×	`egg-rr`
209×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	44
1	256	36
2	3464	36

Stop Event

1×	node limit

Counts

3 → 238

Calls

3 calls:

92.0ms	(/.f64 (neg.f64 t) (-.f64 1 z))
92.0ms	(fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z)))
92.0ms	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))

simplify55.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

678×	`fma-neg_binary64`
595×	`cancel-sign-sub-inv_binary64`
304×	`fma-def_binary64`
217×	`associate-+l+_binary64`
177×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1662
1	231	1636
2	697	1575
3	2301	1541

Stop Event

1×	node limit

Counts

346 → 287

prune314.0ms (5.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	287	6	293

Error

Counts

293 → 6

Alt Table

Status	Error	Program
	6.9b	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))
	6.6b	(-.f64 (.f64 y (.f64 x (/.f64 1 z))) (.f64 (.f64 x t) (/.f64 1 (-.f64 1 z))))
	20.4b	(*.f64 (/.f64 x z) (+.f64 y t))
	5.7b	(-.f64 (pow.f64 (/.f64 z (.f64 y x)) -1) (.f64 (*.f64 x t) (/.f64 1 (-.f64 1 z))))
	44.4b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3)) x) (fma.f64 (/.f64 t (-.f64 1 z)) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (pow.f64 (/.f64 y z) 2)))
✓	5.4b	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))

Compiler

Compiled 10375 to 6444 computations (37.9% saved)

regimes1.9s (32.7%)

Accuracy

Total 1.3b remaining (97.6%)

Threshold costs 0b (0%)

Counts

149 → 5

Compiler

Compiled 17935 to 11992 computations (33.1% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

92×	`distribute-rgt-neg-in_binary64`
77×	`cancel-sign-sub-inv_binary64`
67×	`distribute-lft-neg-in_binary64`
64×	`neg-sub0_binary64`
63×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	197
1	79	197
2	117	195
3	151	191
4	199	191
5	236	191
6	257	191
7	280	191
8	316	191
9	360	191
10	413	191
11	503	191
12	601	191
13	680	191
14	715	191
15	736	191
16	751	191
17	755	191

Stop Event

1×

saturated

end119.0ms (2.1%)

Compiler: Compiled 394 to 228 computations (42.1% saved)

Iter	Nodes	Cost
0	50	197
1	79	197
2	117	195
3	151	191
4	199	191
5	236	191
6	257	191
7	280	191
8	316	191
9	360	191
10	413	191
11	503	191
12	601	191
13	680	191
14	715	191
15	736	191
16	751	191
17	755	191

Iter	Nodes	Cost
0	50	197
1	79	197
2	117	195
3	151	191
4	199	191
5	236	191
6	257	191
7	280	191
8	316	191
9	360	191
10	413	191
11	503	191
12	601	191
13	680	191
14	715	191
15	736	191
16	751	191
17	755	191

Details

analyze891.0ms (15.4%)

sample1.2s (20.8%)

simplify22.0ms (0.4%)

prune2.0ms (0%)

localize10.0ms (0.2%)

series49.0ms (0.9%)

rewrite78.0ms (1.4%)

simplify44.0ms (0.8%)

prune175.0ms (3%)

localize12.0ms (0.2%)

series53.0ms (0.9%)

rewrite81.0ms (1.4%)

simplify37.0ms (0.6%)

prune185.0ms (3.2%)

localize13.0ms (0.2%)

series51.0ms (0.9%)

rewrite65.0ms (1.1%)

simplify47.0ms (0.8%)

prune175.0ms (3%)

localize8.0ms (0.1%)

series73.0ms (1.3%)

rewrite99.0ms (1.7%)

simplify55.0ms (0.9%)

prune314.0ms (5.4%)

regimes1.9s (32.7%)

bsearch5.0ms (0.1%)

simplify26.0ms (0.4%)

end119.0ms (2.1%)

Profiling

Iter	Nodes	Cost
0	50	197
1	79	197
2	117	195
3	151	191
4	199	191
5	236	191
6	257	191
7	280	191
8	316	191
9	360	191
10	413	191
11	503	191
12	601	191
13	680	191
14	715	191
15	736	191
16	751	191
17	755	191