Details

analyze1.7s (17.6%)

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
0.6%	99.1%	0.3%	11
1.8%	98%	0.3%	12
2.6%	97.1%	0.3%	13
4%	95.7%	0.3%	14

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample1.3s (13.5%)

Results

1.2s	8256×	body	128	valid
64.0ms	424×	body	128	invalid

Compiler

Compiled 71 to 44 computations (38% saved)

simplify27.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

920×	`times-frac_binary64`
583×	`fma-def_binary64`
508×	`div-sub_binary64`
452×	`fma-neg_binary64`
447×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	25	21
2	50	21
3	105	21
4	195	21
5	334	21
6	559	21
7	990	21
8	2152	21

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

18.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.7b	(/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y))

Compiler

Compiled 80 to 41 computations (48.8% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (-.f64 b y) y)
✓	0.5b	(fma.f64 z (-.f64 t a) (*.f64 x y))
✓	18.1b	(/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y))

series165.0ms (1.7%)

Counts

3 → 168

Calls

3 calls:

146.0ms	(/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y))
13.0ms	(fma.f64 z (-.f64 t a) (*.f64 x y))
6.0ms	(fma.f64 z (-.f64 b y) y)

rewrite70.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

976×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
142×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	285	40
2	4020	40

Stop Event

1×	node limit

Counts

3 → 79

Calls

3 calls:

62.0ms	(fma.f64 z (-.f64 b y) y)
62.0ms	(fma.f64 z (-.f64 t a) (*.f64 x y))
62.0ms	(/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y))

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

768×	`times-frac_binary64`
647×	`associate-/l*_binary64`
486×	`fma-def_binary64`
258×	`+-commutative_binary64`
206×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	611	7996
1	2468	7320

Stop Event

1×	node limit

Counts

247 → 188

prune194.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	180	8	188
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	180	9	189

Error

0.0b

Counts

189 → 9

Alt Table

Status	Error	Program
	19.5b	(/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3))
✓	18.7b	(/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y))
	18.8b	(.f64 (fma.f64 z (-.f64 t a) (.f64 x y)) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	39.3b	(.f64 (/.f64 y (+.f64 y (.f64 z (-.f64 b y)))) x)
▶	17.0b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (/.f64 (-.f64 (.f64 x y) (.f64 z a)) (+.f64 y (.f64 z (-.f64 b y)))))
	27.9b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	32.0b	(/.f64 (-.f64 t a) (-.f64 b y))
	44.9b	(-.f64 (+.f64 (fma.f64 x z (/.f64 z (/.f64 y t))) x) (+.f64 (.f64 (/.f64 a y) z) (.f64 (/.f64 z y) (*.f64 x b))))
	30.4b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (/.f64 x (-.f64 1 z))) (fma.f64 (/.f64 z y) (/.f64 (*.f64 x b) (pow.f64 (-.f64 1 z) 2)) (/.f64 a (/.f64 (-.f64 1 z) (/.f64 z y)))))

Compiler

Compiled 9904 to 4131 computations (58.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 x y) (.f64 z a))
✓	3.6b	(/.f64 t (/.f64 (+.f64 y (*.f64 z (-.f64 b y))) z))
✓	10.1b	(/.f64 (+.f64 y (*.f64 z (-.f64 b y))) z)
✓	15.9b	(/.f64 (-.f64 (.f64 x y) (.f64 z a)) (+.f64 y (*.f64 z (-.f64 b y))))

series162.0ms (1.6%)

Counts

4 → 192

Calls

4 calls:

89.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z a)) (+.f64 y (*.f64 z (-.f64 b y))))
53.0ms	(/.f64 t (/.f64 (+.f64 y (*.f64 z (-.f64 b y))) z))
11.0ms	(/.f64 (+.f64 y (*.f64 z (-.f64 b y))) z)
8.0ms	(-.f64 (.f64 x y) (.f64 z a))

rewrite42.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

198×	`add-sqr-sqrt_binary64`
188×	`log1p-expm1-u_binary64`
188×	`expm1-log1p-u_binary64`
187×	`add-cbrt-cube_binary64`
183×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	61
1	378	55

Stop Event

1×	node limit

Counts

4 → 145

Calls

4 calls:

39.0ms	(-.f64 (.f64 x y) (.f64 z a))
39.0ms	(/.f64 t (/.f64 (+.f64 y (*.f64 z (-.f64 b y))) z))
39.0ms	(/.f64 (+.f64 y (*.f64 z (-.f64 b y))) z)
39.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z a)) (+.f64 y (*.f64 z (-.f64 b y))))

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

819×	`times-frac_binary64`
704×	`associate-/l*_binary64`
374×	`fma-def_binary64`
204×	`+-commutative_binary64`
161×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	601	7646
1	2392	7220

Stop Event

1×	node limit

Counts

337 → 294

prune296.0ms (3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	292	2	294
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	295	8	303

Error

0.0b

Counts

303 → 8

Alt Table

Status	Error	Program
	18.8b	(.f64 (fma.f64 z (-.f64 t a) (.f64 x y)) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	27.6b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (-.f64 (/.f64 x (-.f64 1 z)) (fma.f64 (/.f64 b y) (/.f64 x (/.f64 (pow.f64 (-.f64 1 z) 2) z)) (/.f64 a (.f64 (-.f64 1 z) (/.f64 y z))))))
	19.5b	(/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3))
✓	18.7b	(/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y))
▶	12.9b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (-.f64 (.f64 (/.f64 y (+.f64 y (.f64 z (-.f64 b y)))) x) (.f64 (/.f64 a (+.f64 y (*.f64 z (-.f64 b y)))) z)))
✓	17.0b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (/.f64 (-.f64 (.f64 x y) (.f64 z a)) (+.f64 y (.f64 z (-.f64 b y)))))
	27.9b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	32.0b	(/.f64 (-.f64 t a) (-.f64 b y))

Compiler

Compiled 15201 to 4920 computations (67.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.6b	(/.f64 t (/.f64 (+.f64 y (*.f64 z (-.f64 b y))) z))
✓	6.2b	(/.f64 y (+.f64 y (*.f64 z (-.f64 b y))))
✓	8.7b	(.f64 (/.f64 a (+.f64 y (.f64 z (-.f64 b y)))) z)
	10.1b	(/.f64 (+.f64 y (*.f64 z (-.f64 b y))) z)

series79.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

52.0ms	(.f64 (/.f64 a (+.f64 y (.f64 z (-.f64 b y)))) z)
26.0ms	(/.f64 y (+.f64 y (*.f64 z (-.f64 b y))))

rewrite54.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

401×	`fma-def_binary64`
238×	`expm1-udef_binary64`
238×	`log1p-udef_binary64`
196×	`fma-neg_binary64`
130×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	248	25
2	3747	25

Stop Event

1×	node limit

Counts

2 → 60

Calls

2 calls:

53.0ms	(/.f64 y (+.f64 y (*.f64 z (-.f64 b y))))
53.0ms	(.f64 (/.f64 a (+.f64 y (.f64 z (-.f64 b y)))) z)

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

525×	`times-frac_binary64`
394×	`associate-/l*_binary64`
371×	`associate-/r*_binary64`
210×	`associate-r_binary64`
168×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	434	4305
1	1631	4171

Stop Event

1×	node limit

Counts

144 → 183

prune365.0ms (3.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	311	2	313
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	314	7	321

Error

0.0b

Counts

321 → 7

Alt Table

Status	Error	Program
	18.8b	(.f64 (fma.f64 z (-.f64 t a) (.f64 x y)) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	12.9b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (-.f64 (.f64 (pow.f64 (/.f64 (fma.f64 z (-.f64 b y) y) y) -1) x) (.f64 (/.f64 a (+.f64 y (.f64 z (-.f64 b y)))) z)))
	27.6b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (-.f64 (/.f64 x (-.f64 1 z)) (fma.f64 (/.f64 b y) (/.f64 x (/.f64 (pow.f64 (-.f64 1 z) 2) z)) (/.f64 a (.f64 (-.f64 1 z) (/.f64 y z))))))
✓	17.0b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (/.f64 (-.f64 (.f64 x y) (.f64 z a)) (+.f64 y (.f64 z (-.f64 b y)))))
▶	12.5b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (-.f64 (.f64 (/.f64 y (+.f64 y (*.f64 z (-.f64 b y)))) x) (/.f64 a (-.f64 b y))))
✓	18.7b	(/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y))
	27.9b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))

Compiler

Compiled 17349 to 5149 computations (70.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.0b	(.f64 (/.f64 y (+.f64 y (.f64 z (-.f64 b y)))) x)
	3.6b	(/.f64 t (/.f64 (+.f64 y (*.f64 z (-.f64 b y))) z))
	6.2b	(/.f64 y (+.f64 y (*.f64 z (-.f64 b y))))
	10.1b	(/.f64 (+.f64 y (*.f64 z (-.f64 b y))) z)

series60.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

60.0ms

(*.f64 (/.f64 y (+.f64 y (*.f64 z (-.f64 b y)))) x)

rewrite48.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

395×	`fma-def_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
189×	`log-pow_binary64`
187×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	224	14
2	3339	14

Stop Event

1×	node limit

Counts

1 → 25

Calls

1 calls:

48.0ms

(*.f64 (/.f64 y (+.f64 y (*.f64 z (-.f64 b y)))) x)

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

342×	`times-frac_binary64`
300×	`associate-/l*_binary64`
230×	`fma-neg_binary64`
229×	`unswap-sqr_binary64`
208×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	2510
1	973	2252
2	4099	2195

Stop Event

1×	node limit

Counts

73 → 88

prune379.0ms (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	312	0	312
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	312	7	319

Error

0.0b

Counts

319 → 7

Alt Table

Status	Error	Program
	18.8b	(.f64 (fma.f64 z (-.f64 t a) (.f64 x y)) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	12.9b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (-.f64 (.f64 (pow.f64 (/.f64 (fma.f64 z (-.f64 b y) y) y) -1) x) (.f64 (/.f64 a (+.f64 y (.f64 z (-.f64 b y)))) z)))
	27.6b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (-.f64 (/.f64 x (-.f64 1 z)) (fma.f64 (/.f64 b y) (/.f64 x (/.f64 (pow.f64 (-.f64 1 z) 2) z)) (/.f64 a (.f64 (-.f64 1 z) (/.f64 y z))))))
✓	17.0b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (/.f64 (-.f64 (.f64 x y) (.f64 z a)) (+.f64 y (.f64 z (-.f64 b y)))))
✓	12.5b	(+.f64 (/.f64 t (/.f64 (+.f64 y (.f64 z (-.f64 b y))) z)) (-.f64 (.f64 (/.f64 y (+.f64 y (*.f64 z (-.f64 b y)))) x) (/.f64 a (-.f64 b y))))
✓	18.7b	(/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y))
	27.9b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))

Compiler

Compiled 15048 to 4904 computations (67.4% saved)

regimes4.3s (43.9%)

Accuracy

Total 2.0b remaining (95.2%)

Threshold costs 0b (0%)

Counts

241 → 4

Compiler

Compiled 64556 to 34795 computations (46.1% saved)

bsearch13.0ms (0.1%)

Compiler: Compiled 23 to 14 computations (39.1% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	312
1	78	312
2	98	312
3	110	312
4	116	312

Stop Event

1×

saturated

end163.0ms (1.6%)

Compiler: Compiled 684 to 252 computations (63.2% saved)

Details

analyze1.7s (17.6%)

sample1.3s (13.5%)

simplify27.0ms (0.3%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series165.0ms (1.7%)

rewrite70.0ms (0.7%)

simplify84.0ms (0.9%)

prune194.0ms (2%)

localize14.0ms (0.1%)

series162.0ms (1.6%)

rewrite42.0ms (0.4%)

simplify90.0ms (0.9%)

prune296.0ms (3%)

localize14.0ms (0.1%)

series79.0ms (0.8%)

rewrite54.0ms (0.5%)

simplify58.0ms (0.6%)

prune365.0ms (3.7%)

localize13.0ms (0.1%)

series60.0ms (0.6%)

rewrite48.0ms (0.5%)

simplify60.0ms (0.6%)

prune379.0ms (3.8%)

regimes4.3s (43.9%)

bsearch13.0ms (0.1%)

simplify10.0ms (0.1%)

end163.0ms (1.6%)

Profiling