Details

analyze1.5s (17.5%)

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
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
14%	83.4%	2.5%	11
18.7%	78.2%	3.1%	12
28.1%	65.5%	6.4%	13
30.7%	59.4%	9.9%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample2.1s (25.7%)

Results

1.2s	8256×	body	128	valid
905.0ms	6229×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`associate-/l*_binary64`
6×	`associate-*r/_binary64`
6×	`associate-/r/_binary64`
6×	`fma-def_binary64`
4×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	20
2	45	20
3	59	20
4	61	20

Stop Event

1×

saturated

Counts

1 → 2

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

12.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.2b	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (/.f64 x (.f64 y y))))
	31.3b	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))

Compiler

Compiled 107 to 55 computations (48.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (/.f64 x (.f64 y y))))
✓	5.1b	(.f64 x (/.f64 x (.f64 y y)))
✓	7.9b	(/.f64 x (*.f64 y y))

series118.0ms (1.4%)

Counts

3 → 96

Calls

3 calls:

64.0ms	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (/.f64 x (.f64 y y))))
27.0ms	(/.f64 x (*.f64 y y))
27.0ms	(.f64 x (/.f64 x (.f64 y y)))

rewrite67.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

565×	`log-prod_binary64`
257×	`prod-diff_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`
180×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	211	27
2	2881	27

Stop Event

1×	node limit

Counts

3 → 95

Calls

3 calls:

65.0ms	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (/.f64 x (.f64 y y))))
65.0ms	(.f64 x (/.f64 x (.f64 y y)))
65.0ms	(/.f64 x (*.f64 y y))

simplify66.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

652×	`unswap-sqr_binary64`
529×	`associate-/l*_binary64`
347×	`associate-/r*_binary64`
289×	`associate-/l/_binary64`
229×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	1320
1	29	1320
2	55	1248
3	143	1248
4	622	1248
5	3635	1248
6	4970	1248

Stop Event

1×	node limit

Counts

191 → 103

prune137.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Error

0.1b

Counts

105 → 10

Alt Table

Status	Error	Program
▶	0.4b	(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)
	39.1b	(/.f64 z (/.f64 (*.f64 t t) z))
	1.2b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) 3)
	42.6b	(/.f64 (pow.f64 z 2) (pow.f64 t 2))
	5.1b	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) y) (/.f64 (cbrt.f64 x) y))))
	4.7b	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (.f64 (/.f64 x y) (/.f64 1 y))))
	11.0b	(fma.f64 (/.f64 z t) (/.f64 z t) (/.f64 (/.f64 (*.f64 x x) y) y))
	12.6b	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (.f64 x (pow.f64 y -2))))
	26.0b	(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2) 2)))
	34.4b	(fma.f64 (/.f64 z t) (/.f64 z t) (*.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2)))

Compiler

Compiled 2084 to 918 computations (56% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (/.f64 z t) (/.f64 x y))
✓	0.4b	(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)

series253.0ms (3%)

Counts

2 → 96

Calls

2 calls:

216.0ms	(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)
37.0ms	(hypot.f64 (/.f64 z t) (/.f64 x y))

rewrite55.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`log-prod_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`
176×	`pow3_binary64`
171×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	212	23
2	2683	23

Stop Event

1×	node limit

Counts

2 → 71

Calls

2 calls:

53.0ms	(hypot.f64 (/.f64 z t) (/.f64 x y))
53.0ms	(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

907×	`associate-/l*_binary64`
766×	`associate-/r*_binary64`
196×	`fma-def_binary64`
140×	`associate-/r/_binary64`
140×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	2816
1	275	2768
2	1183	2632

Stop Event

1×	node limit

Counts

167 → 107

prune109.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	106	11	117

Error

0.0b

Counts

117 → 11

Alt Table

Status	Error	Program
	1.2b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) 3)
	4.7b	(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))
	0.8b	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
	3.1b	(fma.f64 (*.f64 (/.f64 z t) z) (/.f64 1 t) (pow.f64 (/.f64 x y) 2))
	11.0b	(fma.f64 (/.f64 z t) (/.f64 z t) (/.f64 (/.f64 (*.f64 x x) y) y))
	12.6b	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (.f64 x (pow.f64 y -2))))
	0.8b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (*.f64 (cbrt.f64 (/.f64 x y)) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))
	39.1b	(/.f64 z (/.f64 (*.f64 t t) z))
	4.8b	(fma.f64 z (*.f64 (/.f64 1 t) (/.f64 z t)) (pow.f64 (/.f64 x y) 2))
	34.4b	(fma.f64 (/.f64 z t) (/.f64 z t) (*.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2)))
▶	0.8b	(.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))

Compiler

Compiled 2574 to 1252 computations (51.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)))
	0.4b	(pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)
✓	1.3b	(cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))
✓	9.4b	(cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2))

series439.0ms (5.3%)

Counts

3 → 144

Calls

3 calls:

188.0ms

(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)))

141.0ms

(cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2))

110.0ms

(cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

rewrite71.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`log-prod_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
212×	`log-pow_binary64`
138×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54
1	267	54
2	3278	54

Stop Event

1×	node limit

Counts

3 → 73

Calls

3 calls:

69.0ms

(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)))

69.0ms

(cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

69.0ms

(cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2))

simplify120.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l*_binary64`
560×	`associate-/r*_binary64`
263×	`fma-def_binary64`
227×	`*-commutative_binary64`
224×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	582	10302
1	2127	9808

Stop Event

1×	node limit

Counts

217 → 265

prune354.0ms (4.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	315	3	318
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	316	13	329

Error

0.0b

Counts

329 → 13

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
	11.0b	(fma.f64 (/.f64 z t) (/.f64 z t) (/.f64 (/.f64 (*.f64 x x) y) y))
	1.2b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) 3)
	4.7b	(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))
▶	0.8b	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
	3.1b	(fma.f64 (*.f64 (/.f64 z t) z) (/.f64 1 t) (pow.f64 (/.f64 x y) 2))
	12.6b	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (.f64 x (pow.f64 y -2))))
	2.7b	(.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 1/6))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
	1.1b	(.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (.f64 (cbrt.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (pow.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 2))) (cbrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
	39.1b	(/.f64 z (/.f64 (*.f64 t t) z))
	4.8b	(fma.f64 z (*.f64 (/.f64 1 t) (/.f64 z t)) (pow.f64 (/.f64 x y) 2))
	34.4b	(fma.f64 (/.f64 z t) (/.f64 z t) (*.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2)))
✓	0.8b	(.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))

Compiler

Compiled 17877 to 8801 computations (50.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 (/.f64 z t) (/.f64 x y))
✓	0.3b	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
✓	0.7b	(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3)
✓	0.8b	(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series374.0ms (4.5%)

Counts

3 → 96

Calls

3 calls:

213.0ms

(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))

107.0ms

(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3)

53.0ms

(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

rewrite71.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

598×	`log-prod_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
204×	`log-pow_binary64`
138×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	259	38
2	3208	38

Stop Event

1×	node limit

Counts

3 → 99

Calls

3 calls:

69.0ms

(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))

69.0ms

(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3)

69.0ms

(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

743×	`times-frac_binary64`
412×	`associate-/r*_binary64`
371×	`associate-/l*_binary64`
311×	`associate-l_binary64`
308×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	3276
1	351	3234
2	1156	3036

Stop Event

1×	node limit

Counts

195 → 135

prune272.0ms (3.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	281	3	284
Fresh	5	6	11
Picked	0	1	1
Done	0	1	1
Total	286	11	297

Error

Counts

297 → 11

Alt Table

Status	Error	Program
	1.2b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) 3)
	4.7b	(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))
✓	0.8b	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
	0.4b	(.f64 (.f64 (pow.f64 1 3/2) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2)) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
	0.6b	(.f64 (.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/4) (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/4)) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
	36.4b	(cbrt.f64 (*.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2) (pow.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3/2) 3)))
	1.1b	(.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (.f64 (cbrt.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (pow.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 2))) (cbrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
	39.1b	(/.f64 z (/.f64 (*.f64 t t) z))
	4.8b	(fma.f64 z (*.f64 (/.f64 1 t) (/.f64 z t)) (pow.f64 (/.f64 x y) 2))
	34.4b	(fma.f64 (/.f64 z t) (/.f64 z t) (*.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2)))
✓	0.8b	(.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))

Compiler

Compiled 8687 to 3502 computations (59.7% saved)

regimes1.9s (22.6%)

Accuracy

Total 0.4b remaining (87.1%)

Threshold costs 0.4b (87.1%)

Counts

142 → 1

Compiler

Compiled 34055 to 19760 computations (42% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	14	13

Stop Event

1×

saturated

end170.0ms (2%)

Compiler: Compiled 296 to 156 computations (47.3% saved)

Details

analyze1.5s (17.5%)

sample2.1s (25.7%)

simplify8.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series118.0ms (1.4%)

rewrite67.0ms (0.8%)

simplify66.0ms (0.8%)

prune137.0ms (1.6%)

localize7.0ms (0.1%)

series253.0ms (3%)

rewrite55.0ms (0.7%)

simplify56.0ms (0.7%)

prune109.0ms (1.3%)

localize15.0ms (0.2%)

series439.0ms (5.3%)

rewrite71.0ms (0.9%)

simplify120.0ms (1.4%)

prune354.0ms (4.2%)

localize10.0ms (0.1%)

series374.0ms (4.5%)

rewrite71.0ms (0.8%)

simplify62.0ms (0.7%)

prune272.0ms (3.3%)

regimes1.9s (22.6%)

simplify4.0ms (0%)

end170.0ms (2%)

Profiling