Details

analyze735.0ms (11.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
6.2%	93.6%	0.1%	6
12.5%	87.4%	0.1%	7
15.6%	84.3%	0.1%	8
18.7%	71.8%	9.5%	9
23.4%	56%	20.6%	10
26.3%	52.2%	21.5%	11
31%	40.1%	28.9%	12
35.6%	28.9%	35.5%	13
36.8%	27.5%	35.7%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.4s (21.9%)

Symmetry

(sort x y z)

Results

1.1s	8256×	body	128	valid
259.0ms	2393×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
8×	`+-commutative_binary64`
8×	`*-commutative_binary64`
5×	`distribute-rgt-out_binary64`
3×	`associate-+r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	23	16
2	43	16
3	59	16
4	61	16
5	62	16
6	62	16

prune5.0ms (0.1%)

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

20.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.4b	(.f64 2 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))

Compiler

Compiled 56 to 34 computations (39.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.5b	(fma.f64 x (+.f64 y z) (*.f64 y z))
✓	19.3b	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

series182.0ms (2.9%)

Counts

2 → 48

Calls

2 calls:

174.0ms	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
7.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64`
3×	`sqrt-prod_binary64`
3×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

2 → 25

Calls

2 calls:

1.0ms	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
0.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

631×	`associate-l_binary64`
605×	`cancel-sign-sub-inv_binary64`
565×	`associate-r_binary64`
297×	`fma-neg_binary64`
197×	`fma-def_binary64`

Counts

73 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	214	1615
1	531	1523
2	1873	1478
3	4933	1478
4	5115	1478

prune167.0ms (2.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	59	11	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	11	71

Error

19.8b

Counts

71 → 11

Alt Table

Status	Error	Program
	48.2b	(.f64 2 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 y x (.f64 z (+.f64 y x))) 3))))
	41.9b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	63.3b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
	20.9b	(.f64 2 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))))
	42.9b	(.f64 2 (sqrt.f64 (.f64 y z)))
	21.3b	(.f64 2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	31.1b	(.f64 2 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	40.2b	(.f64 2 (sqrt.f64 (.f64 (+.f64 y z) x)))
▶	20.4b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))
	44.5b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	40.8b	(.f64 2 (sqrt.f64 (.f64 y x)))

Compiler

Compiled 2346 to 1149 computations (51% saved)

localize188.0ms (3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (+.f64 y x))
✓	1.7b	(fma.f64 y x (*.f64 z (+.f64 y x)))
✓	19.3b	(sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))

series212.0ms (3.4%)

Counts

3 → 72

Calls

3 calls:

198.0ms	(sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))
8.0ms	(fma.f64 y x (*.f64 z (+.f64 y x)))
6.0ms	(*.f64 z (+.f64 y x))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 50

Calls

3 calls:

6.0ms	(*.f64 z (+.f64 y x))
1.0ms	(sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))
0.0ms	(fma.f64 y x (*.f64 z (+.f64 y x)))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

608×	`cancel-sign-sub-inv_binary64`
468×	`times-frac_binary64`
347×	`distribute-rgt-in_binary64`
321×	`distribute-lft-in_binary64`
216×	`fma-def_binary64`

Counts

122 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	2028
1	619	1906
2	2320	1861
3	4705	1861
4	5405	1861

prune143.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	114	11	125

Error

19.8b

Counts

125 → 11

Alt Table

Status	Error	Program
	43.2b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 (*.f64 z (sqrt.f64 (+.f64 y x))) (sqrt.f64 (+.f64 y x))))))
	20.9b	(.f64 2 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))))
▶	20.6b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (+.f64 y x))))))
	40.8b	(.f64 2 (sqrt.f64 (.f64 y x)))
	63.3b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
	42.9b	(.f64 2 (sqrt.f64 (.f64 y z)))
	21.3b	(.f64 2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	31.1b	(.f64 2 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	41.9b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	40.2b	(.f64 2 (sqrt.f64 (.f64 (+.f64 y z) x)))
	44.5b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))

Compiler

Compiled 3054 to 1432 computations (53.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	1.7b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (+.f64 y x))))
✓	19.3b	(sqrt.f64 (fma.f64 y x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (+.f64 y x)))))

series330.0ms (5.3%)

Counts

4 → 72

Calls

4 calls:

238.0ms	(sqrt.f64 (fma.f64 y x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (+.f64 y x)))))
38.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
35.0ms	(cbrt.f64 z)
18.0ms	(fma.f64 y x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (+.f64 y x))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
12×	`pow1_binary64`

Counts

4 → 80

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(sqrt.f64 (fma.f64 y x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (+.f64 y x)))))
1.0ms	(cbrt.f64 z)
0.0ms	(fma.f64 y x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (+.f64 y x))))

simplify117.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

696×	`cancel-sign-sub-inv_binary64`
618×	`times-frac_binary64`
276×	`unswap-sqr_binary64`
259×	`associate-r_binary64`
215×	`associate-l_binary64`

Counts

152 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	268	2300
1	627	2112
2	2455	2062
3	4486	2047
4	4953	2047
5	4972	2047

prune195.0ms (3.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	189	11	200

Error

19.8b

Counts

200 → 11

Alt Table

Status	Error	Program
	43.2b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 (*.f64 z (sqrt.f64 (+.f64 y x))) (sqrt.f64 (+.f64 y x))))))
▶	20.9b	(.f64 2 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))))
✓	20.6b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (+.f64 y x))))))
	40.8b	(.f64 2 (sqrt.f64 (.f64 y x)))
	63.3b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
	42.9b	(.f64 2 (sqrt.f64 (.f64 y z)))
	21.3b	(.f64 2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	31.1b	(.f64 2 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	41.9b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	40.2b	(.f64 2 (sqrt.f64 (.f64 (+.f64 y z) x)))
	44.5b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))

Compiler

Compiled 5204 to 2075 computations (60.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x)))))
✓	0.4b	(.f64 (fabs.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))))
	1.7b	(fma.f64 y x (*.f64 z (+.f64 y x)))
✓	19.9b	(cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))

series275.0ms (4.4%)

Counts

3 → 108

Calls

3 calls:

137.0ms

(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))))

70.0ms

(cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))

67.0ms

(sqrt.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x)))))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
26×	`cbrt-prod_binary64`
22×	`sqrt-prod_binary64`
15×	`unswap-sqr_binary64`
12×	`fabs-mul_binary64`

Counts

3 → 84

Calls

3 calls:

7.0ms

(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))))

1.0ms

(sqrt.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x)))))

1.0ms

(cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))

simplify204.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

867×	`fma-def_binary64`
430×	`*-commutative_binary64`
197×	`cancel-sign-sub-inv_binary64`
194×	`associate-r_binary64`
174×	`sqr-pow_binary64`

Counts

192 → 344

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	957	14057
1	3246	13209
2	4974	13209

prune624.0ms (9.9%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	493	5	498
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	494	15	509

Error

19.8b

Counts

509 → 15

Alt Table

Status	Error	Program
	43.2b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 (*.f64 z (sqrt.f64 (+.f64 y x))) (sqrt.f64 (+.f64 y x))))))
✓	20.9b	(.f64 2 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))))
	31.1b	(.f64 2 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	21.0b	(.f64 2 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x))))) 3))
	40.2b	(.f64 2 (sqrt.f64 (.f64 (+.f64 y z) x)))
	23.1b	(.f64 2 (.f64 (fabs.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 2/3)) (cbrt.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))) (sqrt.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))))
	21.3b	(.f64 2 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) (.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))))))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x))))))))
	45.3b	(.f64 2 (.f64 (fabs.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (+.f64 z x)) (log.f64 y)))) (sqrt.f64 (cbrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x)))))))
✓	20.6b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (+.f64 y x))))))
	40.8b	(.f64 2 (sqrt.f64 (.f64 y x)))
	63.3b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
	42.9b	(.f64 2 (sqrt.f64 (.f64 y z)))
	41.9b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	21.1b	(.f64 2 (.f64 (fabs.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))) (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))) (cbrt.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x))))))) (sqrt.f64 (cbrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))))
	44.5b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))

Compiler

Compiled 28804 to 11999 computations (58.3% saved)

regimes654.0ms (10.4%)

Accuracy

Total 0.5b remaining (2.6%)

Threshold costs 0.5b (2.6%)

Counts

102 → 1

Compiler

Compiled 14288 to 8288 computations (42% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16
2	13	16

end635.0ms (10.1%)

Compiler: Compiled 424 to 232 computations (45.3% saved)

Details

analyze735.0ms (11.7%)

sample1.4s (21.9%)

simplify7.0ms (0.1%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series182.0ms (2.9%)

rewrite2.0ms (0%)

simplify72.0ms (1.1%)

prune167.0ms (2.7%)

localize188.0ms (3%)

series212.0ms (3.4%)

rewrite9.0ms (0.1%)

simplify82.0ms (1.3%)

prune143.0ms (2.3%)

localize11.0ms (0.2%)

series330.0ms (5.3%)

rewrite10.0ms (0.2%)

simplify117.0ms (1.9%)

prune195.0ms (3.1%)

localize12.0ms (0.2%)

series275.0ms (4.4%)

rewrite17.0ms (0.3%)

simplify204.0ms (3.2%)

prune624.0ms (9.9%)

regimes654.0ms (10.4%)

simplify2.0ms (0%)

end635.0ms (10.1%)

Profiling