Details

analyze2.1s (22.7%)

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%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0%	99.7%	0.3%	13
0%	99.7%	0.3%	14

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample2.2s (24.1%)

Symmetry

(sort x y)

(sort t a)

Results

1.3s	8256×	body	128	valid
819.0ms	4935×	body	128	invalid

Compiler

Compiled 80 to 56 computations (30% saved)

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
568×	`div-sub_binary64`
502×	`associate-/r/_binary64`
476×	`distribute-neg-frac_binary64`
465×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	19	28
1	42	28
2	116	24
3	352	24
4	880	23
5	2041	21
6	4154	21
7	4365	21
8	4941	21

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

9.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.5b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))
▶	16.0b	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) c)

Compiler

Compiled 137 to 92 computations (32.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (*.f64 9 y) b)
✓	0.3b	(fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))
✓	4.1b	(/.f64 (fma.f64 x (*.f64 9 y) b) z)
✓	11.7b	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) c)

series214.0ms (2.3%)

Counts

4 → 240

Calls

4 calls:

106.0ms	(fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))
82.0ms	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) c)
20.0ms	(/.f64 (fma.f64 x (*.f64 9 y) b) z)
6.0ms	(fma.f64 x (*.f64 9 y) b)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 78

Calls

4 calls:

2.0ms	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) c)
2.0ms	(/.f64 (fma.f64 x (*.f64 9 y) b) z)
0.0ms	(fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))
0.0ms	(fma.f64 x (*.f64 9 y) b)

simplify174.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

913×	`div-sub_binary64`
630×	`fma-def_binary64`
477×	`fma-neg_binary64`
332×	`associate-/l/_binary64`
274×	`distribute-rgt-in_binary64`

Counts

318 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	6685
1	296	6160
2	725	5908
3	1995	5341
4	4278	5341
5	6463	5341

prune157.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	163	10	173

Error

9.0b

Counts

173 → 10

Alt Table

Status	Error	Program
	23.5b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))
	48.8b	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
	40.5b	(.f64 (/.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) 1) (/.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) c))
	42.9b	(.f64 -4 (/.f64 (.f64 a t) c))
	26.3b	(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
	33.7b	(/.f64 (+.f64 (.f64 9 (/.f64 (.f64 y x) z)) (/.f64 b z)) c)
	16.0b	(.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
	16.3b	(/.f64 1 (/.f64 c (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))))
▶	16.0b	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (.f64 y x) b)))) c)
	43.4b	(/.f64 b (*.f64 c z))

Compiler

Compiled 4310 to 2334 computations (45.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 z (fma.f64 9 (*.f64 y x) b)))
✓	0.3b	(fma.f64 t (.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (.f64 y x) b))))
✓	4.2b	(/.f64 z (fma.f64 9 (*.f64 y x) b))
✓	11.7b	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (.f64 y x) b)))) c)

series188.0ms (2%)

Counts

4 → 252

Calls

4 calls:

82.0ms	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (.f64 y x) b)))) c)
45.0ms	(/.f64 z (fma.f64 9 (*.f64 y x) b))
39.0ms	(fma.f64 t (.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (.f64 y x) b))))
20.0ms	(/.f64 1 (/.f64 z (fma.f64 9 (*.f64 y x) b)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`times-frac_binary64`
62×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
62×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

4 → 146

Calls

4 calls:

4.0ms	(/.f64 1 (/.f64 z (fma.f64 9 (*.f64 y x) b)))
2.0ms	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (.f64 y x) b)))) c)
2.0ms	(/.f64 z (fma.f64 9 (*.f64 y x) b))
0.0ms	(fma.f64 t (.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (.f64 y x) b))))

simplify221.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

724×	`associate-/r*_binary64`
390×	`associate-/r/_binary64`
356×	`fma-neg_binary64`
301×	`fma-def_binary64`
248×	`associate-/l/_binary64`

Counts

398 → 258

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	9758
1	574	8908
2	1887	8615
3	4915	8615
4	5131	8615

prune413.0ms (4.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	258	10	268

Error

9.0b

Counts

268 → 10

Alt Table

Status	Error	Program
	23.5b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))
	48.8b	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
	40.5b	(.f64 (/.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) 1) (/.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) c))
	42.9b	(.f64 -4 (/.f64 (.f64 a t) c))
	16.3b	(/.f64 1 (/.f64 c (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))))
	44.1b	(/.f64 (/.f64 b z) c)
	26.3b	(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
▶	16.0b	(.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
✓	16.0b	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (.f64 y x) b)))) c)
	43.4b	(/.f64 b (*.f64 c z))

Compiler

Compiled 7342 to 3993 computations (45.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (*.f64 9 y) b)
	0.3b	(fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))
	4.1b	(/.f64 (fma.f64 x (*.f64 9 y) b) z)
✓	11.7b	(.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

series115.0ms (1.2%)

Counts

1 → 84

Calls

1 calls:

114.0ms

(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 38

Calls

1 calls:

5.0ms

(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
740×	`distribute-rgt-in_binary64`
236×	`associate-l_binary64`
202×	`associate-r_binary64`
162×	`fma-neg_binary64`

Counts

122 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	3557
1	231	3078
2	599	2942
3	1901	2744
4	5182	2744

prune160.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	181	10	191

Error

9.0b

Counts

191 → 10

Alt Table

Status	Error	Program
	23.5b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))
	48.8b	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
▶	16.3b	(/.f64 1 (/.f64 c (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))))
	26.3b	(.f64 (fma.f64 t (.f64 a -4) (/.f64 b z)) (/.f64 1 c))
	44.1b	(/.f64 (/.f64 b z) c)
	42.9b	(.f64 -4 (/.f64 (.f64 a t) c))
	40.5b	(.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (/.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
	43.0b	(.f64 (.f64 (*.f64 a t) -4) (/.f64 1 c))
✓	16.0b	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (.f64 y x) b)))) c)
	43.4b	(/.f64 b (*.f64 c z))

Compiler

Compiled 4631 to 2671 computations (42.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))
✓	0.5b	(/.f64 1 (/.f64 c (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))))
	4.1b	(/.f64 (fma.f64 x (*.f64 9 y) b) z)
✓	11.7b	(/.f64 c (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)))

series422.0ms (4.6%)

Counts

2 → 168

Calls

2 calls:

310.0ms	(/.f64 c (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)))
111.0ms	(/.f64 1 (/.f64 c (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 c (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))))
2.0ms	(/.f64 c (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)))

simplify200.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
466×	`associate-/r*_binary64`
436×	`associate-/l*_binary64`
295×	`fma-def_binary64`
167×	`*-commutative_binary64`

Counts

275 → 213

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	532	14808
1	1616	14085
2	5455	14085

prune312.0ms (3.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	292	3	295
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	293	12	305

Error

9.0b

Counts

305 → 12

Alt Table

Status	Error	Program
	37.1b	(/.f64 1 (+.f64 (.f64 4 (/.f64 (.f64 c (.f64 a t)) (pow.f64 (+.f64 (.f64 9 (/.f64 (.f64 y x) z)) (/.f64 b z)) 2))) (/.f64 c (+.f64 (.f64 9 (/.f64 (*.f64 y x) z)) (/.f64 b z)))))
	23.5b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))
	48.8b	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
	43.0b	(.f64 (.f64 (*.f64 a t) -4) (/.f64 1 c))
	43.5b	(/.f64 1 (/.f64 (*.f64 c z) b))
✓	16.3b	(/.f64 1 (/.f64 c (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))))
	26.3b	(.f64 (fma.f64 t (.f64 a -4) (/.f64 b z)) (/.f64 1 c))
	44.1b	(/.f64 (/.f64 b z) c)
	42.9b	(.f64 -4 (/.f64 (.f64 a t) c))
	40.5b	(.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (/.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
	32.3b	(/.f64 1 (/.f64 (.f64 c z) (fma.f64 9 (.f64 y x) b)))
✓	16.0b	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (.f64 y x) b)))) c)

Compiler

Compiled 12392 to 6995 computations (43.6% saved)

regimes1.7s (18.1%)

Accuracy

Total 2.7b remaining (31.5%)

Threshold costs 0b (0%)

Counts

105 → 4

Compiler

Compiled 28826 to 19834 computations (31.2% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 26 to 18 computations (30.8% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64`
13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
10×	`distribute-rgt-neg-in_binary64`
9×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	199
1	76	199
2	97	199
3	118	199
4	137	199
5	145	199
6	147	199
7	145	199

end383.0ms (4.2%)

Remove: (sort x y)
Compiler: Compiled 1402 to 844 computations (39.8% saved)

Details

analyze2.1s (22.7%)

sample2.2s (24.1%)

simplify59.0ms (0.6%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series214.0ms (2.3%)

rewrite9.0ms (0.1%)

simplify174.0ms (1.9%)

prune157.0ms (1.7%)

localize13.0ms (0.1%)

series188.0ms (2%)

rewrite20.0ms (0.2%)

simplify221.0ms (2.4%)

prune413.0ms (4.5%)

localize15.0ms (0.2%)

series115.0ms (1.2%)

rewrite9.0ms (0.1%)

simplify89.0ms (1%)

prune160.0ms (1.7%)

localize16.0ms (0.2%)

series422.0ms (4.6%)

rewrite19.0ms (0.2%)

simplify200.0ms (2.2%)

prune312.0ms (3.4%)

regimes1.7s (18.1%)

bsearch5.0ms (0.1%)

simplify10.0ms (0.1%)

end383.0ms (4.2%)

Profiling