Details

analyze1.1s (12.5%)

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
24.9%	74.7%	0.3%	8
24.9%	74.7%	0.3%	9
24.9%	74.7%	0.3%	10
37.4%	62.3%	0.3%	11
37.4%	62.3%	0.3%	12
37.4%	62.3%	0.3%	13
37.4%	62.3%	0.3%	14

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample1.2s (14.5%)

Infinites

36.9% of outputs are infinite.

Symmetry

(sort x y)

(sort t a)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 80 to 56 computations (30% saved)

simplify62.0ms (0.7%)

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

prune5.0ms (0.1%)

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

5.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	10.4b	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) c)
	13.7b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 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)
✓	1.0b	(fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))
✓	2.9b	(/.f64 (fma.f64 x (*.f64 9 y) b) z)
✓	7.2b	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) c)

series146.0ms (1.7%)

Counts

4 → 240

Calls

4 calls:

76.0ms	(/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) c)
41.0ms	(fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))
22.0ms	(/.f64 (fma.f64 x (*.f64 9 y) b) z)
7.0ms	(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)

simplify172.0ms (2%)

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

prune447.0ms (5.2%)

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

4.5b

Counts

173 → 10

Alt Table

Status	Error	Program
	37.7b	(/.f64 (.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))) c)
	36.6b	(/.f64 (/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
	10.4b	(/.f64 (fma.f64 t (.f64 a -4) (.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z))) c)
	41.2b	(/.f64 b (*.f64 c z))
	10.4b	(/.f64 1 (/.f64 c (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z))))
	36.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)))) (sqrt.f64 c)) (/.f64 (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (sqrt.f64 c)))
	13.7b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))
	23.3b	(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
	10.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) (cbrt.f64 c)))
▶	10.4b	(/.f64 (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z)) c)

Compiler

Compiled 4430 to 2398 computations (45.9% saved)

localize42.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 9 (*.f64 y x) b)
✓	1.0b	(fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z))
✓	2.9b	(/.f64 (fma.f64 9 (*.f64 y x) b) z)
✓	7.2b	(/.f64 (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z)) c)

series142.0ms (1.7%)

Counts

4 → 240

Calls

4 calls:

78.0ms	(/.f64 (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z)) c)
36.0ms	(fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z))
20.0ms	(/.f64 (fma.f64 9 (*.f64 y x) b) z)
7.0ms	(fma.f64 9 (*.f64 y x) 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 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z)) c)
2.0ms	(/.f64 (fma.f64 9 (*.f64 y x) b) z)
0.0ms	(fma.f64 9 (*.f64 y x) b)
0.0ms	(fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z))

simplify175.0ms (2%)

Algorithm

1×	egg-herbie

Rules

912×	`div-sub_binary64`
608×	`fma-def_binary64`
469×	`fma-neg_binary64`
336×	`associate-/l/_binary64`
274×	`distribute-rgt-in_binary64`

Counts

318 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	6685
1	291	6160
2	711	5908
3	1954	5341
4	4239	5341
5	6423	5341

prune162.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	122	10	132

Error

4.5b

Counts

132 → 10

Alt Table

Status	Error	Program
	37.7b	(/.f64 (.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))) c)
	36.6b	(/.f64 (/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
▶	10.4b	(/.f64 1 (/.f64 c (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z))))
	36.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)))) (sqrt.f64 c)) (/.f64 (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (sqrt.f64 c)))
	13.7b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))
	23.3b	(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
	10.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) (cbrt.f64 c)))
✓	10.4b	(/.f64 (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z)) c)
	41.2b	(/.f64 b (*.f64 c z))
	10.4b	(/.f64 (fma.f64 a (.f64 t -4) (.f64 (fma.f64 9 (*.f64 y x) b) (/.f64 1 z))) c)

Compiler

Compiled 3163 to 1637 computations (48.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 c (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z))))
	1.0b	(fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z))
	2.9b	(/.f64 (fma.f64 9 (*.f64 y x) b) z)
✓	7.5b	(/.f64 c (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z)))

series388.0ms (4.5%)

Counts

2 → 168

Calls

2 calls:

308.0ms	(/.f64 c (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z)))
80.0ms	(/.f64 1 (/.f64 c (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z))))

rewrite17.0ms (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 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z))))
3.0ms	(/.f64 c (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z)))

simplify277.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

275 → 213

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	531	14808
1	1609	14085
2	5449	14085

prune576.0ms (6.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	269	11	280

Error

4.5b

Counts

280 → 11

Alt Table

Status	Error	Program
	23.3b	(/.f64 1 (/.f64 c (fma.f64 a (*.f64 t -4) (/.f64 b z))))
	37.7b	(/.f64 (.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))) c)
	36.6b	(/.f64 (/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
	13.7b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))
	23.3b	(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
	10.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) (cbrt.f64 c)))
✓	10.4b	(/.f64 (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z)) c)
	41.2b	(/.f64 b (*.f64 c z))
	36.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)))) (sqrt.f64 c)) (/.f64 (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (sqrt.f64 c)))
▶	10.4b	(/.f64 (fma.f64 a (.f64 t -4) (.f64 (fma.f64 9 (*.f64 y x) b) (/.f64 1 z))) c)
	45.4b	(/.f64 1 (.f64 1/9 (/.f64 (.f64 c z) (*.f64 y x))))

Compiler

Compiled 12032 to 6562 computations (45.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 9 (*.f64 y x) b)
✓	1.0b	(fma.f64 a (.f64 t -4) (.f64 (fma.f64 9 (*.f64 y x) b) (/.f64 1 z)))
✓	3.0b	(.f64 (fma.f64 9 (.f64 y x) b) (/.f64 1 z))
✓	7.2b	(/.f64 (fma.f64 a (.f64 t -4) (.f64 (fma.f64 9 (*.f64 y x) b) (/.f64 1 z))) c)

series137.0ms (1.6%)

Counts

3 → 204

Calls

3 calls:

82.0ms	(/.f64 (fma.f64 a (.f64 t -4) (.f64 (fma.f64 9 (*.f64 y x) b) (/.f64 1 z))) c)
37.0ms	(fma.f64 a (.f64 t -4) (.f64 (fma.f64 9 (*.f64 y x) b) (/.f64 1 z)))
18.0ms	(.f64 (fma.f64 9 (.f64 y x) b) (/.f64 1 z))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`

Counts

3 → 77

Calls

3 calls:

6.0ms	(.f64 (fma.f64 9 (.f64 y x) b) (/.f64 1 z))
2.0ms	(/.f64 (fma.f64 a (.f64 t -4) (.f64 (fma.f64 9 (*.f64 y x) b) (/.f64 1 z))) c)
0.0ms	(fma.f64 a (.f64 t -4) (.f64 (fma.f64 9 (*.f64 y x) b) (/.f64 1 z)))

simplify203.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-neg_binary64`
318×	`associate-/l/_binary64`
294×	`exp-prod_binary64`
290×	`cancel-sign-sub-inv_binary64`
281×	`associate-l_binary64`

Counts

281 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	6399
1	314	5850
2	840	5292
3	2559	4890
4	4500	4890
5	5015	4890

prune184.0ms (2.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	167	11	178

Error

4.5b

Counts

178 → 11

Alt Table

Status	Error	Program
	23.3b	(/.f64 1 (/.f64 c (fma.f64 a (*.f64 t -4) (/.f64 b z))))
	37.7b	(/.f64 (.f64 (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (sqrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))) c)
	36.6b	(/.f64 (/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
	13.7b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))
	23.3b	(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
	10.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)) (cbrt.f64 c)))
✓	10.4b	(/.f64 (fma.f64 a (.f64 t -4) (/.f64 (fma.f64 9 (.f64 y x) b) z)) c)
	41.2b	(/.f64 b (*.f64 c z))
	36.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z)))) (sqrt.f64 c)) (/.f64 (cbrt.f64 (fma.f64 t (.f64 a -4) (/.f64 (fma.f64 x (.f64 9 y) b) z))) (sqrt.f64 c)))
✓	10.4b	(/.f64 (fma.f64 a (.f64 t -4) (.f64 (fma.f64 9 (*.f64 y x) b) (/.f64 1 z))) c)
	45.4b	(/.f64 1 (.f64 1/9 (/.f64 (.f64 c z) (*.f64 y x))))

Compiler

Compiled 4290 to 2316 computations (46% saved)

regimes2.8s (32.4%)

Accuracy

Total 1.7b remaining (30.4%)

Threshold costs 0b (0%)

Counts

164 → 3

Compiler

Compiled 45158 to 31650 computations (29.9% saved)

bsearch64.0ms (0.7%)

Steps

Iters	Range		Point
9	1.9118042370036955e-134	7.767500227243946e-128	3.4192677792128576e-131
6	-2.306570264315408e-6	-3.773396175457599e-7	-6.985953318935387e-7

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
9×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	90
1	59	90
2	74	90
3	90	90
4	100	90
5	105	90
6	106	90
7	104	90

end211.0ms (2.5%)

Remove

(sort t a)

(sort x y)

Compiler

Compiled 704 to 461 computations (34.5% saved)

Details

analyze1.1s (12.5%)

sample1.2s (14.5%)

simplify62.0ms (0.7%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

series146.0ms (1.7%)

rewrite9.0ms (0.1%)

simplify172.0ms (2%)

prune447.0ms (5.2%)

localize42.0ms (0.5%)

series142.0ms (1.7%)

rewrite9.0ms (0.1%)

simplify175.0ms (2%)

prune162.0ms (1.9%)

localize15.0ms (0.2%)

series388.0ms (4.5%)

rewrite17.0ms (0.2%)

simplify277.0ms (3.2%)

prune576.0ms (6.7%)

localize14.0ms (0.2%)

series137.0ms (1.6%)

rewrite12.0ms (0.1%)

simplify203.0ms (2.4%)

prune184.0ms (2.1%)

regimes2.8s (32.4%)

bsearch64.0ms (0.7%)

simplify6.0ms (0.1%)

end211.0ms (2.5%)

Profiling