Details

analyze891.0ms (12.8%)

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
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.9s (27.3%)

Results

1.3s	8256×	body	128	valid
378.0ms	3024×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	72	17
3	227	17
4	512	17
5	1044	17
6	1436	17
7	1492	17
8	1573	17
9	1615	17
10	1631	17
11	1631	17
12	1550	17

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

6.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.5b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z z))
✓	6.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series42.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

37.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
5.0ms	(-.f64 t (*.f64 z z))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-neg_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(-.f64 t (*.f64 z z))
0.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

703×	`distribute-rgt-in_binary64`
653×	`distribute-lft-in_binary64`
495×	`fma-neg_binary64`
369×	`exp-prod_binary64`
193×	`fma-def_binary64`

Counts

103 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	1591
1	187	1301
2	431	1282
3	1535	1282
4	4588	1282
5	5085	1282

prune51.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	6	65

Error

6.0b

Counts

65 → 6

Alt Table

Status	Error	Program
✓	6.5b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	43.7b	(pow.f64 x 2)
	27.3b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
▶	7.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	18.9b	(fma.f64 x x (.f64 4 (.f64 y t)))
	36.5b	(.f64 4 (.f64 y t))

Compiler

Compiled 1243 to 495 computations (60.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
✓	0.6b	(.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
✓	1.5b	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))
	6.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series749.0ms (10.7%)

Counts

3 → 144

Calls

3 calls:

455.0ms

(*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))

250.0ms

(cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))

43.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))

1.0ms

(cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))

simplify285.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

478×	`*-commutative_binary64`
220×	`+-commutative_binary64`
212×	`cancel-sign-sub-inv_binary64`
207×	`fma-def_binary64`
195×	`sub-neg_binary64`

Counts

237 → 282

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1128	19837
1	3968	19315
2	5082	19315

prune910.0ms (13%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	568	1	569
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	568	7	575

Error

6.0b

Counts

575 → 7

Alt Table

Status	Error	Program
	36.5b	(.f64 4 (.f64 y t))
	39.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (pow.f64 (-.f64 (pow.f64 x 2) (.f64 4 (.f64 y (pow.f64 z 2)))) 1/3)) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))
✓	6.5b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	43.7b	(pow.f64 x 2)
	27.3b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
✓	7.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
▶	18.9b	(fma.f64 x x (.f64 4 (.f64 y t)))

Compiler

Compiled 51444 to 29862 computations (42% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 4 (.f64 y t))

series7.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

7.0ms

(*.f64 4 (*.f64 y t))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 4 (*.f64 y t))

simplify78.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

395×	`associate-*l/_binary64`
335×	`*-commutative_binary64`
334×	`associate-l_binary64`
333×	`log-div_binary64`
275×	`log-prod_binary64`

Counts

20 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	208
1	85	172
2	255	172
3	646	172
4	819	172
5	961	172
6	1167	172
7	2632	172
8	4088	172
9	4873	172
10	4966	172

prune26.0ms (0.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	20	7	27

Error

6.0b

Counts

27 → 7

Alt Table

Status	Error	Program
▶	19.4b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t))))
	36.5b	(.f64 4 (.f64 y t))
	39.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (pow.f64 (-.f64 (pow.f64 x 2) (.f64 4 (.f64 y (pow.f64 z 2)))) 1/3)) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))
✓	6.5b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	43.7b	(pow.f64 x 2)
	27.3b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
✓	7.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))

Compiler

Compiled 536 to 317 computations (40.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t)))
✓	0.4b	(.f64 (cbrt.f64 4) (.f64 y t))
✓	1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

series45.0ms (0.6%)

Counts

3 → 24

Calls

3 calls:

32.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t)))
13.0ms	(.f64 (cbrt.f64 4) (.f64 y t))
0.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64`
31×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`pow-prod-down_binary64`
19×	`cbrt-prod_binary64`

Counts

3 → 95

Calls

3 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t)))
6.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
4.0ms	(.f64 (cbrt.f64 4) (.f64 y t))

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

514×	`unswap-sqr_binary64`
426×	`sqr-pow_binary64`
395×	`fma-def_binary64`
342×	`*-commutative_binary64`
295×	`associate-/l*_binary64`

Counts

119 → 120

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	102	1255
1	196	1067
2	701	1063
3	1233	1049
4	2179	973
5	3719	973
6	4906	973

prune133.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	119	8	127

Error

6.0b

Counts

127 → 8

Alt Table

Status	Error	Program
	27.3b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
	35.9b	(fma.f64 x x (cbrt.f64 (.f64 (.f64 4 4) (.f64 (.f64 (.f64 (cbrt.f64 4) (.f64 y t)) (.f64 (cbrt.f64 4) (.f64 y t))) (.f64 (cbrt.f64 4) (.f64 y t))))))
	36.5b	(.f64 4 (.f64 y t))
	39.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (pow.f64 (-.f64 (pow.f64 x 2) (.f64 4 (.f64 y (pow.f64 z 2)))) 1/3)) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))
✓	6.5b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	19.9b	(fma.f64 x x (.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (.f64 (cbrt.f64 4) (.f64 y t))))
	43.7b	(pow.f64 x 2)
✓	7.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))

Compiler

Compiled 2602 to 1825 computations (29.9% saved)

regimes1.4s (20.1%)

Accuracy

Total 0.7b remaining (12.6%)

Threshold costs 0.7b (12.6%)

Counts

131 → 1

Compiler

Compiled 32784 to 22329 computations (31.9% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	17	17
2	24	17
3	28	17
4	30	17
5	30	17

end127.0ms (1.8%)

Compiler: Compiled 234 to 148 computations (36.8% saved)

Details

analyze891.0ms (12.8%)

sample1.9s (27.3%)

simplify62.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series42.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify85.0ms (1.2%)

prune51.0ms (0.7%)

localize11.0ms (0.2%)

series749.0ms (10.7%)

rewrite22.0ms (0.3%)

simplify285.0ms (4.1%)

prune910.0ms (13%)

localize5.0ms (0.1%)

series7.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify78.0ms (1.1%)

prune26.0ms (0.4%)

localize9.0ms (0.1%)

series45.0ms (0.6%)

rewrite25.0ms (0.4%)

simplify79.0ms (1.1%)

prune133.0ms (1.9%)

regimes1.4s (20.1%)

simplify6.0ms (0.1%)

end127.0ms (1.8%)

Profiling