Details

analyze1.0s (16.1%)

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)

sample1.6s (25.7%)

Results

1.0s	8256×	body	128	valid
379.0ms	3097×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify70.0ms (1.1%)

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

3.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z z))
✓	3.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series39.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

34.0ms	(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))

simplify76.0ms (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

prune62.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	7	65

Error

2.8b

Counts

65 → 7

Alt Table

Status	Error	Program
▶	4.1b	(fma.f64 y (.f64 4 (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))
	24.6b	(.f64 (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	16.1b	(fma.f64 x x (.f64 4 (.f64 y t)))
	36.2b	(.f64 4 (.f64 y t))
	23.4b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
✓	3.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	38.9b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (pow.f64 t 3) (pow.f64 z 6)) (+.f64 (pow.f64 z 4) (.f64 t (fma.f64 z z t))))) (*.f64 x x))

Compiler

Compiled 1321 to 537 computations (59.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))) (cbrt.f64 (-.f64 t (*.f64 z z))))
✓	0.5b	(.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z))))
✓	3.1b	(fma.f64 y (.f64 4 (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))
✓	3.7b	(cbrt.f64 (-.f64 t (*.f64 z z)))

series156.0ms (2.5%)

Counts

4 → 120

Calls

4 calls:

56.0ms	(.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z))))
46.0ms	(fma.f64 y (.f64 4 (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))
37.0ms	(cbrt.f64 (-.f64 t (*.f64 z z)))
16.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))) (cbrt.f64 (-.f64 t (*.f64 z z))))

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`
31×	`add-sqr-sqrt_binary64`

Counts

4 → 144

Calls

4 calls:

17.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))) (cbrt.f64 (-.f64 t (*.f64 z z))))
8.0ms	(.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z))))
2.0ms	(cbrt.f64 (-.f64 t (*.f64 z z)))
0.0ms	(fma.f64 y (.f64 4 (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))

simplify189.0ms (3%)

Algorithm

1×	egg-herbie

Rules

935×	`times-frac_binary64`
348×	`associate-r_binary64`
294×	`associate-l_binary64`
294×	`fma-neg_binary64`
191×	`*-commutative_binary64`

Counts

264 → 286

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	366	6920
1	898	6367
2	3025	6113
3	4983	6113
4	4991	6113

prune414.0ms (6.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	407	1	408
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	407	8	415

Error

2.8b

Counts

415 → 8

Alt Table

Status	Error	Program
▶	4.3b	(fma.f64 y (.f64 4 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))
	36.2b	(.f64 4 (.f64 y t))
✓	4.1b	(fma.f64 y (.f64 4 (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))
	24.6b	(.f64 (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	16.1b	(fma.f64 x x (.f64 4 (.f64 y t)))
	23.4b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
✓	3.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	38.9b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (pow.f64 t 3) (pow.f64 z 6)) (+.f64 (pow.f64 z 4) (.f64 t (fma.f64 z z t))))) (*.f64 x x))

Compiler

Compiled 17225 to 6522 computations (62.1% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z))))))
✓	1.6b	(cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z)))))
✓	3.1b	(fma.f64 y (.f64 4 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))
	3.7b	(cbrt.f64 (-.f64 t (*.f64 z z)))

series158.0ms (2.5%)

Counts

3 → 96

Calls

3 calls:

58.0ms

(*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 t (*.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z))))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 t (*.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z))))))

50.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 t (*.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z)))))

50.0ms

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

rewrite82.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

380×	`cbrt-div_binary64`
140×	`frac-times_binary64`
114×	`flip--_binary64`
114×	`flip3--_binary64`
46×	`associate-*r/_binary64`

Counts

3 → 145

Calls

3 calls:

8.0ms

(*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 t (*.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z))))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 t (*.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z))))))

6.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 t (*.f64 z z))) (cbrt.f64 (-.f64 t (*.f64 z z)))))

2.0ms

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

simplify352.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-def_binary64`
521×	`cancel-sign-sub-inv_binary64`
432×	`unswap-sqr_binary64`
294×	`associate-r_binary64`
219×	`fma-neg_binary64`

Counts

241 → 252

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	396	13105
1	751	11916
2	2320	11644
3	4944	11618
4	4998	11618
5	4915	11618

prune965.0ms (15.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	775	0	775
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	775	8	783

Error

2.8b

Counts

783 → 8

Alt Table

Status	Error	Program
✓	4.3b	(fma.f64 y (.f64 4 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))
	36.2b	(.f64 4 (.f64 y t))
✓	4.1b	(fma.f64 y (.f64 4 (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))
	24.6b	(.f64 (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
▶	16.1b	(fma.f64 x x (.f64 4 (.f64 y t)))
	23.4b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
✓	3.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	38.9b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (pow.f64 t 3) (pow.f64 z 6)) (+.f64 (pow.f64 z 4) (.f64 t (fma.f64 z z t))))) (*.f64 x x))

Compiler

Compiled 60672 to 16969 computations (72% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

5.0ms

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

rewrite5.0ms (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))

simplify81.0ms (1.3%)

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

prune25.0ms (0.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	20	8	28

Error

2.8b

Counts

28 → 8

Alt Table

Status	Error	Program
✓	4.3b	(fma.f64 y (.f64 4 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))
	36.2b	(.f64 4 (.f64 y t))
✓	4.1b	(fma.f64 y (.f64 4 (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z z))) (cbrt.f64 (-.f64 t (.f64 z z)))) (cbrt.f64 (-.f64 t (.f64 z z))))) (*.f64 x x))
	24.6b	(.f64 (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	16.6b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t))))
	23.4b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
✓	3.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	38.9b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (pow.f64 t 3) (pow.f64 z 6)) (+.f64 (pow.f64 z 4) (.f64 t (fma.f64 z z t))))) (*.f64 x x))

Compiler

Compiled 489 to 258 computations (47.2% saved)

regimes753.0ms (12%)

Accuracy

Total 0.8b remaining (12.6%)

Threshold costs 0.8b (12.6%)

Counts

62 → 1

Compiler

Compiled 15285 to 8614 computations (43.6% saved)

simplify3.0ms (0%)

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 (2%)

Compiler: Compiled 252 to 130 computations (48.4% saved)

Details

analyze1.0s (16.1%)

sample1.6s (25.7%)

simplify70.0ms (1.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series39.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify76.0ms (1.2%)

prune62.0ms (1%)

localize12.0ms (0.2%)

series156.0ms (2.5%)

rewrite48.0ms (0.8%)

simplify189.0ms (3%)

prune414.0ms (6.6%)

localize17.0ms (0.3%)

series158.0ms (2.5%)

rewrite82.0ms (1.3%)

simplify352.0ms (5.6%)

prune965.0ms (15.4%)

localize6.0ms (0.1%)

series5.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify81.0ms (1.3%)

prune25.0ms (0.4%)

regimes753.0ms (12%)

simplify3.0ms (0%)

end127.0ms (2%)

Profiling