Details

analyze926.0ms (10.9%)

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)

sample246.0ms (2.9%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
4.0ms	102×	body	128	invalid

Compiler

Compiled 39 to 27 computations (30.8% saved)

simplify66.0ms (0.8%)

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

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

6.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
▶	6.1b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))

Compiler

Compiled 95 to 57 computations (40% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 z z) t)
✓	0.0b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
✓	5.6b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

series59.0ms (0.7%)

Counts

3 → 108

Calls

3 calls:

33.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
21.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
4.0ms	(-.f64 (*.f64 z z) t)

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`cancel-sign-sub-inv_binary64`
16×	`prod-diff_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`associate--r+_binary64`
14×	`distribute-lft-in_binary64`

Counts

3 → 88

Calls

3 calls:

8.0ms	(-.f64 (*.f64 z z) t)
7.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
5.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))

simplify101.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
380×	`distribute-rgt-in_binary64`
359×	`distribute-lft-in_binary64`
305×	`exp-prod_binary64`
256×	`cancel-sign-sub-inv_binary64`

Counts

196 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	3201
1	410	2849
2	1537	2665
3	4564	2665
4	4917	2665

prune132.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	150	7	157
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	151	8	159

Error

1.9b

Counts

159 → 8

Alt Table

Status	Error	Program
	22.0b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (/.f64 (-.f64 (pow.f64 z 4) (.f64 t t)) (fma.f64 z z t))))
	37.3b	(.f64 4 (.f64 y t))
	41.9b	(pow.f64 x 2)
	6.8b	(-.f64 (.f64 x x) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))))
	32.3b	(-.f64 (.f64 x x) (cbrt.f64 (.f64 64 (pow.f64 (.f64 y (-.f64 (.f64 z z) t)) 3))))
▶	6.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	31.3b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (+.f64 z (sqrt.f64 t))) (-.f64 z (sqrt.f64 t))))
	26.5b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))

Compiler

Compiled 3557 to 1388 computations (61% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z z))
✓	5.9b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series46.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

37.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
8.0ms	(-.f64 t (*.f64 z z))

rewrite4.0ms (0%)

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))

simplify75.0ms (0.9%)

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 (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	64	8	72

Error

1.9b

Counts

72 → 8

Alt Table

Status	Error	Program
	17.2b	(fma.f64 x x (.f64 4 (.f64 y t)))
▶	6.8b	(-.f64 (.f64 x x) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))))
	32.3b	(-.f64 (.f64 x x) (cbrt.f64 (.f64 64 (pow.f64 (.f64 y (-.f64 (.f64 z z) t)) 3))))
	37.3b	(.f64 4 (.f64 y t))
✓	6.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	31.3b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (+.f64 z (sqrt.f64 t))) (-.f64 z (sqrt.f64 t))))
	26.5b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))
	22.0b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))

Compiler

Compiled 1351 to 565 computations (58.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))))
✓	3.3b	(cbrt.f64 (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))
	5.6b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

series1.5s (17.9%)

Counts

3 → 108

Calls

3 calls:

744.0ms

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

708.0ms

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

67.0ms

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

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

14.0ms

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

8.0ms

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

6.0ms

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

simplify219.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

520×	`associate-r_binary64`
452×	`associate-l_binary64`
315×	`times-frac_binary64`
219×	`fma-def_binary64`
214×	`fma-neg_binary64`

Counts

223 → 279

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	506	8829
1	1392	8314
2	4898	8314
3	4962	8314

prune671.0ms (7.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	588	1	589
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	588	9	597

Error

1.9b

Counts

597 → 9

Alt Table

Status	Error	Program
	17.2b	(fma.f64 x x (.f64 4 (.f64 y t)))
✓	6.8b	(-.f64 (.f64 x x) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))))
✓	6.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
▶	7.2b	(-.f64 (.f64 x x) (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))) (.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))) (cbrt.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))))))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))))
	32.3b	(-.f64 (.f64 x x) (cbrt.f64 (.f64 64 (pow.f64 (.f64 y (-.f64 (.f64 z z) t)) 3))))
	37.3b	(.f64 4 (.f64 y t))
	31.3b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (+.f64 z (sqrt.f64 t))) (-.f64 z (sqrt.f64 t))))
	26.5b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))
	22.0b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))

Compiler

Compiled 31778 to 16379 computations (48.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.3b	(cbrt.f64 (.f64 (.f64 y 4) (-.f64 (*.f64 z z) t)))
✓	3.3b	(cbrt.f64 (.f64 y (.f64 4 (-.f64 (*.f64 z z) t))))
	5.6b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
✓	5.9b	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))

series501.0ms (5.9%)

Counts

2 → 72

Calls

2 calls:

480.0ms	(cbrt.f64 (.f64 y (.f64 4 (-.f64 (*.f64 z z) t))))
20.0ms	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`distribute-lft-in_binary64`
28×	`distribute-rgt-in_binary64`
12×	`cancel-sign-sub-inv_binary64`
12×	`prod-diff_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 63

Calls

2 calls:

7.0ms	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))
5.0ms	(cbrt.f64 (.f64 y (.f64 4 (-.f64 (*.f64 z z) t))))

simplify125.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

399×	`cancel-sign-sub-inv_binary64`
381×	`associate-r_binary64`
314×	`associate-l_binary64`
261×	`fma-neg_binary64`
227×	`*-commutative_binary64`

Counts

135 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	359	3594
1	845	3444
2	3321	3300
3	4885	3240
4	4906	3240

prune1.0s (11.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	652	0	652
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	652	9	661

Error

1.9b

Counts

661 → 9

Alt Table

Status	Error	Program
	17.2b	(fma.f64 x x (.f64 4 (.f64 y t)))
✓	6.8b	(-.f64 (.f64 x x) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))) (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))))
✓	6.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
✓	7.2b	(-.f64 (.f64 x x) (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))) (.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))) (cbrt.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))))))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))))
	32.3b	(-.f64 (.f64 x x) (cbrt.f64 (.f64 64 (pow.f64 (.f64 y (-.f64 (.f64 z z) t)) 3))))
	37.3b	(.f64 4 (.f64 y t))
	31.3b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (+.f64 z (sqrt.f64 t))) (-.f64 z (sqrt.f64 t))))
	26.5b	(-.f64 (.f64 x x) (.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (.f64 z z) t))))
	22.0b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))

Compiler

Compiled 51607 to 26626 computations (48.4% saved)

regimes1.5s (17.5%)

Accuracy

Total 0.6b remaining (18.9%)

Threshold costs 0.6b (18.9%)

Counts

87 → 2

Compiler

Compiled 35654 to 21156 computations (40.7% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
16×	`*-commutative_binary64`
16×	`sub-neg_binary64`
15×	`distribute-rgt-neg-in_binary64`
15×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	54
1	45	52
2	82	52
3	118	52
4	152	52
5	164	52
6	165	52
7	160	52

end1.0ms (0%)

Compiler: Compiled 39 to 22 computations (43.6% saved)

sample1.1s (13%)

Algorithm

1×

intervals

Results

386.0ms	8000×	body	128	valid
159.0ms	3112×	body	128	invalid

Compiler

Compiled 292 to 174 computations (40.4% saved)

Details

analyze926.0ms (10.9%)

sample246.0ms (2.9%)

simplify66.0ms (0.8%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series59.0ms (0.7%)

rewrite24.0ms (0.3%)

simplify101.0ms (1.2%)

prune132.0ms (1.5%)

localize7.0ms (0.1%)

series46.0ms (0.5%)

rewrite4.0ms (0%)

simplify75.0ms (0.9%)

prune51.0ms (0.6%)

localize12.0ms (0.1%)

series1.5s (17.9%)

rewrite51.0ms (0.6%)

simplify219.0ms (2.6%)

prune671.0ms (7.9%)

localize21.0ms (0.2%)

series501.0ms (5.9%)

rewrite20.0ms (0.2%)

simplify125.0ms (1.5%)

prune1.0s (11.9%)

regimes1.5s (17.5%)

bsearch4.0ms (0.1%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.1s (13%)

Profiling