Details

analyze1.9s (17.1%)

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)

sample65.0ms (0.6%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
8.0ms	94×	body	128	invalid

Compiler

Compiled 39 to 27 computations (30.8% saved)

simplify69.0ms (0.6%)

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

prune6.0ms (0.1%)

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

7.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z z))
✓	6.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series74.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

62.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
12.0ms	(-.f64 t (*.f64 z z))

rewrite8.0ms (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:

5.0ms	(-.f64 t (*.f64 z z))
1.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

simplify129.0ms (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

prune106.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	57	7	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	8	65

Error

6.1b

Counts

65 → 8

Alt Table

Status	Error	Program
	26.5b	(.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))))
▶	7.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
	8.2b	(.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))))
	42.9b	(pow.f64 x 2)
✓	7.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	28.3b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
	20.6b	(fma.f64 x x (.f64 4 (.f64 y t)))
	40.0b	(.f64 4 (.f64 y t))

Compiler

Compiled 1347 to 559 computations (58.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
✓	0.0b	(.f64 4 (.f64 y t))
✓	0.0b	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
✓	9.5b	(*.f64 y (pow.f64 z 2))

series117.0ms (1.1%)

Counts

4 → 21

Calls

4 calls:

67.0ms	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
21.0ms	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
15.0ms	(*.f64 y (pow.f64 z 2))
9.0ms	(.f64 4 (.f64 y t))

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-log-exp_binary64`
10×	`*-un-lft-identity_binary64`

Counts

4 → 85

Calls

4 calls:

15.0ms	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
10.0ms	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
8.0ms	(*.f64 y (pow.f64 z 2))
7.0ms	(.f64 4 (.f64 y t))

simplify168.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
546×	`fma-neg_binary64`
433×	`*-commutative_binary64`
273×	`exp-prod_binary64`
213×	`distribute-rgt-in_binary64`

Counts

106 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	1687
1	387	1360
2	1325	1270
3	3585	1263
4	4745	1263
5	4888	1263

prune269.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	139	7	146

Error

0.0b

Counts

146 → 7

Alt Table

Status	Error	Program
	8.2b	(.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))))
	7.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (pow.f64 z 2)))))
	20.6b	(fma.f64 x x (.f64 4 (.f64 y t)))
▶	0.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
	1.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 y (.f64 z (cbrt.f64 z))) (pow.f64 (cbrt.f64 z) 2))))
✓	7.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	32.7b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) (pow.f64 (sqrt.f64 z) 2))))

Compiler

Compiled 3564 to 2205 computations (38.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
	0.0b	(.f64 4 (.f64 y t))
	0.0b	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
✓	0.2b	(.f64 (.f64 y z) z)

series85.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

65.0ms	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
15.0ms	(.f64 (.f64 y z) z)

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-log-exp_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 42

Calls

2 calls:

15.0ms	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
7.0ms	(.f64 (.f64 y z) z)

simplify143.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-def_binary64`
507×	`distribute-rgt-neg-in_binary64`
429×	`cancel-sign-sub-inv_binary64`
353×	`fma-neg_binary64`
318×	`*-commutative_binary64`

Counts

114 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	2036
1	274	1691
2	1022	1538
3	2997	1529
4	4947	1529
5	4815	1529

prune263.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	127	7	134

Error

0.0b

Counts

134 → 7

Alt Table

Status	Error	Program
	1.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 y (.f64 z (cbrt.f64 z))) (pow.f64 (cbrt.f64 z) 2))))
✓	7.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	7.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (pow.f64 z 2)))))
	34.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y (pow.f64 z 3/2)) (sqrt.f64 z))))
	32.7b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 (.f64 y z) (sqrt.f64 z)) (sqrt.f64 z))))
	20.6b	(fma.f64 x x (.f64 4 (.f64 y t)))
▶	1.0b	(-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t)))) (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t))))) (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t))))) (.f64 4 (.f64 (*.f64 y z) z)))

Compiler

Compiled 3224 to 1692 computations (47.5% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 y z) z)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t)))) (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t))))) (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t)))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t)))) (cbrt.f64 (fma.f64 x x (.f64 4 (*.f64 y t)))))
✓	2.8b	(cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t))))

series267.0ms (2.5%)

Counts

3 → 108

Calls

3 calls:

133.0ms

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

110.0ms

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

23.0ms

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

rewrite40.0ms (0.4%)

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:

13.0ms

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

10.0ms

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

1.0ms

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

simplify288.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

329×	`unswap-sqr_binary64`
298×	`associate-r_binary64`
234×	`associate-/r*_binary64`
223×	`associate-l_binary64`
219×	`times-frac_binary64`

Counts

201 → 234

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	360	6909
1	1077	6543
2	3925	6145
3	5062	6145

prune905.0ms (8.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	404	1	405
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	405	7	412

Error

0.0b

Counts

412 → 7

Alt Table

Status	Error	Program
	34.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y (pow.f64 z 3/2)) (sqrt.f64 z))))
	0.1b	(-.f64 (fma.f64 x x (.f64 4 (.f64 y t))) (.f64 4 (.f64 (*.f64 y z) z)))
	1.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 y (.f64 z (cbrt.f64 z))) (pow.f64 (cbrt.f64 z) 2))))
✓	7.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	7.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (pow.f64 z 2)))))
	32.7b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 (.f64 y z) (sqrt.f64 z)) (sqrt.f64 z))))
✓	1.0b	(-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t)))) (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t))))) (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t))))) (.f64 4 (.f64 (*.f64 y z) z)))

Compiler

Compiled 22382 to 12617 computations (43.6% saved)

regimes3.8s (35.3%)

Accuracy

Total 0.1b remaining (72.5%)

Threshold costs 0.1b (72.5%)

Counts

162 → 1

Compiler

Compiled 45283 to 30687 computations (32.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`distribute-lft-neg-in_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	24	23
2	32	23
3	42	23
4	54	23
5	61	23
6	65	23
7	66	23
8	65	23

end1.0ms (0%)

Compiler: Compiled 20 to 13 computations (35% saved)

sample2.0s (18.3%)

Algorithm

1×

intervals

Results

749.0ms	8000×	body	128	valid
286.0ms	3063×	body	128	invalid

Compiler

Compiled 223 to 149 computations (33.2% saved)

Details

analyze1.9s (17.1%)

sample65.0ms (0.6%)

simplify69.0ms (0.6%)

prune6.0ms (0.1%)

localize17.0ms (0.2%)

series74.0ms (0.7%)

rewrite8.0ms (0.1%)

simplify129.0ms (1.2%)

prune106.0ms (1%)

localize23.0ms (0.2%)

series117.0ms (1.1%)

rewrite48.0ms (0.4%)

simplify168.0ms (1.5%)

prune269.0ms (2.5%)

localize22.0ms (0.2%)

series85.0ms (0.8%)

rewrite27.0ms (0.2%)

simplify143.0ms (1.3%)

prune263.0ms (2.4%)

localize28.0ms (0.3%)

series267.0ms (2.5%)

rewrite40.0ms (0.4%)

simplify288.0ms (2.6%)

prune905.0ms (8.3%)

regimes3.8s (35.3%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample2.0s (18.3%)

Profiling