Details

analyze3.2s (25.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.5%	0.5%	0
0%	99.5%	0.5%	1
0%	99.5%	0.5%	2
0%	99.5%	0.5%	3
0%	99.5%	0.5%	4
0%	99.5%	0.5%	5
0%	99.5%	0.5%	6
0%	99.5%	0.5%	7
0%	99.5%	0.5%	8
0%	99.5%	0.5%	9
0%	99.5%	0.5%	10
0%	99.5%	0.5%	11
0%	99.5%	0.5%	12
0%	99.5%	0.5%	13
0%	99.5%	0.5%	14

Compiler

Compiled 42 to 30 computations (28.6% saved)

sample4.1s (33.1%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results

2.0s	8614×	body	128	invalid
2.0s	8256×	body	128	valid

Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify334.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

6437×	`fma-neg_binary64`
684×	`unsub-neg_binary64`
621×	`distribute-rgt-neg-in_binary64`
515×	`distribute-rgt-in_binary64`
434×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	43
1	77	37
2	255	35
3	773	35
4	1711	35
5	2777	35
6	3474	35
7	3470	35
8	3493	35
9	3516	35
10	3534	35
11	3534	35
12	3526	35
13	3549	35
14	3549	35
15	3549	35
16	3639	35
17	4131	35
18	3675	35
19	3675	35
20	3675	35
21	9384	35

prune9.0ms (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

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
	6.8b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))

Status

Error

Program

▶

6.4b

(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))

6.8b

(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))

Compiler

Compiled 218 to 148 computations (32.1% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 18 (.f64 y (.f64 z t)) (*.f64 i -4))
✓	0.1b	(fma.f64 -27 (.f64 j k) (.f64 b c))
✓	3.8b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
✓	7.2b	(.f64 y (.f64 z t))

series149.0ms (1.2%)

Counts

4 → 252

Calls

4 calls:

110.0ms	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
18.0ms	(fma.f64 -27 (.f64 j k) (.f64 b c))
13.0ms	(fma.f64 18 (.f64 y (.f64 z t)) (*.f64 i -4))
8.0ms	(.f64 y (.f64 z t))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

4 → 50

Calls

4 calls:

7.0ms	(.f64 y (.f64 z t))
0.0ms	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
0.0ms	(fma.f64 -27 (.f64 j k) (.f64 b c))
0.0ms	(fma.f64 18 (.f64 y (.f64 z t)) (*.f64 i -4))

simplify364.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

856×	`fma-neg_binary64`
688×	`associate-l_binary64`
535×	`associate-r_binary64`
523×	`cancel-sign-sub-inv_binary64`
490×	`exp-prod_binary64`

Counts

302 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	6517
1	311	5980
2	924	5783
3	2865	5781
4	4860	5781
5	5149	5781

prune319.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	117	6	123

Error

0.0b

Counts

123 → 6

Alt Table

Status	Error	Program
✓	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
	38.2b	(.f64 (sqrt.f64 (fma.f64 c b (fma.f64 t (fma.f64 y (.f64 18 (.f64 z x)) (.f64 a -4)) (fma.f64 (.f64 k j) -27 (.f64 (.f64 x i) -4))))) (sqrt.f64 (fma.f64 c b (fma.f64 t (fma.f64 y (.f64 18 (.f64 z x)) (.f64 a -4)) (fma.f64 (.f64 k j) -27 (.f64 (*.f64 x i) -4))))))
	6.8b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	44.9b	(.f64 (-.f64 (.f64 18 (.f64 y (.f64 z x))) (*.f64 4 a)) t)
▶	4.9b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 t (.f64 z x))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 27 (*.f64 k j)))))
	17.0b	(fma.f64 x (fma.f64 y (.f64 (.f64 t z) 18) (.f64 i -4)) (fma.f64 c b (.f64 (*.f64 k j) -27)))

Compiler

Compiled 3770 to 1779 computations (52.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 18 (.f64 y (.f64 t (.f64 z x))))
✓	0.3b	(.f64 27 (.f64 k j))
✓	4.5b	(.f64 t (.f64 z x))
✓	5.2b	(.f64 y (.f64 t (*.f64 z x)))

series62.0ms (0.5%)

Counts

4 → 0

Calls

4 calls:

24.0ms	(.f64 18 (.f64 y (.f64 t (.f64 z x))))
18.0ms	(.f64 y (.f64 t (*.f64 z x)))
13.0ms	(.f64 t (.f64 z x))
7.0ms	(.f64 27 (.f64 k j))

rewrite145.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-cbrt-cube_binary64`
37×	`add-exp-log_binary64`
37×	`pow1_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`

Counts

4 → 89

Calls

4 calls:

74.0ms	(.f64 y (.f64 t (*.f64 z x)))
45.0ms	(.f64 27 (.f64 k j))
11.0ms	(.f64 t (.f64 z x))
9.0ms	(.f64 18 (.f64 y (.f64 t (.f64 z x))))

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

620×	`unswap-sqr_binary64`
594×	`*-commutative_binary64`
389×	`associate-/l/_binary64`
385×	`sqr-pow_binary64`
333×	`associate-/r/_binary64`

Counts

89 → 95

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	131	1275
1	288	990
2	1009	990
3	1695	990
4	2239	990
5	3346	990
6	5183	990

prune209.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	93	8	101

Error

0.0b

Counts

101 → 8

Alt Table

Status	Error	Program
	5.9b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 (.f64 y t) (.f64 z x)))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 27 (*.f64 k j)))))
	6.8b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
▶	4.9b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 t (.f64 z x))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 (*.f64 27 k) j))))
	5.1b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 t (.f64 z x))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 (.f64 (cbrt.f64 (.f64 27 (.f64 k j))) (cbrt.f64 (.f64 27 (.f64 k j)))) (cbrt.f64 (.f64 27 (*.f64 k j)))))))
✓	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
	4.9b	(-.f64 (+.f64 (.f64 c b) (.f64 (sqrt.f64 18) (.f64 (sqrt.f64 18) (.f64 y (.f64 t (.f64 z x)))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 27 (.f64 k j)))))
	20.3b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 t (.f64 z x))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (cbrt.f64 (.f64 (.f64 (.f64 27 27) 27) (.f64 (.f64 (.f64 k j) (.f64 k j)) (*.f64 k j)))))))
	4.9b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 (.f64 t z) x)))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 27 (*.f64 k j)))))

Compiler

Compiled 4228 to 1955 computations (53.8% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 27 k) j)
	0.2b	(.f64 18 (.f64 y (.f64 t (.f64 z x))))
	4.5b	(.f64 t (.f64 z x))
	5.2b	(.f64 y (.f64 t (*.f64 z x)))

series5.0ms (0%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(*.f64 (*.f64 27 k) j)

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

5.0ms

(*.f64 (*.f64 27 k) j)

simplify78.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

537×	`associate-l_binary64`
367×	`associate-r_binary64`
353×	`*-commutative_binary64`
340×	`cube-div_binary64`
340×	`log-div_binary64`

Counts

44 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	380
1	97	344
2	352	344
3	971	344
4	1135	344
5	1335	344
6	1591	344
7	2659	344
8	4026	344
9	4880	344

prune263.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	102	8	110

Error

0.0b

Counts

110 → 8

Alt Table

Status	Error	Program
	5.9b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 (.f64 y t) (.f64 z x)))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 27 (*.f64 k j)))))
	6.8b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
✓	4.9b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 t (.f64 z x))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 (*.f64 27 k) j))))
	5.1b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 t (.f64 z x))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 (.f64 (cbrt.f64 (.f64 27 (.f64 k j))) (cbrt.f64 (.f64 27 (.f64 k j)))) (cbrt.f64 (.f64 27 (*.f64 k j)))))))
✓	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
	20.3b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 t (.f64 z x))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (cbrt.f64 (.f64 19683 (pow.f64 (*.f64 k j) 3))))))
	4.9b	(-.f64 (+.f64 (.f64 c b) (.f64 (sqrt.f64 18) (.f64 (sqrt.f64 18) (.f64 y (.f64 t (.f64 z x)))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 27 (.f64 k j)))))
▶	4.9b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 (.f64 t z) x)))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 27 (*.f64 k j)))))

Compiler

Compiled 4408 to 2105 computations (52.2% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 18 (.f64 y (.f64 (.f64 t z) x)))
	0.3b	(.f64 27 (.f64 k j))
✓	4.6b	(.f64 (.f64 t z) x)
✓	5.2b	(.f64 y (.f64 (*.f64 t z) x))

series51.0ms (0.4%)

Counts

3 → 132

Calls

3 calls:

23.0ms	(.f64 y (.f64 (*.f64 t z) x))
19.0ms	(.f64 18 (.f64 y (.f64 (.f64 t z) x)))
9.0ms	(.f64 (.f64 t z) x)

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
31×	`pow1_binary64`
19×	`cbrt-unprod_binary64`
19×	`prod-exp_binary64`

Counts

3 → 69

Calls

3 calls:

8.0ms	(.f64 18 (.f64 y (.f64 (.f64 t z) x)))
5.0ms	(.f64 y (.f64 (*.f64 t z) x))
4.0ms	(.f64 (.f64 t z) x)

simplify121.0ms (1%)

Algorithm

1×	egg-herbie

Rules

746×	`unswap-sqr_binary64`
549×	`*-commutative_binary64`
415×	`sqr-pow_binary64`
251×	`associate-r_binary64`
224×	`associate-l_binary64`

Counts

201 → 93

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	98	2426
1	220	2177
2	917	2177
3	1615	2177
4	2292	2177
5	3470	2177
6	5406	2177

prune212.0ms (1.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	113	8	121

Error

0.0b

Counts

121 → 8

Alt Table

Status	Error	Program
	5.9b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 (.f64 y t) (.f64 z x)))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 27 (*.f64 k j)))))
	6.8b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
✓	4.9b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 t (.f64 z x))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 (*.f64 27 k) j))))
	5.1b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 t (.f64 z x))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 (.f64 (cbrt.f64 (.f64 27 (.f64 k j))) (cbrt.f64 (.f64 27 (.f64 k j)))) (cbrt.f64 (.f64 27 (*.f64 k j)))))))
✓	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
	20.3b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 t (.f64 z x))))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (cbrt.f64 (.f64 19683 (pow.f64 (*.f64 k j) 3))))))
	4.9b	(-.f64 (+.f64 (.f64 c b) (.f64 (.f64 18 y) (.f64 (.f64 t z) x))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 27 (*.f64 k j)))))
✓	4.9b	(-.f64 (+.f64 (.f64 c b) (.f64 18 (.f64 y (.f64 (.f64 t z) x)))) (+.f64 (.f64 4 (.f64 i x)) (+.f64 (.f64 4 (.f64 a t)) (.f64 27 (*.f64 k j)))))

Compiler

Compiled 4518 to 1977 computations (56.2% saved)

regimes2.1s (17%)

Accuracy

Total 1.1b remaining (97.5%)

Threshold costs 0b (0%)

Counts

55 → 3

Compiler

Compiled 31971 to 22943 computations (28.2% saved)

bsearch3.0ms (0%)

Compiler: Compiled 41 to 29 computations (29.3% saved)

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

43×	`*-commutative_binary64`
30×	`+-commutative_binary64`
25×	`sub-neg_binary64`
24×	`distribute-rgt-neg-in_binary64`
21×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	240
1	100	240
2	153	240
3	194	240
4	239	240
5	265	240
6	272	240
7	274	240
8	272	240

end498.0ms (4%)

Remove

(sort b c)

(sort y z)

Compiler

Compiled 2050 to 1259 computations (38.6% saved)

Iter	Nodes	Cost
0	55	240
1	100	240
2	153	240
3	194	240
4	239	240
5	265	240
6	272	240
7	274	240
8	272	240

Iter	Nodes	Cost
0	55	240
1	100	240
2	153	240
3	194	240
4	239	240
5	265	240
6	272	240
7	274	240
8	272	240

Details

analyze3.2s (25.4%)

sample4.1s (33.1%)

simplify334.0ms (2.7%)

prune9.0ms (0.1%)

localize25.0ms (0.2%)

series149.0ms (1.2%)

rewrite10.0ms (0.1%)

simplify364.0ms (2.9%)

prune319.0ms (2.5%)

localize22.0ms (0.2%)

series62.0ms (0.5%)

rewrite145.0ms (1.2%)

simplify83.0ms (0.7%)

prune209.0ms (1.7%)

localize25.0ms (0.2%)

series5.0ms (0%)

rewrite6.0ms (0%)

simplify78.0ms (0.6%)

prune263.0ms (2.1%)

localize33.0ms (0.3%)

series51.0ms (0.4%)

rewrite28.0ms (0.2%)

simplify121.0ms (1%)

prune212.0ms (1.7%)

regimes2.1s (17%)

bsearch3.0ms (0%)

simplify20.0ms (0.2%)

end498.0ms (4%)

Profiling

Iter	Nodes	Cost
0	55	240
1	100	240
2	153	240
3	194	240
4	239	240
5	265	240
6	272	240
7	274	240
8	272	240