Details

analyze2.8s (21.1%)

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)

sample3.7s (27.2%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results

1.8s	8256×	body	128	valid
1.7s	8485×	body	128	invalid

Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify330.0ms (2.5%)

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

prune5.0ms (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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.9b	(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))))
	7.1b	(-.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

▶

3.9b

(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))))

7.1b

(-.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)

localize18.0ms (0.1%)

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))
✓	1.5b	(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))))
✓	6.7b	(.f64 y (.f64 z t))

series235.0ms (1.7%)

Counts

4 → 252

Calls

4 calls:

200.0ms	(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))))
14.0ms	(fma.f64 18 (.f64 y (.f64 z t)) (*.f64 i -4))
11.0ms	(fma.f64 -27 (.f64 j k) (.f64 b c))
9.0ms	(.f64 y (.f64 z t))

rewrite6.0ms (0%)

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:

4.0ms	(.f64 y (.f64 z t))
0.0ms	(fma.f64 -27 (.f64 j k) (.f64 b c))
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 18 (.f64 y (.f64 z t)) (*.f64 i -4))

simplify208.0ms (1.6%)

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

prune156.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	117	6	123

Error

0.0b

Counts

123 → 6

Alt Table

Status	Error	Program
	29.9b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (.f64 (sqrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))) (sqrt.f64 (fma.f64 -27 (.f64 j k) (*.f64 b c))))))
	4.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (.f64 (.f64 (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c)))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))))))
	7.1b	(-.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))
	5.1b	(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))))
▶	4.1b	(-.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 27 (*.f64 k j)))))
	27.0b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4))) (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))))

Compiler

Compiled 3893 to 1843 computations (52.7% saved)

localize21.0ms (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))
✓	4.7b	(.f64 t (.f64 z x))
✓	5.5b	(.f64 y (.f64 t (*.f64 z x)))

series51.0ms (0.4%)

Counts

4 → 0

Calls

4 calls:

20.0ms	(.f64 18 (.f64 y (.f64 t (.f64 z x))))
17.0ms	(.f64 y (.f64 t (*.f64 z x)))
8.0ms	(.f64 t (.f64 z x))
6.0ms	(.f64 27 (.f64 k j))

rewrite24.0ms (0.2%)

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:

6.0ms	(.f64 18 (.f64 y (.f64 t (.f64 z x))))
5.0ms	(.f64 y (.f64 t (*.f64 z x)))
3.0ms	(.f64 t (.f64 z x))
3.0ms	(.f64 27 (.f64 k j))

simplify68.0ms (0.5%)

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

prune131.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	96	5	101

Error

0.0b

Counts

101 → 5

Alt Table

Status	Error	Program
	4.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (.f64 (.f64 (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c)))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))))))
▶	4.0b	(-.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))))
	7.1b	(-.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))
	5.1b	(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))))
	27.0b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4))) (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))))

Compiler

Compiled 4017 to 1785 computations (55.6% saved)

localize22.0ms (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))))
	4.7b	(.f64 t (.f64 z x))
	5.5b	(.f64 y (.f64 t (*.f64 z x)))

series4.0ms (0%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite4.0ms (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:

4.0ms

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

simplify102.0ms (0.8%)

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

prune128.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	102	5	107

Error

0.0b

Counts

107 → 5

Alt Table

Status	Error	Program
▶	4.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (.f64 (.f64 (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c)))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))))))
✓	4.0b	(-.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))))
	7.1b	(-.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))
	5.1b	(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))))
	27.0b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4))) (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))))

Compiler

Compiled 4217 to 1943 computations (53.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (*.f64 b c))))
✓	1.5b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (.f64 (.f64 (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c)))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))))))
✓	1.8b	(cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c)))
	6.7b	(.f64 y (.f64 z t))

series290.0ms (2.2%)

Counts

3 → 216

Calls

3 calls:

105.0ms

(*.f64 (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))

104.0ms

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

80.0ms

(cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c)))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`

Counts

3 → 65

Calls

3 calls:

4.0ms

(*.f64 (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))

1.0ms

(cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c)))

0.0ms

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

simplify226.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

619×	`associate-/l*_binary64`
551×	`associate-/r*_binary64`
334×	`fma-def_binary64`
262×	`*-commutative_binary64`
210×	`cancel-sign-sub-inv_binary64`

Counts

281 → 305

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	681	13089
1	2209	12310
2	5569	12310

prune808.0ms (6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	546	0	546
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	546	5	551

Error

0.0b

Counts

551 → 5

Alt Table

Status	Error	Program
✓	4.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (.f64 (.f64 (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c)))) (cbrt.f64 (fma.f64 -27 (.f64 j k) (.f64 b c))))))
✓	4.0b	(-.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))))
	7.1b	(-.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))
	5.1b	(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))))
	27.0b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4))) (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))))

Compiler

Compiled 38426 to 20513 computations (46.6% saved)

regimes3.6s (27%)

Accuracy

Total 0.9b remaining (95.7%)

Threshold costs 0.9b (95.7%)

Counts

128 → 3

Compiler

Compiled 84691 to 58785 computations (30.6% saved)

bsearch7.0ms (0.1%)

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

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

45×	`*-commutative_binary64`
28×	`+-commutative_binary64`
24×	`distribute-rgt-neg-in_binary64`
24×	`sub-neg_binary64`
21×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	229
1	106	229
2	156	229
3	197	229
4	242	229
5	268	229
6	275	229
7	277	229
8	275	229

end409.0ms (3%)

Remove

(sort j k)

(sort b c)

Compiler

Compiled 1881 to 1160 computations (38.3% saved)

Iter	Nodes	Cost
0	62	229
1	106	229
2	156	229
3	197	229
4	242	229
5	268	229
6	275	229
7	277	229
8	275	229

Iter	Nodes	Cost
0	62	229
1	106	229
2	156	229
3	197	229
4	242	229
5	268	229
6	275	229
7	277	229
8	275	229

Details

analyze2.8s (21.1%)

sample3.7s (27.2%)

simplify330.0ms (2.5%)

prune5.0ms (0%)

localize18.0ms (0.1%)

series235.0ms (1.7%)

rewrite6.0ms (0%)

simplify208.0ms (1.6%)

prune156.0ms (1.2%)

localize21.0ms (0.2%)

series51.0ms (0.4%)

rewrite24.0ms (0.2%)

simplify68.0ms (0.5%)

prune131.0ms (1%)

localize22.0ms (0.2%)

series4.0ms (0%)

rewrite4.0ms (0%)

simplify102.0ms (0.8%)

prune128.0ms (1%)

localize22.0ms (0.2%)

series290.0ms (2.2%)

rewrite10.0ms (0.1%)

simplify226.0ms (1.7%)

prune808.0ms (6%)

regimes3.6s (27%)

bsearch7.0ms (0.1%)

simplify11.0ms (0.1%)

end409.0ms (3%)

Profiling

Iter	Nodes	Cost
0	62	229
1	106	229
2	156	229
3	197	229
4	242	229
5	268	229
6	275	229
7	277	229
8	275	229