Details

analyze2.8s (26.8%)

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 (35.4%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results

1.8s	8256×	body	128	valid
1.8s	8122×	body	128	invalid

Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify299.0ms (2.9%)

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`

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

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.8b	(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))))
▶	3.6b	(-.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

5.8b

(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))))

▶

3.6b

(-.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)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 j 27) k)
✓	0.2b	(.f64 (.f64 x 18) y)
✓	4.4b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
✓	5.8b	(.f64 (.f64 (*.f64 x 18) y) z)

series41.0ms (0.4%)

Counts

4 → 132

Calls

4 calls:

21.0ms	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
10.0ms	(.f64 (.f64 (*.f64 x 18) y) z)
6.0ms	(.f64 (.f64 j 27) k)
4.0ms	(.f64 (.f64 x 18) y)

rewrite61.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

823×	`log-prod_binary64`
273×	`expm1-udef_binary64`
273×	`log1p-udef_binary64`
243×	`log-pow_binary64`
158×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	304	37
2	3529	37
3	5972	37

Stop Event

1×	node limit

Counts

4 → 72

Calls

4 calls:

60.0ms	(.f64 (.f64 j 27) k)
60.0ms	(.f64 (.f64 x 18) y)
60.0ms	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
60.0ms	(.f64 (.f64 (*.f64 x 18) y) z)

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

161×	`associate-l_binary64`
85×	`associate-r_binary64`
49×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	1320
1	41	1320
2	98	1320
3	178	1320
4	202	1320
5	201	1320
6	201	1320

Stop Event

1×

saturated

Counts

204 → 77

prune100.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Error

0.0b

Counts

79 → 5

Alt Table

Status	Error	Program
	5.8b	(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))))
	21.8b	(-.f64 (-.f64 (+.f64 (-.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t)) 2) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	18.6b	(-.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)) (cbrt.f64 (pow.f64 (.f64 (*.f64 j 27) k) 3)))
▶	3.8b	(-.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)) (pow.f64 (cbrt.f64 (.f64 (*.f64 j 27) k)) 3))
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))

Compiler

Compiled 3159 to 1984 computations (37.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 (.f64 j 27) k)) 3)
	4.4b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
	5.8b	(.f64 (.f64 (*.f64 x 18) y) z)
✓	10.5b	(cbrt.f64 (.f64 (.f64 j 27) k))

series698.0ms (6.7%)

Counts

2 → 48

Calls

2 calls:

371.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 j 27) k)) 3)
327.0ms	(cbrt.f64 (.f64 (.f64 j 27) k))

rewrite46.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

664×	`log1p-expm1-u_binary64`
664×	`expm1-log1p-u_binary64`
369×	`log-prod_binary64`
133×	`expm1-udef_binary64`
133×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	166	16
2	1763	16
3	5103	16

Stop Event

1×	node limit

Counts

2 → 73

Calls

2 calls:

45.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 j 27) k)) 3)
45.0ms	(cbrt.f64 (.f64 (.f64 j 27) k))

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-def_binary64`
424×	`unswap-sqr_binary64`
273×	`exp-diff_binary64`
268×	`distribute-neg-out_binary64`
267×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	904
1	124	904
2	215	856
3	568	448
4	1843	448
5	4611	448
6	5077	448

Stop Event

1×	node limit

Counts

121 → 87

prune197.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	125	6	131

Error

0.0b

Counts

131 → 6

Alt Table

Status	Error	Program
	18.6b	(-.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)) (cbrt.f64 (pow.f64 (.f64 (*.f64 j 27) k) 3)))
▶	3.6b	(-.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 j (*.f64 27 k)))
	5.8b	(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))))
	21.8b	(-.f64 (-.f64 (+.f64 (-.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t)) 2) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	3.9b	(-.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)) (pow.f64 (.f64 3 (cbrt.f64 (*.f64 k j))) 3))

Compiler

Compiled 5351 to 3426 computations (36% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 j (.f64 27 k))
	0.2b	(.f64 (.f64 x 18) y)
	4.4b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
	5.8b	(.f64 (.f64 (*.f64 x 18) y) z)

series4.0ms (0%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite35.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
387×	`unpow-prod-down_binary64`
299×	`log-prod_binary64`
153×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1358	7
3	5055	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

1 calls:

34.0ms

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	10	168
2	16	168
3	16	168
4	16	168

Stop Event

1×

saturated

Counts

41 → 18

prune123.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Error

0.0b

Counts

82 → 6

Alt Table

Status	Error	Program
	18.6b	(-.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)) (cbrt.f64 (pow.f64 (.f64 (*.f64 j 27) k) 3)))
✓	3.6b	(-.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 j (*.f64 27 k)))
	5.8b	(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))))
	21.8b	(-.f64 (-.f64 (+.f64 (-.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t)) 2) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
▶	3.9b	(-.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)) (pow.f64 (.f64 3 (cbrt.f64 (*.f64 k j))) 3))

Compiler

Compiled 3157 to 1982 computations (37.2% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (.f64 3 (cbrt.f64 (.f64 k j))) 3)
	4.4b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
	5.8b	(.f64 (.f64 (*.f64 x 18) y) z)
✓	10.5b	(cbrt.f64 (*.f64 k j))

series675.0ms (6.5%)

Counts

2 → 48

Calls

2 calls:

365.0ms	(pow.f64 (.f64 3 (cbrt.f64 (.f64 k j))) 3)
310.0ms	(cbrt.f64 (*.f64 k j))

rewrite41.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

660×	`log1p-expm1-u_binary64`
660×	`expm1-log1p-u_binary64`
379×	`log-prod_binary64`
133×	`expm1-udef_binary64`
133×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	164	13
2	1769	13
3	5131	13

Stop Event

1×	node limit

Counts

2 → 56

Calls

2 calls:

40.0ms	(pow.f64 (.f64 3 (cbrt.f64 (.f64 k j))) 3)
40.0ms	(cbrt.f64 (*.f64 k j))

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-def_binary64`
424×	`unswap-sqr_binary64`
268×	`distribute-neg-out_binary64`
264×	`exp-diff_binary64`
261×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	856
1	118	856
2	213	808
3	558	400
4	1817	400
5	4600	400
6	5046	400

Stop Event

1×	node limit

Counts

104 → 69

prune154.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	108	6	114

Error

0.0b

Counts

114 → 6

Alt Table

Status	Error	Program
	18.6b	(-.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)) (cbrt.f64 (pow.f64 (.f64 (*.f64 j 27) k) 3)))
✓	3.6b	(-.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 j (*.f64 27 k)))
	5.8b	(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))))
	21.8b	(-.f64 (-.f64 (+.f64 (-.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t)) 2) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
✓	3.9b	(-.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)) (pow.f64 (.f64 3 (cbrt.f64 (*.f64 k j))) 3))

Compiler

Compiled 4460 to 2645 computations (40.7% saved)

regimes519.0ms (5%)

Accuracy

Total 0.9b remaining (91.3%)

Threshold costs 0.9b (91.3%)

Counts

16 → 3

Compiler

Compiled 12757 to 9215 computations (27.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 35 to 25 computations (28.6% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
16×	`+-commutative_binary64`
15×	`sub-neg_binary64`
12×	`distribute-rgt-neg-in_binary64`
12×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	200
1	79	200
2	116	200
3	144	200
4	162	200
5	169	200
6	170	200
7	168	200

Stop Event

1×

saturated

end638.0ms (6.1%)

Remove: (sort b c)
Compiler: Compiled 2013 to 1210 computations (39.9% saved)

Details

analyze2.8s (26.8%)

sample3.7s (35.4%)

simplify299.0ms (2.9%)

prune5.0ms (0.1%)

localize23.0ms (0.2%)

series41.0ms (0.4%)

rewrite61.0ms (0.6%)

simplify44.0ms (0.4%)

prune100.0ms (1%)

localize24.0ms (0.2%)

series698.0ms (6.7%)

rewrite46.0ms (0.4%)

simplify63.0ms (0.6%)

prune197.0ms (1.9%)

localize22.0ms (0.2%)

series4.0ms (0%)

rewrite35.0ms (0.3%)

simplify10.0ms (0.1%)

prune123.0ms (1.2%)

localize29.0ms (0.3%)

series675.0ms (6.5%)

rewrite41.0ms (0.4%)

simplify62.0ms (0.6%)

prune154.0ms (1.5%)

regimes519.0ms (5%)

bsearch1.0ms (0%)

simplify9.0ms (0.1%)

end638.0ms (6.1%)

Profiling