Details

analyze2.8s (29.1%)

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)

sample3.6s (36.5%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results

1.8s	8393×	body	128	invalid
1.7s	8256×	body	128	valid

Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify334.0ms (3.4%)

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 (0.1%)

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
	5.1b	(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))))
▶	4.1b	(-.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

5.1b

(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))))

▶

4.1b

(-.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)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x 18) y)
✓	0.3b	(.f64 (.f64 j 27) k)
✓	4.0b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
✓	4.4b	(.f64 (.f64 (*.f64 x 18) y) z)

series39.0ms (0.4%)

Counts

4 → 132

Calls

4 calls:

17.0ms	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
12.0ms	(.f64 (.f64 (*.f64 x 18) y) z)
6.0ms	(.f64 (.f64 j 27) k)
4.0ms	(.f64 (.f64 x 18) y)

rewrite70.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 76

Calls

4 calls:

68.0ms	(.f64 (.f64 x 18) y)
68.0ms	(.f64 (.f64 j 27) k)
68.0ms	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
68.0ms	(.f64 (.f64 (*.f64 x 18) y) z)

Iterations

Useful iterations: 0 (0.0ms)

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

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

208 → 81

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

prune123.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Error

0.0b

Counts

83 → 7

Alt Table

Status	Error	Program
	5.1b	(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))))
	4.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 18 (.f64 y (.f64 z x))) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
▶	4.1b	(-.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 27 (*.f64 k j)))
	4.9b	(-.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))
	4.3b	(-.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))
	14.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 x 18) y) z) 3)) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	30.5b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.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 3445 to 2170 computations (37% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 x 18) y)
✓	0.3b	(.f64 27 (.f64 k j))
	4.0b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
	4.4b	(.f64 (.f64 (*.f64 x 18) y) z)

series4.0ms (0%)

Counts

1 → 0

Calls

1 calls:

4.0ms

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

rewrite39.0ms (0.4%)

Algorithm

2×	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`

Counts

1 → 18

Calls

1 calls:

38.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune236.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	79	7	86

Error

0.0b

Counts

86 → 7

Alt Table

Status	Error	Program
	5.1b	(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))))
	4.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 18 (.f64 y (.f64 z x))) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
✓	4.1b	(-.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 27 (*.f64 k j)))
	4.9b	(-.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))
▶	4.3b	(-.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))
	14.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 x 18) y) z) 3)) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	30.5b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.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 3330 to 2020 computations (39.3% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 (.f64 j 27) k)) 3)
	4.0b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
	4.4b	(.f64 (.f64 (*.f64 x 18) y) z)
✓	7.9b	(cbrt.f64 (.f64 (.f64 j 27) k))

series657.0ms (6.7%)

Counts

2 → 48

Calls

2 calls:

330.0ms	(cbrt.f64 (.f64 (.f64 j 27) k))
327.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 j 27) k)) 3)

rewrite45.0ms (0.5%)

Algorithm

2×	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`

Counts

2 → 74

Calls

2 calls:

44.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 j 27) k)) 3)
44.0ms	(cbrt.f64 (.f64 (.f64 j 27) k))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify64.0ms (0.7%)

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`

Counts

122 → 88

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

prune193.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	5	5
Picked	1	0	1
Done	1	0	1
Total	130	6	136

Error

0.0b

Counts

136 → 6

Alt Table

Status	Error	Program
	5.1b	(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))))
	4.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 18 (.f64 y (.f64 z x))) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	4.9b	(-.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))
▶	4.1b	(-.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 j (*.f64 27 k)))
	14.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 x 18) y) z) 3)) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	30.5b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.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 5445 to 3481 computations (36.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 x 18) y)
✓	0.3b	(.f64 j (.f64 27 k))
	4.0b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
	4.4b	(.f64 (.f64 (*.f64 x 18) y) z)

series4.0ms (0%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite37.0ms (0.4%)

Algorithm

2×	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`

Counts

1 → 18

Calls

1 calls:

36.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

42 → 19

Iterations

Useful iterations: 0 (0.0ms)

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

prune112.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	80	6	86

Error

0.0b

Counts

86 → 6

Alt Table

Status	Error	Program
	5.1b	(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))))
	4.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 18 (.f64 y (.f64 z x))) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	4.9b	(-.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))
✓	4.1b	(-.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 j (*.f64 27 k)))
	14.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 x 18) y) z) 3)) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	30.5b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.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 3069 to 1901 computations (38.1% saved)

regimes508.0ms (5.2%)

Accuracy

Total 1.7b remaining (97.7%)

Threshold costs 0b (0%)

Counts

12 → 3

Compiler

Compiled 10719 to 7691 computations (28.2% saved)

bsearch105.0ms (1.1%)

Steps

Iters	Range		Point
6	4.34136673072213e-11	6.128690484421741e-7	1.0923338603745131e-8
6	-3.341481426481937e+54	-7.367365425687979e+53	-7.432234198452891e+53

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify8.0ms (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	139
1	79	139
2	122	139
3	146	139
4	164	139
5	170	139
6	168	139

end630.0ms (6.4%)

Remove: (sort b c)
Compiler: Compiled 1505 to 942 computations (37.4% saved)

Details

analyze2.8s (29.1%)

sample3.6s (36.5%)

simplify334.0ms (3.4%)

prune5.0ms (0.1%)

localize20.0ms (0.2%)

series39.0ms (0.4%)

rewrite70.0ms (0.7%)

simplify52.0ms (0.5%)

prune123.0ms (1.3%)

localize20.0ms (0.2%)

series4.0ms (0%)

rewrite39.0ms (0.4%)

simplify6.0ms (0.1%)

prune236.0ms (2.4%)

localize23.0ms (0.2%)

series657.0ms (6.7%)

rewrite45.0ms (0.5%)

simplify64.0ms (0.7%)

prune193.0ms (2%)

localize23.0ms (0.2%)

series4.0ms (0%)

rewrite37.0ms (0.4%)

simplify10.0ms (0.1%)

prune112.0ms (1.1%)

regimes508.0ms (5.2%)

bsearch105.0ms (1.1%)

simplify8.0ms (0.1%)

end630.0ms (6.4%)

Profiling