Details

analyze2.1s (25.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.9s (23.3%)

Symmetry

(sort y z t)

(sort a b)

Results

1.2s	8256×	body	128	valid
436.0ms	3140×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
641×	`fma-def_binary64`
213×	`cancel-sign-sub-inv_binary64`
172×	`distribute-rgt-neg-in_binary64`
157×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	39	23
2	115	21
3	308	21
4	552	21
5	902	21
6	1201	21
7	1433	21
8	1672	21
9	1787	21
10	1791	21
11	1791	21
12	1791	21
13	1674	21

prune8.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
▶	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
✓	0.2b	(.f64 (.f64 y 9) z)
✓	0.2b	(.f64 (.f64 a 27) b)
✓	7.3b	(.f64 (.f64 (*.f64 y 9) z) t)

series34.0ms (0.4%)

Counts

4 → 132

Calls

4 calls:

16.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
10.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
4.0ms	(.f64 (.f64 a 27) b)
4.0ms	(.f64 (.f64 y 9) z)

rewrite81.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

94× egg-rr

Counts

4 → 94

Calls

2 calls:

78.0ms	((.f64 (.f64 (.f64 y 9) z) t) (.f64 (.f64 a 27) b) (.f64 (.f64 y 9) z) (-.f64 (.f64 x 2) (.f64 (.f64 (*.f64 y 9) z) t)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	361	40
2	4262	40
3	5106	40
0	0	0
1	0	0

simplify107.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
290×	`fma-neg_binary64`
132×	`distribute-rgt-neg-in_binary64`
130×	`cancel-sign-sub-inv_binary64`
110×	`associate-l_binary64`

Counts

226 → 102

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	1362
1	44	1290
2	97	1290
3	207	1290
4	322	1290
5	390	1290
6	528	1290
7	663	1290
8	841	1290
9	973	1290
10	1066	1290
11	1096	1290
12	1096	1290
13	1007	1290

prune133.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Error

0.0b

Counts

104 → 9

Alt Table

Status	Error	Program
	3.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 27 (.f64 a b)))
▶	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 (.f64 a 27) b))
	3.2b	(+.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (+.f64 (fma.f64 (neg.f64 t) (.f64 (.f64 y 9) z) (.f64 (.f64 (.f64 y 9) z) t)) (fma.f64 (neg.f64 t) (.f64 (.f64 y 9) z) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (.f64 a 27) b))
	8.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (expm1.f64 (log1p.f64 (.f64 (.f64 y 9) z))) t)) (.f64 (.f64 a 27) b))
	20.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (cbrt.f64 (pow.f64 (.f64 (.f64 a 27) b) 3)))
	3.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (pow.f64 (cbrt.f64 (.f64 (.f64 a 27) b)) 3))
	3.4b	(+.f64 (-.f64 (.f64 x 2) (pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 y 9) z) t)) 3)) (.f64 (.f64 a 27) b))

Compiler

Compiled 3165 to 2145 computations (32.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z))))
	0.2b	(.f64 (.f64 a 27) b)
✓	0.3b	(.f64 9 (.f64 y (*.f64 t z)))
✓	8.1b	(.f64 y (.f64 t z))

series36.0ms (0.4%)

Counts

3 → 48

Calls

3 calls:

14.0ms	(.f64 9 (.f64 y (*.f64 t z)))
14.0ms	(-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z))))
8.0ms	(.f64 y (.f64 t z))

rewrite94.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

205× egg-rr

Counts

3 → 205

Calls

2 calls:

89.0ms	((.f64 y (.f64 t z)) (.f64 9 (.f64 y (.f64 t z))) (-.f64 (.f64 x 2) (.f64 9 (.f64 y (*.f64 t z)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	262	31
2	3195	31
3	5934	31
0	0	0
1	0	0

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
290×	`fma-neg_binary64`
130×	`distribute-rgt-neg-in_binary64`
130×	`cancel-sign-sub-inv_binary64`
109×	`associate-l_binary64`

Counts

253 → 209

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	666
1	30	594
2	76	594
3	191	594
4	306	594
5	375	594
6	513	594
7	648	594
8	826	594
9	958	594
10	1051	594
11	1081	594
12	1081	594
13	992	594

prune276.0ms (3.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	227	7	234

Error

0.0b

Counts

234 → 7

Alt Table

Status	Error	Program
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 27 (.f64 a b)))
	20.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (cbrt.f64 (pow.f64 (.f64 (.f64 a 27) b) 3)))
	4.7b	(+.f64 (fma.f64 (.f64 -9 (.f64 y t)) z (+.f64 x x)) (.f64 (.f64 a 27) b))
	3.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.2b	(+.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (+.f64 (fma.f64 (neg.f64 t) (.f64 (.f64 y 9) z) (.f64 (.f64 (.f64 y 9) z) t)) (fma.f64 (neg.f64 t) (.f64 (.f64 y 9) z) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (.f64 a 27) b))
▶	3.2b	(+.f64 (fma.f64 x 2 (fma.f64 (.f64 y (.f64 t z)) -9 (fma.f64 (.f64 y (.f64 t z)) -9 (.f64 (.f64 y (.f64 t z)) 9)))) (.f64 (*.f64 a 27) b))
	3.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (pow.f64 (cbrt.f64 (.f64 (.f64 a 27) b)) 3))

Compiler

Compiled 7445 to 3399 computations (54.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 (.f64 y (.f64 t z)) -9 (fma.f64 (.f64 y (.f64 t z)) -9 (.f64 (.f64 y (*.f64 t z)) 9)))
✓	0.3b	(.f64 (.f64 y (*.f64 t z)) 9)
	8.1b	(.f64 y (.f64 t z))
✓	41.1b	(fma.f64 (.f64 y (.f64 t z)) -9 (.f64 (.f64 y (*.f64 t z)) 9))

series63.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

28.0ms	(fma.f64 (.f64 y (.f64 t z)) -9 (fma.f64 (.f64 y (.f64 t z)) -9 (.f64 (.f64 y (*.f64 t z)) 9)))
21.0ms	(fma.f64 (.f64 y (.f64 t z)) -9 (.f64 (.f64 y (*.f64 t z)) 9))
14.0ms	(.f64 (.f64 y (*.f64 t z)) 9)

rewrite119.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

76× egg-rr

Counts

3 → 76

Calls

2 calls:

117.0ms

((fma.f64 (*.f64 y (*.f64 t z)) -9 (*.f64 (*.f64 y (*.f64 t z)) 9)) (*.f64 (*.f64 y (*.f64 t z)) 9) (fma.f64 (*.f64 y (*.f64 t z)) -9 (fma.f64 (*.f64 y (*.f64 t z)) -9 (*.f64 (*.f64 y (*.f64 t z)) 9))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	60
1	224	40
2	2519	40
3	4867	40
4	4893	40
5	5378	40
0	0	0
1	0	0

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

49×	`associate-l_binary64`
37×	`associate-r_binary64`
29×	`*-commutative_binary64`

Counts

184 → 80

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	756
1	21	756
2	55	756
3	95	756
4	95	756
5	95	756

prune180.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Error

0.0b

Counts

141 → 7

Alt Table

Status	Error	Program
▶	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 27 (.f64 a b)))
	20.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (cbrt.f64 (pow.f64 (.f64 (.f64 a 27) b) 3)))
	4.7b	(+.f64 (fma.f64 (.f64 -9 (.f64 y t)) z (+.f64 x x)) (.f64 (.f64 a 27) b))
	3.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.2b	(+.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (+.f64 (fma.f64 (neg.f64 t) (.f64 (.f64 y 9) z) (.f64 (.f64 (.f64 y 9) z) t)) (fma.f64 (neg.f64 t) (.f64 (.f64 y 9) z) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (.f64 a 27) b))
✓	3.2b	(+.f64 (fma.f64 x 2 (fma.f64 (.f64 y (.f64 t z)) -9 (fma.f64 (.f64 y (.f64 t z)) -9 (.f64 (.f64 y (.f64 t z)) 9)))) (.f64 (*.f64 a 27) b))
	3.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (pow.f64 (cbrt.f64 (.f64 (.f64 a 27) b)) 3))

Compiler

Compiled 4797 to 2279 computations (52.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z))))
	0.3b	(.f64 9 (.f64 y (*.f64 t z)))
✓	0.3b	(.f64 27 (.f64 a b))
	8.1b	(.f64 y (.f64 t z))

series6.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

6.0ms

(*.f64 27 (*.f64 a b))

rewrite37.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

17× egg-rr

Counts

1 → 17

Calls

2 calls:

36.0ms	((.f64 27 (.f64 a b)))
0.0ms	()

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

17 → 17

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune247.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	226	7	233

Error

0.0b

Counts

233 → 7

Alt Table

Status	Error	Program
✓	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 27 (.f64 a b)))
	20.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (cbrt.f64 (pow.f64 (.f64 (.f64 a 27) b) 3)))
	4.7b	(+.f64 (fma.f64 (.f64 -9 (.f64 y t)) z (+.f64 x x)) (.f64 (.f64 a 27) b))
	3.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.2b	(+.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (+.f64 (fma.f64 (neg.f64 t) (.f64 (.f64 y 9) z) (.f64 (.f64 (.f64 y 9) z) t)) (fma.f64 (neg.f64 t) (.f64 (.f64 y 9) z) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (.f64 a 27) b))
✓	3.2b	(+.f64 (fma.f64 x 2 (fma.f64 (.f64 y (.f64 t z)) -9 (fma.f64 (.f64 y (.f64 t z)) -9 (.f64 (.f64 y (.f64 t z)) 9)))) (.f64 (*.f64 a 27) b))
	3.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (pow.f64 (cbrt.f64 (.f64 (.f64 a 27) b)) 3))

Compiler

Compiled 7275 to 3056 computations (58% saved)

regimes1.9s (23.5%)

Accuracy

Total 0.7b remaining (95.1%)

Threshold costs 0.7b (95.1%)

Counts

80 → 2

Compiler

Compiled 34066 to 24106 computations (29.2% saved)

bsearch17.0ms (0.2%)

Steps

Iters	Range		Point
3	8.892207337883427e-93	6.206304619294511e-88	1.5397415417505267e-88

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
9×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	54
1	47	54
2	63	54
3	79	54
4	89	54
5	94	54
6	95	54
7	94	54

end634.0ms (7.7%)

Remove: (sort a b)
Compiler: Compiled 553 to 375 computations (32.2% saved)

Details

analyze2.1s (25.1%)

sample1.9s (23.3%)

simplify68.0ms (0.8%)

prune8.0ms (0.1%)

localize11.0ms (0.1%)

series34.0ms (0.4%)

rewrite81.0ms (1%)

simplify107.0ms (1.3%)

prune133.0ms (1.6%)

localize16.0ms (0.2%)

series36.0ms (0.4%)

rewrite94.0ms (1.1%)

simplify76.0ms (0.9%)

prune276.0ms (3.3%)

localize16.0ms (0.2%)

series63.0ms (0.8%)

rewrite119.0ms (1.4%)

simplify29.0ms (0.4%)

prune180.0ms (2.2%)

localize11.0ms (0.1%)

series6.0ms (0.1%)

rewrite37.0ms (0.4%)

simplify6.0ms (0.1%)

prune247.0ms (3%)

regimes1.9s (23.5%)

bsearch17.0ms (0.2%)

simplify6.0ms (0.1%)

end634.0ms (7.7%)

Profiling