Details

analyze2.2s (29.1%)

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)

sample2.0s (26.8%)

Symmetry

(sort y z t)

(sort a b)

Results

1.2s	8256×	body	128	valid
510.0ms	3109×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify72.0ms (1%)

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

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.4b	(+.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	(fma.f64 x 2 (.f64 (.f64 a 27) b))
✓	0.2b	(.f64 (.f64 z t) -9)
✓	0.3b	(.f64 (.f64 a 27) b)
✓	0.3b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series54.0ms (0.7%)

Counts

4 → 156

Calls

4 calls:

36.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
7.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))
6.0ms	(.f64 (.f64 z t) -9)
4.0ms	(.f64 (.f64 a 27) b)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

4.0ms	(.f64 (.f64 z t) -9)
4.0ms	(.f64 (.f64 a 27) b)
0.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
0.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

868×	`unswap-sqr_binary64`
419×	`*-commutative_binary64`
321×	`distribute-lft-in_binary64`
321×	`distribute-rgt-in_binary64`
310×	`fma-def_binary64`

Counts

216 → 107

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	122	2976
1	250	2724
2	873	2724
3	1485	2724
4	2922	2724
5	5289	2724

prune112.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	7	109

Error

0.0b

Counts

109 → 7

Alt Table

Status	Error	Program
	2.4b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	0.5b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	42.5b	(cbrt.f64 (pow.f64 (fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9))) 3))
	33.4b	(fma.f64 y (.f64 (sqrt.f64 (.f64 (.f64 z t) -9)) (sqrt.f64 (.f64 (.f64 z t) -9))) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))
	14.3b	(fma.f64 y (cbrt.f64 (pow.f64 (.f64 (.f64 t z) -9) 3)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
▶	0.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	1.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b))))) (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))))

Compiler

Compiled 2498 to 1456 computations (41.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series42.0ms (0.6%)

Counts

3 → 132

Calls

3 calls:

30.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
7.0ms	(fma.f64 x 2 (.f64 a (.f64 27 b)))
4.0ms	(.f64 a (.f64 27 b))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 40

Calls

3 calls:

9.0ms	(.f64 a (.f64 27 b))
0.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
0.0ms	(fma.f64 x 2 (.f64 a (.f64 27 b)))

simplify96.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

576×	`distribute-lft-in_binary64`
576×	`distribute-rgt-in_binary64`
548×	`associate-l_binary64`
426×	`fma-def_binary64`
385×	`associate-r_binary64`

Counts

172 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	82	2594
1	159	2378
2	475	2378
3	1528	2378
4	4509	2378
5	5090	2378

prune102.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	107	7	114

Error

0.0b

Counts

114 → 7

Alt Table

Status	Error	Program
	2.4b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
▶	0.5b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	42.5b	(cbrt.f64 (pow.f64 (fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9))) 3))
	33.4b	(fma.f64 y (.f64 (sqrt.f64 (.f64 (.f64 z t) -9)) (sqrt.f64 (.f64 (.f64 z t) -9))) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))
	14.3b	(fma.f64 y (cbrt.f64 (pow.f64 (.f64 (.f64 t z) -9) 3)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
✓	0.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	1.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b))))) (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))))

Compiler

Compiled 2477 to 1440 computations (41.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
✓	0.1b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
✓	0.3b	(.f64 (.f64 y (*.f64 t z)) -9)
✓	4.8b	(.f64 y (.f64 t z))

series66.0ms (0.9%)

Counts

4 → 156

Calls

4 calls:

31.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
14.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
13.0ms	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
8.0ms	(.f64 y (.f64 t z))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
18×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

4 → 63

Calls

4 calls:

5.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
3.0ms	(.f64 y (.f64 t z))
0.0ms	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
0.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))

simplify108.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

507×	`distribute-rgt-in_binary64`
501×	`distribute-lft-in_binary64`
416×	`fma-def_binary64`
360×	`*-commutative_binary64`
190×	`associate-+l+_binary64`

Counts

219 → 94

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	3305
1	213	3114
2	739	3114
3	1576	3114
4	4976	3114
5	4981	3114

prune95.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	93	8	101

Error

0.0b

Counts

101 → 8

Alt Table

Status	Error	Program
	0.5b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y (.f64 t z)) (.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))))
	14.3b	(fma.f64 y (cbrt.f64 (pow.f64 (.f64 (.f64 t z) -9) 3)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.7b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
	57.0b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 t z))) -9)))
✓	0.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	2.4b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
▶	0.5b	(fma.f64 -9 (.f64 y (.f64 t z)) (fma.f64 2 x (.f64 27 (.f64 a b))))
	1.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b))))) (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))))

Compiler

Compiled 2354 to 1173 computations (50.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 x (.f64 27 (.f64 a b)))
✓	0.1b	(fma.f64 -9 (.f64 y (.f64 t z)) (fma.f64 2 x (.f64 27 (.f64 a b))))
✓	0.3b	(.f64 27 (.f64 a b))
	4.8b	(.f64 y (.f64 t z))

series48.0ms (0.6%)

Counts

3 → 108

Calls

3 calls:

33.0ms	(fma.f64 -9 (.f64 y (.f64 t z)) (fma.f64 2 x (.f64 27 (.f64 a b))))
9.0ms	(fma.f64 2 x (.f64 27 (.f64 a b)))
5.0ms	(.f64 27 (.f64 a b))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 40

Calls

3 calls:

4.0ms	(.f64 27 (.f64 a b))
0.0ms	(fma.f64 2 x (.f64 27 (.f64 a b)))
0.0ms	(fma.f64 -9 (.f64 y (.f64 t z)) (fma.f64 2 x (.f64 27 (.f64 a b))))

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

544×	`distribute-lft-in_binary64`
544×	`distribute-rgt-in_binary64`
511×	`*-commutative_binary64`
442×	`unswap-sqr_binary64`
425×	`associate-l_binary64`

Counts

148 → 67

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	76	2426
1	147	2210
2	410	2210
3	1325	2210
4	3533	2210
5	5049	2210

prune99.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	87	8	95

Error

0.0b

Counts

95 → 8

Alt Table

Status	Error	Program
	0.5b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y (.f64 t z)) (.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))))
	14.3b	(fma.f64 y (cbrt.f64 (pow.f64 (.f64 (.f64 t z) -9) 3)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	0.5b	(fma.f64 -9 (.f64 y (.f64 t z)) (fma.f64 2 x (.f64 (sqrt.f64 27) (.f64 (sqrt.f64 27) (*.f64 a b)))))
	4.7b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
	57.0b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 t z))) -9)))
	0.8b	(fma.f64 -9 (.f64 y (.f64 t z)) (fma.f64 2 x (.f64 (.f64 (cbrt.f64 (.f64 27 (.f64 a b))) (cbrt.f64 (.f64 27 (.f64 a b)))) (cbrt.f64 (.f64 27 (.f64 a b))))))
✓	0.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	2.4b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 1934 to 965 computations (50.1% saved)

regimes1.3s (18%)

Accuracy

Total 3.0b remaining (99.3%)

Threshold costs 0b (0%)

Counts

84 → 1

Compiler

Compiled 30977 to 22126 computations (28.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	23
1	23	23
2	23	23

end758.0ms (10.3%)

Compiler: Compiled 335 to 243 computations (27.5% saved)

Details

analyze2.2s (29.1%)

sample2.0s (26.8%)

simplify72.0ms (1%)

prune4.0ms (0.1%)

localize11.0ms (0.1%)

series54.0ms (0.7%)

rewrite10.0ms (0.1%)

simplify95.0ms (1.3%)

prune112.0ms (1.5%)

localize14.0ms (0.2%)

series42.0ms (0.6%)

rewrite11.0ms (0.2%)

simplify96.0ms (1.3%)

prune102.0ms (1.4%)

localize10.0ms (0.1%)

series66.0ms (0.9%)

rewrite11.0ms (0.2%)

simplify108.0ms (1.5%)

prune95.0ms (1.3%)

localize11.0ms (0.1%)

series48.0ms (0.6%)

rewrite6.0ms (0.1%)

simplify86.0ms (1.2%)

prune99.0ms (1.3%)

regimes1.3s (18%)

simplify2.0ms (0%)

end758.0ms (10.3%)

Profiling