Details

analyze1.9s (29.5%)

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)

sample258.0ms (4.1%)

Algorithm

1×

intervals

Symmetry

(sort y z t)

(sort a b)

Results

15.0ms	256×	body	128	valid
6.0ms	106×	body	128	invalid

Compiler

Compiled 53 to 41 computations (22.6% saved)

simplify71.0ms (1.1%)

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
▶	3.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize13.0ms (0.2%)

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)
✓	0.5b	(.f64 (.f64 a 27) b)
✓	3.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series49.0ms (0.8%)

Counts

4 → 156

Calls

4 calls:

30.0ms	(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))
7.0ms	(.f64 (.f64 z t) -9)
4.0ms	(.f64 (.f64 a 27) b)

rewrite10.0ms (0.2%)

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))

simplify113.0ms (1.8%)

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

prune96.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Error

0.0b

Counts

109 → 6

Alt Table

Status	Error	Program
	4.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	4.0b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))
	3.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	4.8b	(.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)))))
	3.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
▶	3.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))

Compiler

Compiled 2442 to 1410 computations (42.3% saved)

localize14.0ms (0.2%)

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)))
✓	0.2b	(.f64 (.f64 y (*.f64 t z)) -9)
✓	7.6b	(.f64 y (.f64 t z))

series66.0ms (1%)

Counts

4 → 156

Calls

4 calls:

32.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
16.0ms	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
10.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
8.0ms	(.f64 y (.f64 t z))

rewrite12.0ms (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)
4.0ms	(.f64 y (.f64 t z))
0.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
0.0ms	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))

simplify115.0ms (1.8%)

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

prune91.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Error

0.0b

Counts

100 → 7

Alt Table

Status	Error	Program
	4.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	4.0b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))
	3.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	3.6b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (cbrt.f64 (.f64 (.f64 y (.f64 t z)) -9)) (cbrt.f64 (.f64 (.f64 y (.f64 t z)) -9))) (cbrt.f64 (.f64 (.f64 y (.f64 t z)) -9)))))
▶	2.7b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
	3.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
✓	3.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))

Compiler

Compiled 2266 to 1101 computations (51.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 x (.f64 (.f64 (*.f64 y t) z) -9))
✓	0.1b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
✓	0.2b	(.f64 (.f64 (*.f64 y t) z) -9)
✓	2.5b	(.f64 (.f64 y t) z)

series74.0ms (1.2%)

Counts

4 → 192

Calls

4 calls:

42.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
14.0ms	(fma.f64 2 x (.f64 (.f64 (*.f64 y t) z) -9))
10.0ms	(.f64 (.f64 (*.f64 y t) z) -9)
8.0ms	(.f64 (.f64 y t) z)

rewrite12.0ms (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 (*.f64 y t) z) -9)
4.0ms	(.f64 (.f64 y t) z)
0.0ms	(fma.f64 2 x (.f64 (.f64 (*.f64 y t) z) -9))
0.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))

simplify141.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

508×	`distribute-rgt-in_binary64`
502×	`distribute-lft-in_binary64`
470×	`fma-def_binary64`
406×	`*-commutative_binary64`
210×	`associate-l_binary64`

Counts

255 → 103

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	106	3556
1	218	3365
2	841	3365
3	1712	3365
4	4932	3365
5	5004	3365

prune130.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	102	8	110

Error

0.0b

Counts

110 → 8

Alt Table

Status	Error	Program
	4.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 (.f64 y t) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)) -9)))
	2.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 y t) z)) (cbrt.f64 (.f64 (.f64 y t) z))) (cbrt.f64 (.f64 (.f64 y t) z))) -9)))
	4.0b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))
▶	2.7b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y t) (.f64 z -9))))
	3.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
✓	3.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))

Compiler

Compiled 2484 to 1203 computations (51.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 x (.f64 (.f64 y t) (*.f64 z -9)))
✓	0.1b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y t) (.f64 z -9))))
✓	2.6b	(.f64 (.f64 y t) (*.f64 z -9))

series61.0ms (1%)

Counts

3 → 156

Calls

3 calls:

34.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y t) (.f64 z -9))))
14.0ms	(fma.f64 2 x (.f64 (.f64 y t) (*.f64 z -9)))
13.0ms	(.f64 (.f64 y t) (*.f64 z -9))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`
15×	`pow1_binary64`
8×	`cbrt-unprod_binary64`
8×	`prod-exp_binary64`

Counts

3 → 44

Calls

3 calls:

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

simplify122.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

510×	`distribute-rgt-in_binary64`
505×	`distribute-lft-in_binary64`
489×	`fma-def_binary64`
356×	`*-commutative_binary64`
167×	`exp-prod_binary64`

Counts

200 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	88	3110
1	184	2946
2	678	2946
3	1419	2946
4	4923	2946
5	4982	2946

prune75.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	75	8	83

Error

0.0b

Counts

83 → 8

Alt Table

Status	Error	Program
	4.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 (.f64 y t) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)) -9)))
	2.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 y t) z)) (cbrt.f64 (.f64 (.f64 y t) z))) (cbrt.f64 (.f64 (.f64 y t) z))) -9)))
	4.0b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))
	3.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	3.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 y (.f64 t (.f64 z -9)))))
✓	2.7b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y t) (.f64 z -9))))
✓	3.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))

Compiler

Compiled 1753 to 905 computations (48.4% saved)

regimes966.0ms (15.4%)

Accuracy

Total 0.5b remaining (96%)

Threshold costs 0.5b (96%)

Counts

41 → 2

Compiler

Compiled 14270 to 10024 computations (29.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 9 to 8 computations (11.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	51
1	35	51
2	35	51

end70.0ms (1.1%)

Remove: (sort a b)
Compiler: Compiled 294 to 196 computations (33.3% saved)

sample1.8s (29%)

Algorithm

1×

intervals

Results

528.0ms	8000×	body	128	valid
187.0ms	2960×	body	128	invalid

Compiler

Compiled 271 to 183 computations (32.5% saved)

Details

analyze1.9s (29.5%)

sample258.0ms (4.1%)

simplify71.0ms (1.1%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

series49.0ms (0.8%)

rewrite10.0ms (0.2%)

simplify113.0ms (1.8%)

prune96.0ms (1.5%)

localize14.0ms (0.2%)

series66.0ms (1%)

rewrite12.0ms (0.2%)

simplify115.0ms (1.8%)

prune91.0ms (1.5%)

localize15.0ms (0.2%)

series74.0ms (1.2%)

rewrite12.0ms (0.2%)

simplify141.0ms (2.2%)

prune130.0ms (2.1%)

localize11.0ms (0.2%)

series61.0ms (1%)

rewrite7.0ms (0.1%)

simplify122.0ms (1.9%)

prune75.0ms (1.2%)

regimes966.0ms (15.4%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end70.0ms (1.1%)

sample1.8s (29%)

Profiling