Details

analyze1.2s (22.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
28.1%	68.6%	3.3%	10
29.6%	65.5%	4.9%	11
32%	61.7%	6.3%	12
35.5%	56.9%	7.6%	13
48%	38.7%	13.4%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.6s (28.9%)

Symmetry

(sort d2 d4)

Results

1.0s	8256×	body	128	valid
295.0ms	2428×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1400×	`fma-neg_binary64`
654×	`fma-def_binary64`
233×	`sub-neg_binary64`
210×	`unsub-neg_binary64`
158×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	32	14
2	94	13
3	263	13
4	655	13
5	1556	13
6	1691	13
7	1500	13
8	1500	13
9	2739	13
10	2707	13
11	2707	13
12	2632	13

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 92 to 53 computations (42.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

series16.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

16.0ms

(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
6×	`associate-r_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`distribute-lft-out--_binary64`
3×	`distribute-lft-out_binary64`

Counts

1 → 27

Calls

1 calls:

9.0ms

(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

617×	`distribute-rgt-in_binary64`
603×	`distribute-lft-in_binary64`
446×	`fma-neg_binary64`
407×	`associate-l_binary64`
313×	`associate-r_binary64`

Counts

75 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	1262
1	195	1056
2	718	940
3	3249	940
4	4599	940
5	4980	940

prune29.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	54	3	57

Error

Counts

57 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
▶	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (cbrt.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))) (cbrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))

Compiler

Compiled 925 to 211 computations (77.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	0.0b	(-.f64 (.f64 d1 d2) (.f64 d1 d3))
✓	0.0b	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))

series38.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

19.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
12.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
7.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`diff-log_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 64

Calls

3 calls:

6.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
5.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
3.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-l_binary64`
685×	`fma-def_binary64`
488×	`fma-neg_binary64`
459×	`distribute-rgt-in_binary64`
440×	`distribute-lft-in_binary64`

Counts

196 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2558
1	361	2139
2	1230	2096
3	4966	2096
4	5229	2096

prune99.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	127	3	130

Error

Counts

130 → 3

Alt Table

Status	Error	Program
▶	1.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (.f64 d1 d1))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 2616 to 493 computations (81.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (.f64 d1 d1))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (cbrt.f64 (*.f64 (-.f64 (+.f64 d2 d4) d3) d1)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (*.f64 (-.f64 (+.f64 d2 d4) d3) d1)))
✓	1.4b	(cbrt.f64 (*.f64 (-.f64 (+.f64 d2 d4) d3) d1))

series977.0ms (17.9%)

Counts

4 → 192

Calls

4 calls:

530.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (*.f64 (-.f64 (+.f64 d2 d4) d3) d1)))
368.0ms	(cbrt.f64 (*.f64 (-.f64 (+.f64 d2 d4) d3) d1))
53.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (.f64 d1 d1))
25.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (cbrt.f64 (*.f64 (-.f64 (+.f64 d2 d4) d3) d1)))

rewrite75.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`associate-*l/_binary64`
68×	`cbrt-div_binary64`
35×	`flip--_binary64`
35×	`flip3--_binary64`
32×	`frac-times_binary64`

Counts

4 → 131

Calls

4 calls:

20.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (.f64 d1 d1))
16.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (cbrt.f64 (*.f64 (-.f64 (+.f64 d2 d4) d3) d1)))
11.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (*.f64 (-.f64 (+.f64 d2 d4) d3) d1)))
5.0ms	(cbrt.f64 (*.f64 (-.f64 (+.f64 d2 d4) d3) d1))

simplify286.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

429×	`*-commutative_binary64`
215×	`+-commutative_binary64`
202×	`cancel-sign-sub-inv_binary64`
202×	`sub-neg_binary64`
192×	`fma-def_binary64`

Counts

323 → 370

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1082	15622
1	3389	14272
2	4858	13953
3	4957	13953

prune520.0ms (9.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	570	0	570
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	570	3	573

Error

Counts

573 → 3

Alt Table

Status	Error	Program
✓	1.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1)) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (cbrt.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1))) (.f64 d1 d1))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 38168 to 15850 computations (58.5% saved)

regimes235.0ms (4.3%)

Accuracy

Total 0.0b remaining (65.7%)

Threshold costs 0.0b (65.7%)

Counts

51 → 1

Compiler

Compiled 4513 to 2554 computations (43.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	23	13
3	27	13
4	29	13
5	29	13

end54.0ms (1%)

Remove: (sort d2 d4)
Compiler: Compiled 118 to 63 computations (46.6% saved)

Details

analyze1.2s (22.5%)

sample1.6s (28.9%)

simplify92.0ms (1.7%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series16.0ms (0.3%)

rewrite11.0ms (0.2%)

simplify77.0ms (1.4%)

prune29.0ms (0.5%)

localize10.0ms (0.2%)

series38.0ms (0.7%)

rewrite18.0ms (0.3%)

simplify89.0ms (1.6%)

prune99.0ms (1.8%)

localize11.0ms (0.2%)

series977.0ms (17.9%)

rewrite75.0ms (1.4%)

simplify286.0ms (5.2%)

prune520.0ms (9.5%)

regimes235.0ms (4.3%)

simplify2.0ms (0%)

end54.0ms (1%)

Profiling