Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
99.8%	0%	0.2%	1

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.2s (21.8%)

Infinites

33.2% of outputs are infinite.

Symmetry

(sort d2 d4)

Results

933.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify94.0ms (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)))
	7.8b	(-.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)))

series13.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

13.0ms

(*.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:

10.0ms

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

simplify79.0ms (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

prune42.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	55	2	57

Error

Counts

57 → 2

Alt Table

Status	Error	Program
▶	0.9b	(.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)))))
	7.8b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Status

Error

Program

▶

0.9b

(*.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)))))

7.8b

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

Compiler

Compiled 912 to 203 computations (77.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.2b	(.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)))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (cbrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))
✓	21.1b	(cbrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

series806.0ms (14.6%)

Counts

3 → 144

Calls

3 calls:

547.0ms

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

232.0ms

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

25.0ms

(*.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)))))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

12.0ms

(*.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)))))

6.0ms

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

5.0ms

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

simplify274.0ms (5%)

Algorithm

1×	egg-herbie

Rules

551×	`fma-def_binary64`
393×	`associate-r_binary64`
287×	`associate-*r/_binary64`
287×	`associate-/l*_binary64`
112×	`associate-l_binary64`

Counts

259 → 351

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2284	28139
1	5193	28139

prune1.3s (23.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	731	1	732
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	732	2	734

Error

Counts

734 → 2

Alt Table

Status	Error	Program
▶	7.3b	(-.f64 (fma.f64 d2 d1 (.f64 d1 d4)) (+.f64 (.f64 d1 d1) (*.f64 d1 d3)))
✓	0.9b	(.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)))))

Status

Error

Program

▶

7.3b

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

✓

0.9b

(*.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 76182 to 37400 computations (50.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.3b	(fma.f64 d2 d1 (*.f64 d1 d4))
✓	2.6b	(+.f64 (.f64 d1 d1) (.f64 d1 d3))
✓	5.2b	(-.f64 (fma.f64 d2 d1 (.f64 d1 d4)) (+.f64 (.f64 d1 d1) (*.f64 d1 d3)))

series35.0ms (0.6%)

Counts

3 → 108

Calls

3 calls:

21.0ms	(-.f64 (fma.f64 d2 d1 (.f64 d1 d4)) (+.f64 (.f64 d1 d1) (*.f64 d1 d3)))
7.0ms	(fma.f64 d2 d1 (*.f64 d1 d4))
6.0ms	(+.f64 (.f64 d1 d1) (.f64 d1 d3))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
12×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`

Counts

3 → 62

Calls

3 calls:

5.0ms	(-.f64 (fma.f64 d2 d1 (.f64 d1 d4)) (+.f64 (.f64 d1 d1) (*.f64 d1 d3)))
3.0ms	(+.f64 (.f64 d1 d1) (.f64 d1 d3))
1.0ms	(fma.f64 d2 d1 (*.f64 d1 d4))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
680×	`fma-neg_binary64`
409×	`distribute-rgt-in_binary64`
374×	`distribute-lft-in_binary64`
171×	`cancel-sign-sub-inv_binary64`

Counts

170 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	2334
1	281	1960
2	1070	1783
3	4599	1783
4	5073	1783

prune84.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	119	2	121

Error

Counts

121 → 2

Alt Table

Status	Error	Program
✓	7.3b	(-.f64 (fma.f64 d2 d1 (.f64 d1 d4)) (+.f64 (.f64 d1 d1) (*.f64 d1 d3)))
✓	0.9b	(.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)))))

Status

Error

Program

✓

7.3b

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

✓

0.9b

(*.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 2720 to 404 computations (85.1% saved)

regimes1.2s (21%)

Accuracy

Total 0.0b remaining (32.1%)

Threshold costs 0.0b (32.1%)

Counts

189 → 1

Compiler

Compiled 23268 to 12349 computations (46.9% saved)

simplify3.0ms (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	16	13
1	24	13
2	31	13
3	35	13
4	37	13
5	34	13

end254.0ms (4.6%)

Compiler: Compiled 106 to 53 computations (50% saved)

Details

analyze3.0ms (0%)

sample1.2s (21.8%)

simplify94.0ms (1.7%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series13.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify79.0ms (1.4%)

prune42.0ms (0.8%)

localize10.0ms (0.2%)

series806.0ms (14.6%)

rewrite43.0ms (0.8%)

simplify274.0ms (5%)

prune1.3s (23.3%)

localize9.0ms (0.2%)

series35.0ms (0.6%)

rewrite13.0ms (0.2%)

simplify83.0ms (1.5%)

prune84.0ms (1.5%)

regimes1.2s (21%)

simplify3.0ms (0%)

end254.0ms (4.6%)

Profiling