Details

analyze2.0ms (0.1%)

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)

sample1.0s (38.9%)

Symmetry

(sort d2 d4)

Results

809.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify95.0ms (3.5%)

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

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
	7.5b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 92 to 53 computations (42.4% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series43.0ms (1.6%)

Counts

2 → 96

Calls

2 calls:

28.0ms	(+.f64 d4 (-.f64 (-.f64 d2 d3) d1))
14.0ms	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

rewrite26.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
32×	`associate-+r+_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
21×	`add-cube-cbrt_binary64`

Counts

2 → 81

Calls

2 calls:

10.0ms	(+.f64 d4 (-.f64 (-.f64 d2 d3) d1))
9.0ms	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

simplify121.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1002×	`fma-neg_binary64`
693×	`fma-def_binary64`
566×	`exp-prod_binary64`
374×	`*-commutative_binary64`
197×	`cancel-sign-sub-inv_binary64`

Counts

177 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2211
1	316	1984
2	1276	1866
3	3067	1866
4	4524	1866
5	4962	1866
6	4951	1866

prune115.0ms (4.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	140	4	144

Error

Counts

144 → 4

Alt Table

Status	Error	Program
	7.5b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
	35.6b	(cbrt.f64 (.f64 (.f64 (.f64 d1 d1) d1) (.f64 (*.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))
	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)))))
▶	0.0b	(*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1))))

Compiler

Compiled 2570 to 609 computations (76.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series26.0ms (1%)

Counts

2 → 96

Calls

2 calls:

20.0ms	(*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1))))
7.0ms	(+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))

rewrite29.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
17×	`associate-+r+_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`

Counts

2 → 66

Calls

2 calls:

16.0ms	(+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))
8.0ms	(*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1))))

simplify118.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

659×	`distribute-rgt-in_binary64`
640×	`distribute-lft-in_binary64`
557×	`fma-neg_binary64`
393×	`fma-def_binary64`
236×	`exp-prod_binary64`

Counts

162 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	2091
1	271	1864
2	889	1746
3	3638	1746
4	4575	1746
5	4937	1746

prune61.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	97	4	101

Error

Counts

101 → 4

Alt Table

Status	Error	Program
▶	4.3b	(pow.f64 (-.f64 (.f64 d1 (+.f64 d2 d4)) (.f64 d1 (+.f64 d3 d1))) 1)
	28.7b	(/.f64 (.f64 d1 (fma.f64 (-.f64 d4 (+.f64 d3 d1)) (-.f64 (+.f64 d3 d1) d4) (.f64 d2 d2))) (-.f64 d2 (-.f64 d4 (+.f64 d3 d1))))
	35.6b	(cbrt.f64 (.f64 (.f64 (.f64 d1 d1) d1) (.f64 (*.f64 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))
✓	0.0b	(*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1))))

Compiler

Compiled 1731 to 402 computations (76.8% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d3 d1))
✓	0.0b	(*.f64 d1 (+.f64 d2 d4))
✓	4.1b	(-.f64 (.f64 d1 (+.f64 d2 d4)) (.f64 d1 (+.f64 d3 d1)))

series38.0ms (1.4%)

Counts

3 → 108

Calls

3 calls:

27.0ms	(-.f64 (.f64 d1 (+.f64 d2 d4)) (.f64 d1 (+.f64 d3 d1)))
6.0ms	(*.f64 d1 (+.f64 d2 d4))
5.0ms	(*.f64 d1 (+.f64 d3 d1))

rewrite36.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-*r/_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 75

Calls

3 calls:

23.0ms	(-.f64 (.f64 d1 (+.f64 d2 d4)) (.f64 d1 (+.f64 d3 d1)))
5.0ms	(*.f64 d1 (+.f64 d2 d4))
5.0ms	(*.f64 d1 (+.f64 d3 d1))

simplify94.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

300×	`associate-+r+_binary64`
296×	`associate-+l+_binary64`
206×	`+-commutative_binary64`
199×	`fma-neg_binary64`
190×	`associate-l_binary64`

Counts

183 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	2068
1	475	2023
2	1884	1998
3	4552	1998
4	4957	1998

prune92.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	128	3	131

Error

Counts

131 → 3

Alt Table

Status	Error	Program
	26.4b	(pow.f64 (-.f64 (.f64 d1 (+.f64 d2 d4)) (cbrt.f64 (.f64 (.f64 (.f64 d1 d1) d1) (.f64 (.f64 (+.f64 d3 d1) (+.f64 d3 d1)) (+.f64 d3 d1))))) 1)
▶	0.8b	(pow.f64 (fma.f64 d1 (+.f64 d2 d4) (neg.f64 (*.f64 d1 (+.f64 d3 d1)))) 1)
✓	0.0b	(*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1))))

Compiler

Compiled 2570 to 788 computations (69.3% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 d1 (+.f64 d3 d1))
✓	0.8b	(fma.f64 d1 (+.f64 d2 d4) (neg.f64 (*.f64 d1 (+.f64 d3 d1))))

series67.0ms (2.5%)

Counts

1 → 48

Calls

1 calls:

67.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify119.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
478×	`fma-neg_binary64`
393×	`unsub-neg_binary64`
322×	`exp-prod_binary64`
320×	`exp-sum_binary64`

Counts

58 → 34

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	888
1	83	708
2	224	708
3	889	708
4	2783	708
5	4392	708
6	4905	708
7	4925	708

prune121.0ms (4.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	67	3	70

Error

Counts

70 → 3

Alt Table

Status	Error	Program
	26.4b	(pow.f64 (-.f64 (.f64 d1 (+.f64 d2 d4)) (cbrt.f64 (.f64 (.f64 (.f64 d1 d1) d1) (.f64 (.f64 (+.f64 d3 d1) (+.f64 d3 d1)) (+.f64 d3 d1))))) 1)
✓	0.8b	(pow.f64 (fma.f64 d1 (+.f64 d2 d4) (neg.f64 (*.f64 d1 (+.f64 d3 d1)))) 1)
✓	0.0b	(*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1))))

Compiler

Compiled 1140 to 406 computations (64.4% saved)

regimes304.0ms (11.3%)

Accuracy

Total 0.0b remaining (58.7%)

Threshold costs 0.0b (58.7%)

Counts

50 → 1

Compiler

Compiled 3518 to 2189 computations (37.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	14	13
2	23	13
3	31	13
4	36	13
5	38	13
6	38	13

end100.0ms (3.7%)

Remove: (sort d2 d4)
Compiler: Compiled 112 to 67 computations (40.2% saved)

Details

analyze2.0ms (0.1%)

sample1.0s (38.9%)

simplify95.0ms (3.5%)

prune4.0ms (0.1%)

localize7.0ms (0.3%)

series43.0ms (1.6%)

rewrite26.0ms (1%)

simplify121.0ms (4.5%)

prune115.0ms (4.3%)

localize6.0ms (0.2%)

series26.0ms (1%)

rewrite29.0ms (1.1%)

simplify118.0ms (4.4%)

prune61.0ms (2.3%)

localize8.0ms (0.3%)

series38.0ms (1.4%)

rewrite36.0ms (1.3%)

simplify94.0ms (3.5%)

prune92.0ms (3.4%)

localize9.0ms (0.3%)

series67.0ms (2.5%)

rewrite1.0ms (0%)

simplify119.0ms (4.4%)

prune121.0ms (4.5%)

regimes304.0ms (11.3%)

simplify3.0ms (0.1%)

end100.0ms (3.7%)

Profiling