Details

analyze508.0ms (15.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
37.4%	62.4%	0.1%	8
40.6%	57.7%	1.7%	9
45.2%	51.1%	3.7%	10
57.7%	33.5%	8.7%	11
59.7%	29.4%	10.9%	12
62%	25%	13%	13
68.3%	17.4%	14.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample29.0ms (0.9%)

Algorithm

1×

intervals

Results

9.0ms	242×	body	128	valid
1.0ms	24×	body	128	invalid
1.0ms	8×	body	512	valid
1.0ms	5×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`distribute-lft-out_binary64`
6×	`associate-+r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	10
2	44	10
3	64	10
4	66	10
5	67	10
6	67	10

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

Compiler

Compiled 58 to 39 computations (32.8% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

rewrite45.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`flip3-+_binary64`
6×	`add-exp-log_binary64`
6×	`distribute-rgt-in_binary64`

Counts

1 → 49

Calls

1 calls:

15.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 668 to 349 computations (47.8% saved)

series24.0ms (0.7%)

Error

0.1b

Counts

1 → 15

Calls

1 calls:

19.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 323 to 205 computations (36.5% saved)

simplify80.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

431×	`fma-neg_binary64`
413×	`fma-def_binary64`
365×	`unswap-sqr_binary64`
323×	`*-commutative_binary64`
273×	`cancel-sign-sub-inv_binary64`

Counts

64 → 30

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	768
1	268	695
2	1146	690
3	2748	684
4	4901	684
5	4925	684

prune18.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	26	4	30
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	26	6	32

Error

0.0b

Counts

32 → 6

Alt Table

Status	Error	Program
	32.1b	(/.f64 d1 (/.f64 (fma.f64 (+.f64 d2 d3) (+.f64 (+.f64 d2 d3) -3) 9) (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))))
	40.7b	(/.f64 (.f64 d1 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))) (.f64 d1 (-.f64 3 (+.f64 d2 d3))))
	33.6b	(/.f64 1 (/.f64 (fma.f64 (+.f64 d2 d3) (+.f64 (+.f64 d2 d3) -3) 9) (*.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3)))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	33.6b	(/.f64 (*.f64 d1 (-.f64 -27 (pow.f64 (+.f64 d2 d3) 3))) (fma.f64 (+.f64 d2 d3) (-.f64 3 (+.f64 d2 d3)) -9))
▶	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

Compiler

Compiled 503 to 285 computations (43.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 d1 3) (.f64 d1 d2))
0.0b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

rewrite83.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-log-exp_binary64`
12×	`add-cube-cbrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`flip3-+_binary64`
8×	`pow1_binary64`

Counts

2 → 85

Calls

2 calls:

17.0ms	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
16.0ms	(+.f64 (.f64 d1 3) (.f64 d1 d2))

Compiler

Compiled 1513 to 710 computations (53.1% saved)

series66.0ms (2%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

38.0ms	(+.f64 (.f64 d1 3) (.f64 d1 d2))
21.0ms	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

Compiler

Compiled 560 to 344 computations (38.6% saved)

simplify86.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
761×	`fma-neg_binary64`
611×	`distribute-rgt-in_binary64`
301×	`distribute-rgt-neg-in_binary64`
298×	`cancel-sign-sub-inv_binary64`

Counts

109 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1296
1	320	1218
2	1484	1162
3	4827	1162
4	5209	1162

prune37.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	72	7	79

Error

Counts

79 → 7

Alt Table

Status	Error	Program
▶	28.9b	(+.f64 (/.f64 (.f64 (.f64 d1 d1) (-.f64 9 (.f64 d2 d2))) (.f64 d1 (-.f64 3 d2))) (*.f64 d1 d3))
	32.1b	(/.f64 d1 (/.f64 (fma.f64 (+.f64 d2 d3) (+.f64 (+.f64 d2 d3) -3) 9) (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))))
	40.7b	(/.f64 (.f64 d1 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))) (.f64 d1 (-.f64 3 (+.f64 d2 d3))))
	35.7b	(.f64 (+.f64 (pow.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) 3) (pow.f64 (.f64 d1 d3) 3)) (/.f64 1 (fma.f64 (.f64 d1 d3) (.f64 d1 (-.f64 d3 (+.f64 d2 3))) (pow.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 3))) 6))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	33.6b	(/.f64 (*.f64 d1 (-.f64 -27 (pow.f64 (+.f64 d2 d3) 3))) (fma.f64 (+.f64 d2 d3) (-.f64 3 (+.f64 d2 d3)) -9))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

Compiler

Compiled 1062 to 644 computations (39.4% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 9 (*.f64 d2 d2))
0.0b	(+.f64 (/.f64 (.f64 (.f64 d1 d1) (-.f64 9 (.f64 d2 d2))) (.f64 d1 (-.f64 3 d2))) (*.f64 d1 d3))
9.4b	(.f64 (.f64 d1 d1) (-.f64 9 (*.f64 d2 d2)))
23.5b	(/.f64 (.f64 (.f64 d1 d1) (-.f64 9 (.f64 d2 d2))) (.f64 d1 (-.f64 3 d2)))

rewrite186.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

35×	`add-cube-cbrt_binary64`
24×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`
17×	`pow1_binary64`

Counts

4 → 183

Calls

4 calls:

23.0ms	(/.f64 (.f64 (.f64 d1 d1) (-.f64 9 (.f64 d2 d2))) (.f64 d1 (-.f64 3 d2)))
19.0ms	(.f64 (.f64 d1 d1) (-.f64 9 (*.f64 d2 d2)))
17.0ms	(-.f64 9 (*.f64 d2 d2))
17.0ms	(+.f64 (/.f64 (.f64 (.f64 d1 d1) (-.f64 9 (.f64 d2 d2))) (.f64 d1 (-.f64 3 d2))) (*.f64 d1 d3))

Compiler

Compiled 4951 to 2368 computations (52.2% saved)

series147.0ms (4.5%)

Error

Counts

4 → 39

Calls

4 calls:

86.0ms	(+.f64 (/.f64 (.f64 (.f64 d1 d1) (-.f64 9 (.f64 d2 d2))) (.f64 d1 (-.f64 3 d2))) (*.f64 d1 d3))
21.0ms	(/.f64 (.f64 (.f64 d1 d1) (-.f64 9 (.f64 d2 d2))) (.f64 d1 (-.f64 3 d2)))
20.0ms	(.f64 (.f64 d1 d1) (-.f64 9 (*.f64 d2 d2)))
7.0ms	(-.f64 9 (*.f64 d2 d2))

Compiler

Compiled 1458 to 998 computations (31.6% saved)

simplify117.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

390×	`fma-neg_binary64`
378×	`unswap-sqr_binary64`
285×	`associate-l_binary64`
242×	`associate-r_binary64`
145×	`fma-def_binary64`

Counts

222 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	4129
1	689	3328
2	3157	3173
3	4936	3173

prune69.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	2	2	4
Picked	0	1	1
Done	1	1	2
Total	139	5	144

Error

Counts

144 → 5

Alt Table

Status	Error	Program
✓	28.9b	(+.f64 (/.f64 (.f64 (.f64 d1 d1) (-.f64 9 (.f64 d2 d2))) (.f64 d1 (-.f64 3 d2))) (*.f64 d1 d3))
▶	15.7b	(+.f64 (/.f64 (.f64 (-.f64 9 (.f64 d2 d2)) d1) (-.f64 3 d2)) (*.f64 d1 d3))
	35.7b	(.f64 (+.f64 (pow.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) 3) (pow.f64 (.f64 d1 d3) 3)) (/.f64 1 (fma.f64 (.f64 d1 d3) (.f64 d1 (-.f64 d3 (+.f64 d2 3))) (pow.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 3))) 6))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	33.6b	(/.f64 (*.f64 d1 (-.f64 -27 (pow.f64 (+.f64 d2 d3) 3))) (fma.f64 (+.f64 d2 d3) (-.f64 3 (+.f64 d2 d3)) -9))

Compiler

Compiled 2506 to 1363 computations (45.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 9 (*.f64 d2 d2))
0.0b	(+.f64 (/.f64 (.f64 (-.f64 9 (.f64 d2 d2)) d1) (-.f64 3 d2)) (*.f64 d1 d3))
5.7b	(.f64 (-.f64 9 (.f64 d2 d2)) d1)
9.2b	(/.f64 (.f64 (-.f64 9 (.f64 d2 d2)) d1) (-.f64 3 d2))

rewrite234.0ms (7.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

33×	`add-cube-cbrt_binary64`
23×	`pow1_binary64`
21×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`

Counts

4 → 177

Calls

4 calls:

20.0ms	(/.f64 (.f64 (-.f64 9 (.f64 d2 d2)) d1) (-.f64 3 d2))
19.0ms	(-.f64 9 (*.f64 d2 d2))
18.0ms	(.f64 (-.f64 9 (.f64 d2 d2)) d1)
18.0ms	(+.f64 (/.f64 (.f64 (-.f64 9 (.f64 d2 d2)) d1) (-.f64 3 d2)) (*.f64 d1 d3))

Compiler

Compiled 3924 to 2110 computations (46.2% saved)

series106.0ms (3.2%)

Error

Counts

4 → 39

Calls

4 calls:

56.0ms	(+.f64 (/.f64 (.f64 (-.f64 9 (.f64 d2 d2)) d1) (-.f64 3 d2)) (*.f64 d1 d3))
19.0ms	(/.f64 (.f64 (-.f64 9 (.f64 d2 d2)) d1) (-.f64 3 d2))
15.0ms	(.f64 (-.f64 9 (.f64 d2 d2)) d1)
7.0ms	(-.f64 9 (*.f64 d2 d2))

Compiler

Compiled 1279 to 881 computations (31.1% saved)

simplify136.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-def_binary64`
384×	`cancel-sign-sub-inv_binary64`
259×	`fma-neg_binary64`
154×	`associate-l_binary64`
144×	`associate-r_binary64`

Counts

216 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	3500
1	572	3177
2	2293	2994
3	4764	2994
4	4904	2994

prune68.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	133	5	138

Error

Counts

138 → 5

Alt Table

Status	Error	Program
	28.9b	(+.f64 (/.f64 (.f64 (.f64 d1 d1) (-.f64 9 (.f64 d2 d2))) (.f64 d1 (-.f64 3 d2))) (*.f64 d1 d3))
	15.7b	(+.f64 (/.f64 (.f64 (-.f64 9 (.f64 d2 d2)) d1) (-.f64 3 d2)) (*.f64 d1 d3))
	35.7b	(.f64 (+.f64 (pow.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) 3) (pow.f64 (.f64 d1 d3) 3)) (/.f64 1 (fma.f64 (.f64 d1 d3) (.f64 d1 (-.f64 d3 (+.f64 d2 3))) (pow.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 3))) 6))))
	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	33.6b	(/.f64 (*.f64 d1 (-.f64 -27 (pow.f64 (+.f64 d2 d3) 3))) (fma.f64 (+.f64 d2 d3) (-.f64 3 (+.f64 d2 d3)) -9))

Compiler

Compiled 2154 to 1243 computations (42.3% saved)

regimes472.0ms (14.3%)

Accuracy

Total 0.0b remaining (43.5%)

Threshold costs 0.0b (43.5%)

Compiler

Compiled 8499 to 5727 computations (32.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end6.0ms (0.2%)

Remove: (sort d2 d3)
Compiler: Compiled 33 to 21 computations (36.4% saved)

sample737.0ms (22.3%)

Algorithm

1×

intervals

Results

310.0ms	7494×	body	128	valid
29.0ms	225×	body	512	valid
27.0ms	709×	body	128	invalid
24.0ms	177×	body	1024	valid
8.0ms	104×	body	256	valid

Compiler

Compiled 142 to 94 computations (33.8% saved)

Details

analyze508.0ms (15.4%)

sample29.0ms (0.9%)

simplify10.0ms (0.3%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

rewrite45.0ms (1.4%)

series24.0ms (0.7%)

simplify80.0ms (2.4%)

prune18.0ms (0.5%)

localize7.0ms (0.2%)

rewrite83.0ms (2.5%)

series66.0ms (2%)

simplify86.0ms (2.6%)

prune37.0ms (1.1%)

localize12.0ms (0.4%)

rewrite186.0ms (5.6%)

series147.0ms (4.5%)

simplify117.0ms (3.5%)

prune69.0ms (2.1%)

localize10.0ms (0.3%)

rewrite234.0ms (7.1%)

series106.0ms (3.2%)

simplify136.0ms (4.1%)

prune68.0ms (2.1%)

regimes472.0ms (14.3%)

simplify3.0ms (0.1%)

end6.0ms (0.2%)

sample737.0ms (22.3%)

Profiling