Details

analyze1.1s (27.9%)

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
9.4%	90.4%	0.2%	8
9.4%	90.4%	0.2%	9
10.9%	88.9%	0.2%	10
25.9%	73.9%	0.2%	11
47.1%	52.7%	0.2%	12
55.3%	44.5%	0.2%	13
59.2%	40.6%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 47 to 33 computations (29.8% saved)

simplify58.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

504×	`associate-*l/_binary64`
495×	`div-sub_binary64`
454×	`cancel-sign-sub-inv_binary64`
429×	`sub-neg_binary64`
348×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	29	25
2	68	25
3	167	22
4	460	19
5	999	19
6	2280	19
7	4268	19
8	5059	19

prune4.0ms (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

2.2b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	2.4b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	9.1b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 93 to 61 computations (34.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
0.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
3.4b	(/.f64 (.f64 y t) (.f64 2 z))
6.5b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

rewrite198.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

45×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
33×	`times-frac_binary64`
26×	`cancel-sign-sub-inv_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 111

Calls

4 calls:

9.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
6.0ms	(/.f64 (.f64 y t) (.f64 2 z))
5.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
4.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

Compiler

Compiled 2586 to 1313 computations (49.2% saved)

series124.0ms (3.2%)

Error

Counts

4 → 57

Calls

4 calls:

43.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
33.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
22.0ms	(/.f64 (.f64 y t) (.f64 2 z))
19.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

Compiler

Compiled 1528 to 1033 computations (32.4% saved)

simplify147.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

471×	`associate-/l/_binary64`
229×	`distribute-rgt-neg-in_binary64`
213×	`cancel-sign-sub-inv_binary64`
210×	`distribute-neg-frac_binary64`
202×	`exp-prod_binary64`

Counts

168 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	209	3329
1	587	3254
2	2110	3058
3	4459	3052
4	4982	3052

prune48.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	132	4	136

Error

Counts

136 → 4

Alt Table

Status	Error	Program
✓	2.4b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	20.9b	(+.f64 x (*.f64 (/.f64 z t) 2))
	51.1b	(neg.f64 (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
▶	9.1b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 1732 to 791 computations (54.3% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
0.3b	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))
15.7b	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))

rewrite66.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`
10×	`cancel-sign-sub-inv_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

3 → 59

Calls

3 calls:

8.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))
7.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
4.0ms	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))

Compiler

Compiled 1833 to 1030 computations (43.8% saved)

series158.0ms (4.1%)

Error

Counts

3 → 48

Calls

3 calls:

93.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
36.0ms	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))
21.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))

Compiler

Compiled 1400 to 999 computations (28.6% saved)

simplify114.0ms (3%)

Algorithm

1×	egg-herbie

Rules

493×	`associate-/l/_binary64`
412×	`associate-/r*_binary64`
291×	`associate-/r/_binary64`
192×	`distribute-rgt-neg-in_binary64`
176×	`distribute-lft-neg-in_binary64`

Counts

107 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	2256
1	438	2150
2	1741	2013
3	4857	2013
4	4944	2013

prune36.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	79	4	83

Error

Counts

83 → 4

Alt Table

Status	Error	Program
✓	2.4b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
▶	20.9b	(+.f64 x (*.f64 (/.f64 z t) 2))
	51.1b	(neg.f64 (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
✓	9.1b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 1300 to 672 computations (48.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 (/.f64 z t) 2))
0.0b	(*.f64 (/.f64 z t) 2)

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
10×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

4.0ms	(*.f64 (/.f64 z t) 2)
2.0ms	(+.f64 x (*.f64 (/.f64 z t) 2))

Compiler

Compiled 601 to 311 computations (48.3% saved)

series37.0ms (1%)

Error

Counts

2 → 24

Calls

2 calls:

25.0ms	(+.f64 x (*.f64 (/.f64 z t) 2))
10.0ms	(*.f64 (/.f64 z t) 2)

Compiler

Compiled 415 to 301 computations (27.5% saved)

simplify104.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

576×	`associate-/l*_binary64`
388×	`distribute-rgt-out_binary64`
264×	`distribute-rgt-in_binary64`
240×	`times-frac_binary64`
234×	`associate-l_binary64`

Counts

67 → 34

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	92	682
1	219	661
2	570	661
3	1566	661
4	3542	661
5	4518	661
6	4882	661
7	5023	661

prune21.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	34	4	38

Error

Counts

38 → 4

Alt Table

Status	Error	Program
✓	2.4b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
✓	20.9b	(+.f64 x (*.f64 (/.f64 z t) 2))
▶	51.1b	(neg.f64 (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
✓	9.1b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 501 to 264 computations (47.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 1/2 (.f64 (/.f64 y z) t))
0.0b	(-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))
6.5b	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
8.1b	(*.f64 (/.f64 y z) t)

rewrite60.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 94

Calls

4 calls:

6.0ms	(*.f64 (/.f64 y z) t)
5.0ms	(.f64 1/2 (.f64 (/.f64 y z) t))
3.0ms	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
2.0ms	(-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))

Compiler

Compiled 1880 to 849 computations (54.8% saved)

series108.0ms (2.8%)

Error

Counts

4 → 50

Calls

4 calls:

32.0ms	(-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))
29.0ms	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
24.0ms	(.f64 1/2 (.f64 (/.f64 y z) t))
21.0ms	(*.f64 (/.f64 y z) t)

Compiler

Compiled 1483 to 1061 computations (28.5% saved)

simplify161.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

576×	`associate-*l/_binary64`
527×	`associate-*r/_binary64`
433×	`associate-/l*_binary64`
293×	`times-frac_binary64`
188×	`associate-/r*_binary64`

Counts

144 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	2201
1	382	2050
2	1224	2049
3	4560	2049
4	4997	2049
5	4999	2049
6	5021	2049

prune33.0ms (0.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	108	4	112

Error

Counts

112 → 4

Alt Table

Status	Error	Program
	2.4b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	20.9b	(+.f64 x (*.f64 (/.f64 z t) 2))
	51.1b	(neg.f64 (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
	9.1b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 1438 to 674 computations (53.1% saved)

regimes348.0ms (9.1%)

Accuracy

Total 1.1b remaining (95.7%)

Threshold costs 0b (0%)

Compiler

Compiled 6934 to 4612 computations (33.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	17	19
2	28	19
3	34	19
4	38	19
5	39	19
6	39	19

end1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample848.0ms (22.1%)

Algorithm

1×

intervals

Results

484.0ms

8000×

body

128

valid

Compiler

Compiled 108 to 74 computations (31.5% saved)

Details

analyze1.1s (27.9%)

sample26.0ms (0.7%)

simplify58.0ms (1.5%)

prune4.0ms (0.1%)

localize10.0ms (0.3%)

rewrite198.0ms (5.2%)

series124.0ms (3.2%)

simplify147.0ms (3.8%)

prune48.0ms (1.3%)

localize11.0ms (0.3%)

rewrite66.0ms (1.7%)

series158.0ms (4.1%)

simplify114.0ms (3%)

prune36.0ms (0.9%)

localize5.0ms (0.1%)

rewrite32.0ms (0.8%)

series37.0ms (1%)

simplify104.0ms (2.7%)

prune21.0ms (0.5%)

localize8.0ms (0.2%)

rewrite60.0ms (1.6%)

series108.0ms (2.8%)

simplify161.0ms (4.2%)

prune33.0ms (0.9%)

regimes348.0ms (9.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample848.0ms (22.1%)

Profiling