Details

analyze1.2s (14.6%)

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
3.1%	71.7%	25.1%	9
4.7%	69.8%	25.5%	10
7%	66.9%	26.1%	11
10.9%	61.5%	27.6%	12
11.1%	47%	41.9%	13
12.8%	44.4%	42.8%	14

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample86.0ms (1.1%)

Algorithm

1×

intervals

Results

28.0ms	347×	body	128	nan
18.0ms	256×	body	128	valid

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify107.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

2067×	`associate-/l*_binary64`
1151×	`associate-/l/_binary64`
961×	`associate-/r/_binary64`
904×	`*-commutative_binary64`
879×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	40	23
2	121	20
3	446	20
4	1750	20
5	3005	20
6	3002	20
7	3002	20
8	3753	20
9	4074	20
10	4215	20
11	4225	20
12	4229	20
13	4230	20
14	5398	20

prune6.0ms (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

1.1b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
	1.9b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (/.f64 x (.f64 y 27)))
1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
3.4b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
5.1b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

rewrite213.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

96×	`add-exp-log_binary64`
92×	`add-cbrt-cube_binary64`
41×	`prod-exp_binary64`
39×	`cbrt-unprod_binary64`
31×	`add-sqr-sqrt_binary64`

Counts

4 → 133

Calls

4 calls:

13.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
10.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
9.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
8.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

Compiler

Compiled 3800 to 2780 computations (26.8% saved)

series155.0ms (2%)

Error

1.0b

Counts

4 → 39

Calls

4 calls:

58.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
38.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
32.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
18.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

Compiler

Compiled 1564 to 1214 computations (22.4% saved)

simplify190.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

430×	`associate--l+_binary64`
309×	`times-frac_binary64`
271×	`sub-neg_binary64`
242×	`associate--l-_binary64`
209×	`associate-l_binary64`

Counts

172 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	4346
1	589	3071
2	2625	3068
3	3150	3068
4	4894	3068
5	4986	3068
6	4935	3068

prune85.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	139	3	142

Error

Counts

142 → 3

Alt Table

Status	Error	Program
	0.3b	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
▶	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3)))
	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 z y)) (sqrt.f64 t)))))

Compiler

Compiled 1755 to 1216 computations (30.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3))
0.3b	(*.f64 1/9 (/.f64 x y))
3.4b	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
5.1b	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))

rewrite239.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

61×	`add-exp-log_binary64`
60×	`add-cbrt-cube_binary64`
39×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64` `times-frac_binary64` `*-un-lft-identity_binary64`
23×	`prod-exp_binary64` `cbrt-unprod_binary64`

Counts

4 → 135

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
8.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
7.0ms	(*.f64 1/9 (/.f64 x y))
4.0ms	(/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3))

Compiler

Compiled 4505 to 3211 computations (28.7% saved)

series191.0ms (2.4%)

Error

Counts

4 → 39

Calls

4 calls:

63.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
60.0ms	(/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3))
38.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
21.0ms	(*.f64 1/9 (/.f64 x y))

Compiler

Compiled 2166 to 1824 computations (15.8% saved)

simplify205.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

778×	`associate-/r/_binary64`
586×	`*-commutative_binary64`
231×	`times-frac_binary64`
179×	`log-prod_binary64`
173×	`sub-neg_binary64` `associate-/l*_binary64`

Counts

174 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	4246
1	555	3346
2	2131	3346
3	3525	3342
4	4837	3342
5	4983	3342
6	4941	3342

prune105.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	131	3	134

Error

Counts

134 → 3

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
✓	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3)))
	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 z y)) (sqrt.f64 t)))))

Compiler

Compiled 2445 to 1630 computations (33.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
1.0b	(/.f64 1 (sqrt.f64 3))
3.4b	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
5.1b	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))

rewrite304.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

98×	`add-sqr-sqrt_binary64`
80×	`add-exp-log_binary64`
78×	`times-frac_binary64`
68×	`add-cbrt-cube_binary64`
54×	`*-un-lft-identity_binary64`

Counts

4 → 191

Calls

4 calls:

18.0ms	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
12.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
8.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
4.0ms	(/.f64 1 (sqrt.f64 3))

Compiler

Compiled 5332 to 3871 computations (27.4% saved)

series171.0ms (2.2%)

Error

Counts

4 → 33

Calls

4 calls:

64.0ms	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
62.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
38.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
0.0ms	(/.f64 1 (sqrt.f64 3))

Compiler

Compiled 1546 to 1249 computations (19.2% saved)

simplify232.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

669×	`associate-/r/_binary64`
249×	`times-frac_binary64`
242×	`associate-l_binary64`
236×	`associate-r_binary64`
235×	`associate-/l*_binary64`

Counts

224 → 184

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	258	6203
1	677	4751
2	2754	4750
3	4128	4710
4	4879	4710
5	4925	4710

prune98.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	185	2	187

Error

Counts

187 → 2

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
▶	1.0b	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))) 3)

Status

Error

Program

✓

0.3b

(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (sqrt.f64 3)))

▶

1.0b

(/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))) 3)

Compiler

Compiled 2402 to 1552 computations (35.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/18 (.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))
1.0b	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))) 3)
3.3b	(.f64 (/.f64 x (.f64 z y)) (sqrt.f64 t))
3.8b	(/.f64 x (*.f64 z y))

rewrite96.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
23×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`prod-exp_binary64` `cbrt-unprod_binary64`

Counts

4 → 103

Calls

4 calls:

9.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))
8.0ms	(.f64 (/.f64 x (.f64 z y)) (sqrt.f64 t))
4.0ms	(/.f64 x (*.f64 z y))
3.0ms	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))) 3)

Compiler

Compiled 2079 to 904 computations (56.5% saved)

series174.0ms (2.2%)

Error

Counts

4 → 45

Calls

4 calls:

56.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))
50.0ms	(.f64 (/.f64 x (.f64 z y)) (sqrt.f64 t))
37.0ms	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))) 3)
28.0ms	(/.f64 x (*.f64 z y))

Compiler

Compiled 1651 to 1244 computations (24.7% saved)

simplify186.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

601×	`associate-/l*_binary64`
491×	`associate-/r*_binary64`
399×	`*-commutative_binary64`
275×	`sub-neg_binary64`
201×	`associate-+l+_binary64`

Counts

148 → 106

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	183	2802
1	389	2495
2	1274	2495
3	3289	2495
4	4464	2495
5	4635	2495
6	4994	2495
7	4956	2495

prune40.0ms (0.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	106	2	108

Error

Counts

108 → 2

Alt Table

Status	Error	Program
	0.3b	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
	1.0b	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))) 3)

Status

Error

Program

0.3b

(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (sqrt.f64 3)))

1.0b

(/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))) 3)

Compiler

Compiled 1096 to 537 computations (51% saved)

regimes1.7s (20.9%)

Accuracy

Total 0.2b remaining (95.7%)

Threshold costs 0.2b (95.7%)

Compiler

Compiled 29922 to 24589 computations (17.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	35
1	25	35
2	24	35

end8.0ms (0.1%)

Remove: (sort y z)
Compiler: Compiled 78 to 66 computations (15.4% saved)

sample2.1s (27.1%)

Algorithm

1×

intervals

Results

715.0ms	10346×	body	128	nan
596.0ms	8000×	body	128	valid

Compiler

Compiled 96 to 80 computations (16.7% saved)

Details

analyze1.2s (14.6%)

sample86.0ms (1.1%)

simplify107.0ms (1.4%)

prune6.0ms (0.1%)

localize14.0ms (0.2%)

rewrite213.0ms (2.7%)

series155.0ms (2%)

simplify190.0ms (2.4%)

prune85.0ms (1.1%)

localize16.0ms (0.2%)

rewrite239.0ms (3%)

series191.0ms (2.4%)

simplify205.0ms (2.6%)

prune105.0ms (1.3%)

localize19.0ms (0.2%)

rewrite304.0ms (3.8%)

series171.0ms (2.2%)

simplify232.0ms (2.9%)

prune98.0ms (1.2%)

localize10.0ms (0.1%)

rewrite96.0ms (1.2%)

series174.0ms (2.2%)

simplify186.0ms (2.3%)

prune40.0ms (0.5%)

regimes1.7s (20.9%)

simplify4.0ms (0%)

end8.0ms (0.1%)

sample2.1s (27.1%)

Profiling