Details

analyze1.4s (16.9%)

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
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)

sample100.0ms (1.2%)

Algorithm

1×

intervals

Results

29.0ms	368×	body	128	nan
26.0ms	256×	body	128	valid

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify106.0ms (1.3%)

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

prune3.0ms (0%)

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
▶	1.9b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
	2.0b	(.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)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.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))))
4.0b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
7.0b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

rewrite145.0ms (1.7%)

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:

9.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
7.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
6.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
6.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

Compiler

Compiled 3800 to 2780 computations (26.8% saved)

series121.0ms (1.5%)

Error

1.0b

Counts

4 → 39

Calls

4 calls:

42.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
34.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
26.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
14.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

Compiler

Compiled 1564 to 1216 computations (22.3% saved)

simplify169.0ms (2%)

Algorithm

1×	egg-herbie

Rules

363×	`associate--l+_binary64`
309×	`times-frac_binary64`
262×	`sub-neg_binary64`
231×	`associate--r+_binary64`
203×	`associate-l_binary64`

Counts

172 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	4331
1	571	3056
2	2568	3053
3	3079	3053
4	4757	3053
5	4989	3053
6	4928	3053

prune71.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	120	2	122

Error

0.0b

Counts

122 → 2

Alt Table

Status	Error	Program
	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 x) (.f64 z (*.f64 54 y))) (sqrt.f64 t))))
▶	0.9b	(.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)))

Status

Error

Program

1.2b

(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 (*.f64 3 x) (*.f64 z (*.f64 54 y))) (sqrt.f64 t))))

▶

0.9b

(*.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)))

Compiler

Compiled 1676 to 1158 computations (30.9% saved)

localize15.0ms (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))
4.0b	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
7.0b	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))

rewrite168.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

61×	`add-exp-log_binary64`
60×	`add-cbrt-cube_binary64`
39×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
30×	`times-frac_binary64`

Counts

4 → 135

Calls

4 calls:

9.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
7.0ms	(*.f64 1/9 (/.f64 x y))
6.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
3.0ms	(/.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)

series139.0ms (1.7%)

Error

Counts

4 → 39

Calls

4 calls:

47.0ms	(/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3))
46.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
29.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
14.0ms	(*.f64 1/9 (/.f64 x y))

Compiler

Compiled 2166 to 1826 computations (15.7% saved)

simplify174.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/r/_binary64`
589×	`*-commutative_binary64`
231×	`times-frac_binary64`
183×	`associate--l+_binary64`
179×	`log-prod_binary64`

Counts

174 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	237	4226
1	549	3326
2	2107	3326
3	3480	3322
4	4858	3322
5	4990	3322
6	4943	3322

prune71.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	110	3	113

Error

Counts

113 → 3

Alt Table

Status	Error	Program
✓	0.9b	(.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)))
▶	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 x) (.f64 z (*.f64 54 y))) (sqrt.f64 t))))

Compiler

Compiled 2312 to 1553 computations (32.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3))
0.3b	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
3.9b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
6.1b	(/.f64 x (*.f64 y z))

rewrite148.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

34×	`add-exp-log_binary64`
33×	`add-cbrt-cube_binary64`
30×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 115

Calls

4 calls:

7.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
6.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
3.0ms	(/.f64 x (*.f64 y z))
3.0ms	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3))

Compiler

Compiled 3395 to 2052 computations (39.6% saved)

series158.0ms (1.9%)

Error

Counts

4 → 45

Calls

4 calls:

47.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
45.0ms	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3))
40.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
25.0ms	(/.f64 x (*.f64 y z))

Compiler

Compiled 2444 to 2056 computations (15.9% saved)

simplify157.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

600×	`associate-/l*_binary64`
503×	`associate-/r*_binary64`
384×	`*-commutative_binary64`
182×	`sub-neg_binary64`
169×	`div-sub_binary64`

Counts

160 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	3450
1	397	3135
2	1280	3135
3	3254	3131
4	4074	3131
5	4648	3131
6	4932	3131

prune392.0ms (4.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	109	3	112

Error

Counts

112 → 3

Alt Table

Status	Error	Program
✓	0.9b	(.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)))
✓	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
▶	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 x) (.f64 z (*.f64 54 y))) (sqrt.f64 t))))

Compiler

Compiled 1889 to 1226 computations (35.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 z (.f64 54 y))
1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 x) (.f64 z (*.f64 54 y))) (sqrt.f64 t))))
4.0b	(.f64 (/.f64 (.f64 3 x) (.f64 z (.f64 54 y))) (sqrt.f64 t))
6.1b	(/.f64 (.f64 3 x) (.f64 z (*.f64 54 y)))

rewrite90.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

68×	`add-exp-log_binary64`
64×	`add-cbrt-cube_binary64`
32×	`prod-exp_binary64`
30×	`cbrt-unprod_binary64`
27×	`add-sqr-sqrt_binary64`

Counts

4 → 115

Calls

4 calls:

8.0ms	(.f64 (/.f64 (.f64 3 x) (.f64 z (.f64 54 y))) (sqrt.f64 t))
7.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 x) (.f64 z (*.f64 54 y))) (sqrt.f64 t))))
6.0ms	(/.f64 (.f64 3 x) (.f64 z (*.f64 54 y)))
4.0ms	(.f64 z (.f64 54 y))

Compiler

Compiled 2887 to 2018 computations (30.1% saved)

series194.0ms (2.3%)

Error

Counts

4 → 39

Calls

4 calls:

120.0ms	(.f64 (/.f64 (.f64 3 x) (.f64 z (.f64 54 y))) (sqrt.f64 t))
33.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 x) (.f64 z (*.f64 54 y))) (sqrt.f64 t))))
25.0ms	(/.f64 (.f64 3 x) (.f64 z (*.f64 54 y)))
14.0ms	(.f64 z (.f64 54 y))

Compiler

Compiled 1564 to 1215 computations (22.3% saved)

simplify198.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

539×	`associate-/l/_binary64`
393×	`associate-/r/_binary64`
329×	`times-frac_binary64`
222×	`associate-l_binary64`
202×	`associate-r_binary64`

Counts

154 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	3385
1	467	2507
2	2379	2506
3	4148	2506
4	4831	2506
5	4947	2506

prune38.0ms (0.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	112	3	115

Error

Counts

115 → 3

Alt Table

Status	Error	Program
	0.9b	(.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)))
	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 x) (.f64 z (*.f64 54 y))) (sqrt.f64 t))))

Compiler

Compiled 1443 to 854 computations (40.8% saved)

regimes1.1s (12.8%)

Accuracy

Total 0.3b remaining (99.2%)

Threshold costs 0.3b (99.2%)

Compiler

Compiled 20727 to 17201 computations (17% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	25	38
2	24	38

end6.0ms (0.1%)

Compiler: Compiled 84 to 72 computations (14.3% saved)

sample3.1s (37.6%)

Algorithm

1×

intervals

Results

904.0ms	10419×	body	128	nan
839.0ms	8000×	body	128	valid

Compiler

Compiled 131 to 111 computations (15.3% saved)

Details

analyze1.4s (16.9%)

sample100.0ms (1.2%)

simplify106.0ms (1.3%)

prune3.0ms (0%)

localize13.0ms (0.2%)

rewrite145.0ms (1.7%)

series121.0ms (1.5%)

simplify169.0ms (2%)

prune71.0ms (0.9%)

localize15.0ms (0.2%)

rewrite168.0ms (2%)

series139.0ms (1.7%)

simplify174.0ms (2.1%)

prune71.0ms (0.9%)

localize16.0ms (0.2%)

rewrite148.0ms (1.8%)

series158.0ms (1.9%)

simplify157.0ms (1.9%)

prune392.0ms (4.7%)

localize12.0ms (0.1%)

rewrite90.0ms (1.1%)

series194.0ms (2.3%)

simplify198.0ms (2.4%)

prune38.0ms (0.5%)

regimes1.1s (12.8%)

simplify3.0ms (0%)

end6.0ms (0.1%)

sample3.1s (37.6%)

Profiling