Details

analyze1.2s (11.3%)

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)

sample129.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort y z)

Results

29.0ms	324×	body	128	nan
22.0ms	256×	body	128	valid

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify93.0ms (0.9%)

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 → 2

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

prune4.0ms (0%)

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

1.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.7b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
▶	1.6b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))

Compiler

Compiled 116 to 91 computations (21.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))))
✓	3.0b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	3.9b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series87.0ms (0.8%)

Counts

4 → 144

Calls

4 calls:

44.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
19.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
18.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
7.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

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 → 141

Calls

4 calls:

10.0ms	(.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 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
5.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

simplify194.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

782×	`associate-/r/_binary64`
291×	`times-frac_binary64`
262×	`sub-neg_binary64`
198×	`associate-l_binary64`
191×	`log-prod_binary64`

Counts

285 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	5969
1	547	4670
2	2441	4667
3	4043	4667
4	4793	4667
5	4977	4667

prune620.0ms (6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	211	2	213

Error

0.0b

Counts

213 → 2

Alt Table

Status	Error	Program
	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
▶	0.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))

Status

Error

Program

1.0b

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

▶

0.6b

(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (*.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))

Compiler

Compiled 5856 to 4199 computations (28.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
✓	1.0b	(/.f64 1 (cbrt.f64 3))
	3.0b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
	3.9b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series63.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

62.0ms	(.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
0.0ms	(/.f64 1 (cbrt.f64 3))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
23×	`cbrt-prod_binary64`

Counts

2 → 94

Calls

2 calls:

10.0ms	(.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
3.0ms	(/.f64 1 (cbrt.f64 3))

simplify222.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

958×	`fabs-mul_binary64`
446×	`unswap-sqr_binary64`
434×	`associate-/l*_binary64`
319×	`associate-/l/_binary64`
314×	`associate-*l/_binary64`

Counts

142 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	3282
1	176	2929
2	463	2797
3	974	2775
4	2575	2775
5	2672	2775
6	2888	2775
7	3204	2775
8	4279	2775
9	4834	2775
10	4803	2775
11	5052	2775

prune289.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	236	3	239

Error

Counts

239 → 3

Alt Table

Status	Error	Program
	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
✓	0.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))
▶	0.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t)))))

Compiler

Compiled 8742 to 6909 computations (21% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
	1.0b	(/.f64 1 (cbrt.f64 3))
✓	3.0b	(.f64 (/.f64 3 (.f64 (*.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))
✓	7.0b	(*.f64 (/.f64 z x) y)

series120.0ms (1.2%)

Counts

3 → 120

Calls

3 calls:

63.0ms	(.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
44.0ms	(.f64 (/.f64 3 (.f64 (*.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))
13.0ms	(*.f64 (/.f64 z x) y)

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
43×	`associate-l_binary64`
37×	`add-exp-log_binary64`
35×	`times-frac_binary64`
32×	`add-cbrt-cube_binary64`

Counts

3 → 120

Calls

3 calls:

9.0ms	(.f64 (/.f64 3 (.f64 (*.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))
9.0ms	(.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
5.0ms	(*.f64 (/.f64 z x) y)

simplify220.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-/l*_binary64`
433×	`associate-/r/_binary64`
430×	`*-commutative_binary64`
296×	`fma-def_binary64`
192×	`associate-l_binary64`

Counts

240 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	4748
1	463	4106
2	1473	4106
3	3722	4100
4	4845	4100
5	5091	4100

prune421.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	243	3	246

Error

Counts

246 → 3

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
✓	0.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))
✓	0.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t)))))

Compiler

Compiled 8272 to 5914 computations (28.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54))
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
	3.0b	(.f64 (/.f64 3 (.f64 (*.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))
	7.0b	(*.f64 (/.f64 z x) y)

series41.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

21.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
20.0ms	(/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64`
21×	`add-cbrt-cube_binary64`
19×	`add-sqr-sqrt_binary64`
14×	`times-frac_binary64`
13×	`associate-l_binary64`

Counts

2 → 65

Calls

2 calls:

6.0ms	(/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54))
5.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))

simplify158.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-l_binary64`
445×	`associate-*l/_binary64`
399×	`associate-r_binary64`
372×	`associate-/r*_binary64`
297×	`fma-def_binary64`

Counts

149 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	3016
1	305	2569
2	948	2568
3	3915	2565
4	4837	2565
5	5085	2565

prune200.0ms (1.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	219	3	222

Error

Counts

222 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
✓	0.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))
✓	0.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t)))))

Compiler

Compiled 5376 to 3131 computations (41.8% saved)

regimes3.6s (35%)

Accuracy

Total 0.3b remaining (98%)

Threshold costs 0.3b (98%)

Counts

207 → 1

Compiler

Compiled 79746 to 65529 computations (17.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	41
1	28	41
2	27	41

end6.0ms (0.1%)

Compiler: Compiled 90 to 78 computations (13.3% saved)

sample2.5s (24.5%)

Algorithm

1×

intervals

Results

892.0ms	10301×	body	128	nan
716.0ms	8000×	body	128	valid

Compiler

Compiled 141 to 121 computations (14.2% saved)

Details

analyze1.2s (11.3%)

sample129.0ms (1.2%)

simplify93.0ms (0.9%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series87.0ms (0.8%)

rewrite40.0ms (0.4%)

simplify194.0ms (1.9%)

prune620.0ms (6%)

localize18.0ms (0.2%)

series63.0ms (0.6%)

rewrite19.0ms (0.2%)

simplify222.0ms (2.1%)

prune289.0ms (2.8%)

localize16.0ms (0.2%)

series120.0ms (1.2%)

rewrite33.0ms (0.3%)

simplify220.0ms (2.1%)

prune421.0ms (4.1%)

localize12.0ms (0.1%)

series41.0ms (0.4%)

rewrite17.0ms (0.2%)

simplify158.0ms (1.5%)

prune200.0ms (1.9%)

regimes3.6s (35%)

simplify3.0ms (0%)

end6.0ms (0.1%)

sample2.5s (24.5%)

Profiling