Details

analyze1.1s (15.4%)

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)

sample3.1s (42.3%)

Symmetry

(sort y z)

Results

1.6s	10582×	body	128	invalid
1.4s	8256×	body	128	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify92.0ms (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 → 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

1.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.5b	(.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)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 t) z)
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
✓	2.5b	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
✓	6.1b	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))

series84.0ms (1.1%)

Counts

4 → 120

Calls

4 calls:

37.0ms	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))
22.0ms	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
16.0ms	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
8.0ms	(/.f64 (sqrt.f64 t) z)

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
62×	`*-un-lft-identity_binary64`
62×	`add-cube-cbrt_binary64`
39×	`sqrt-prod_binary64`

Counts

4 → 179

Calls

4 calls:

11.0ms	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))
6.0ms	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
3.0ms	(/.f64 (sqrt.f64 t) z)
2.0ms	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

simplify203.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

740×	`associate-/r*_binary64`
664×	`associate-/l/_binary64`
458×	`*-commutative_binary64`
395×	`associate-/r/_binary64`
173×	`log-div_binary64`

Counts

299 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	5359
1	541	4814
2	1719	4813
3	4107	4813
4	4737	4813
5	4988	4813

prune472.0ms (6.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	243	2	245
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	245	2	247

Error

1.0b

Counts

247 → 2

Alt Table

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

Compiler

Compiled 5234 to 2509 computations (52.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	3.0b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	4.9b	(/.f64 x (*.f64 y z))

series148.0ms (2%)

Counts

4 → 0

Calls

4 calls:

77.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
33.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
20.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
18.0ms	(/.f64 x (*.f64 y z))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64`
34×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
14×	`cbrt-unprod_binary64`
14×	`prod-exp_binary64`

Counts

4 → 101

Calls

4 calls:

6.0ms	(.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))
2.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

950×	`times-frac_binary64`
716×	`associate-*l/_binary64`
462×	`associate-/l*_binary64`
425×	`associate-/r*_binary64`
142×	`log-div_binary64`

Counts

101 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1867
1	327	1566
2	1062	1565
3	4748	1565
4	4996	1565
5	5009	1565

prune82.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	128	2	130

Error

1.0b

Counts

130 → 2

Alt Table

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

Compiler

Compiled 2649 to 1175 computations (55.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
✓	1.0b	(cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))))
	3.0b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
	4.9b	(/.f64 x (*.f64 y z))

series1.5s (20.3%)

Counts

1 → 48

Calls

1 calls:

1.5s	(cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`cbrt-div_binary64`

Counts

1 → 14

Calls

1 calls:

2.0ms

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

simplify91.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

882×	`log-prod_binary64`
562×	`fma-def_binary64`
539×	`distribute-rgt-in_binary64`
500×	`distribute-lft-in_binary64`
365×	`associate-l_binary64`

Counts

62 → 20

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	39	1451
1	56	1451
2	93	1402
3	186	1377
4	371	1377
5	645	1377
6	1585	1373
7	4489	1373
8	4918	1373

prune77.0ms (1.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	115	2	117

Error

1.0b

Counts

117 → 2

Alt Table

Status	Error	Program
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	1.0b	(log.f64 (cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))))

Compiler

Compiled 2440 to 1137 computations (53.4% saved)

regimes125.0ms (1.7%)

Accuracy

Total 0.0b remaining (0.4%)

Threshold costs 0.0b (0.4%)

Counts

6 → 1

Compiler

Compiled 1713 to 1349 computations (21.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	20
1	18	20
2	18	20

end61.0ms (0.8%)

Remove: (sort y z)
Compiler: Compiled 103 to 79 computations (23.3% saved)

Details

analyze1.1s (15.4%)

sample3.1s (42.3%)

simplify92.0ms (1.3%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series84.0ms (1.1%)

rewrite33.0ms (0.5%)

simplify203.0ms (2.8%)

prune472.0ms (6.4%)

localize11.0ms (0.1%)

series148.0ms (2%)

rewrite23.0ms (0.3%)

simplify84.0ms (1.1%)

prune82.0ms (1.1%)

localize17.0ms (0.2%)

series1.5s (20.3%)

rewrite2.0ms (0%)

simplify91.0ms (1.2%)

prune77.0ms (1.1%)

regimes125.0ms (1.7%)

simplify2.0ms (0%)

end61.0ms (0.8%)

Profiling