Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
99.7%	0%	0.3%	1

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.6s (15.6%)

Symmetry

(sort y z t)

(sort a b)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify113.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
641×	`fma-def_binary64`
213×	`cancel-sign-sub-inv_binary64`
172×	`distribute-rgt-neg-in_binary64`
157×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	39	23
2	115	21
3	308	21
4	552	21
5	902	21
6	1201	21
7	1433	21
8	1672	21
9	1787	21
10	1791	21
11	1791	21
12	1791	21
13	1674	21

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.5b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 a 27) b)
✓	0.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
✓	0.6b	(.f64 (.f64 y 9) z)
✓	4.0b	(.f64 (.f64 (*.f64 y 9) z) t)

series106.0ms (1%)

Counts

4 → 156

Calls

4 calls:

63.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
22.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
11.0ms	(.f64 (.f64 a 27) b)
9.0ms	(.f64 (.f64 y 9) z)

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-cbrt-cube_binary64`
23×	`add-exp-log_binary64`
23×	`pow1_binary64`
12×	`cbrt-unprod_binary64`
12×	`prod-exp_binary64`

Counts

4 → 84

Calls

4 calls:

11.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
10.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
8.0ms	(.f64 (.f64 y 9) z)
7.0ms	(.f64 (.f64 a 27) b)

simplify190.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-neg_binary64`
586×	`fma-def_binary64`
359×	`associate-l_binary64`
268×	`associate-r_binary64`
268×	`exp-prod_binary64`

Counts

240 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3457
1	415	3135
2	1736	3112
3	4147	3112
4	4957	3112

prune245.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	128	10	138
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	130	10	140

Error

0.0b

Counts

140 → 10

Alt Table

Status	Error	Program
▶	1.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
	2.5b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
	33.6b	(.f64 (sqrt.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))) (sqrt.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (*.f64 a 27) b))))
	9.6b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (.f64 (*.f64 a 27) b))
	2.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
	22.3b	(fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x))
	2.3b	(-.f64 (.f64 x 2) (fma.f64 a (.f64 b -27) (.f64 9 (.f64 y (*.f64 t z)))))
	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x))))) (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (*.f64 a b) (+.f64 x x)))))
	3.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y 9) (.f64 z t))) (.f64 (.f64 a 27) b))
	34.1b	(cbrt.f64 (.f64 (.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b)) (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))) (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))))

Compiler

Compiled 3755 to 2320 computations (38.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 a 27) b)
✓	0.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
✓	0.2b	(.f64 y (.f64 9 z))
✓	4.0b	(.f64 (.f64 y (*.f64 9 z)) t)

series50.0ms (0.5%)

Counts

3 → 132

Calls

3 calls:

32.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
10.0ms	(.f64 (.f64 y (*.f64 9 z)) t)
7.0ms	(.f64 y (.f64 9 z))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 64

Calls

3 calls:

6.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
5.0ms	(.f64 (.f64 y (*.f64 9 z)) t)
5.0ms	(.f64 y (.f64 9 z))

simplify151.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

751×	`fma-neg_binary64`
540×	`fma-def_binary64`
259×	`associate-l_binary64`
254×	`exp-prod_binary64`
238×	`log-prod_binary64`

Counts

196 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	3145
1	341	2792
2	1413	2769
3	3532	2769
4	4922	2769
5	5010	2769

prune381.0ms (3.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	138	10	148

Error

0.0b

Counts

148 → 10

Alt Table

Status	Error	Program
✓	1.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
	2.5b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
▶	1.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y (.f64 9 z)) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))) (.f64 (.f64 a 27) b))
	33.6b	(.f64 (sqrt.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))) (sqrt.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (*.f64 a 27) b))))
	9.6b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (.f64 (*.f64 a 27) b))
	2.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
	22.3b	(fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x))
	2.3b	(-.f64 (.f64 x 2) (fma.f64 a (.f64 b -27) (.f64 9 (.f64 y (*.f64 t z)))))
	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x))))) (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (*.f64 a b) (+.f64 x x)))))
	3.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y 9) (.f64 z t))) (.f64 (.f64 a 27) b))

Compiler

Compiled 3672 to 2271 computations (38.2% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
✓	0.6b	(cbrt.f64 t)
✓	1.4b	(.f64 (.f64 (.f64 y (.f64 9 z)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	2.8b	(.f64 (.f64 y (.f64 9 z)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))

series1.1s (10.4%)

Counts

4 → 96

Calls

4 calls:

936.0ms	(.f64 (.f64 y (.f64 9 z)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
67.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
64.0ms	(cbrt.f64 t)
25.0ms	(.f64 (.f64 (.f64 y (.f64 9 z)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`pow1_binary64`
56×	`add-exp-log_binary64`
39×	`pow-prod-down_binary64`
38×	`cbrt-unprod_binary64`
38×	`prod-exp_binary64`

Counts

4 → 123

Calls

4 calls:

20.0ms	(.f64 (.f64 (.f64 y (.f64 9 z)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
14.0ms	(.f64 (.f64 y (.f64 9 z)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
6.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)

simplify203.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
620×	`unswap-sqr_binary64`
570×	`log-prod_binary64`
380×	`associate-l_binary64`
355×	`exp-prod_binary64`

Counts

219 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	149	2902
1	321	2430
2	1388	2304
3	2010	2270
4	3819	2170
5	4329	2170
6	4748	2170
7	4978	2170
8	5005	2170

prune436.0ms (4.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	193	11	204

Error

0.0b

Counts

204 → 11

Alt Table

Status	Error	Program
✓	1.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
	2.5b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
✓	1.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y (.f64 9 z)) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))) (.f64 (.f64 a 27) b))
	33.6b	(.f64 (sqrt.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))) (sqrt.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (*.f64 a 27) b))))
	9.6b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (.f64 (*.f64 a 27) b))
	2.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
	22.3b	(fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x))
	2.3b	(-.f64 (.f64 x 2) (fma.f64 a (.f64 b -27) (.f64 9 (.f64 y (*.f64 t z)))))
▶	1.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 (.f64 9 z) (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (cbrt.f64 t))) (.f64 (.f64 a 27) b))
	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x))))) (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (*.f64 a b) (+.f64 x x)))))
	3.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y 9) (.f64 z t))) (.f64 (.f64 a 27) b))

Compiler

Compiled 6202 to 3333 computations (46.3% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
	0.6b	(cbrt.f64 t)
✓	1.4b	(.f64 (.f64 y (.f64 (.f64 9 z) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))) (cbrt.f64 t))
✓	4.3b	(.f64 y (.f64 (.f64 9 z) (.f64 (cbrt.f64 t) (cbrt.f64 t))))

series1.3s (12%)

Counts

2 → 72

Calls

2 calls:

1.2s	(.f64 y (.f64 (.f64 9 z) (.f64 (cbrt.f64 t) (cbrt.f64 t))))
29.0ms	(.f64 (.f64 y (.f64 (.f64 9 z) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))) (cbrt.f64 t))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64`
45×	`pow1_binary64`
32×	`cbrt-unprod_binary64`
32×	`prod-exp_binary64`
32×	`pow-prod-down_binary64`

Counts

2 → 64

Calls

2 calls:

14.0ms	(.f64 (.f64 y (.f64 (.f64 9 z) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))) (cbrt.f64 t))
10.0ms	(.f64 y (.f64 (.f64 9 z) (.f64 (cbrt.f64 t) (cbrt.f64 t))))

simplify135.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

495×	`sqr-pow_binary64`
383×	`fma-def_binary64`
344×	`associate-l_binary64`
283×	`associate-r_binary64`
273×	`associate-+l+_binary64`

Counts

136 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2695
1	305	1927
2	1169	1867
3	1566	1867
4	2431	1867
5	3598	1867
6	4940	1867
7	5105	1867

prune623.0ms (5.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	194	11	205

Error

0.0b

Counts

205 → 11

Alt Table

Status	Error	Program
✓	1.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
	2.5b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
✓	1.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y (.f64 9 z)) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))) (.f64 (.f64 a 27) b))
	33.6b	(.f64 (sqrt.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))) (sqrt.f64 (+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (*.f64 a 27) b))))
	9.6b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (.f64 (*.f64 a 27) b))
	2.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
	22.3b	(fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x))
	2.3b	(-.f64 (.f64 x 2) (fma.f64 a (.f64 b -27) (.f64 9 (.f64 y (*.f64 t z)))))
✓	1.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 (.f64 9 z) (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (cbrt.f64 t))) (.f64 (.f64 a 27) b))
	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x))))) (cbrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (*.f64 a b) (+.f64 x x)))))
	3.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y 9) (.f64 z t))) (.f64 (.f64 a 27) b))

Compiler

Compiled 5957 to 3084 computations (48.2% saved)

regimes2.9s (27.6%)

Accuracy

Total 1.0b remaining (90.8%)

Threshold costs 0b (0%)

Counts

143 → 2

Compiler

Compiled 65745 to 45879 computations (30.2% saved)

bsearch20.0ms (0.2%)

Steps

Iters	Range		Point
3	1.6065801791064525e-208	2.8996055847794243e-208	1.7086528660097502e-208

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
14×	`distribute-rgt-neg-in_binary64`
13×	`+-commutative_binary64`
12×	`distribute-lft-neg-in_binary64`
11×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	56
1	54	56
2	78	56
3	100	56
4	119	56
5	128	56
6	131	56
7	128	56

end734.0ms (7%)

Remove: (sort a b)
Compiler: Compiled 675 to 465 computations (31.1% saved)

Details

analyze3.0ms (0%)

sample1.6s (15.6%)

simplify113.0ms (1.1%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series106.0ms (1%)

rewrite46.0ms (0.4%)

simplify190.0ms (1.8%)

prune245.0ms (2.3%)

localize11.0ms (0.1%)

series50.0ms (0.5%)

rewrite19.0ms (0.2%)

simplify151.0ms (1.4%)

prune381.0ms (3.6%)

localize31.0ms (0.3%)

series1.1s (10.4%)

rewrite53.0ms (0.5%)

simplify203.0ms (1.9%)

prune436.0ms (4.1%)

localize31.0ms (0.3%)

series1.3s (12%)

rewrite31.0ms (0.3%)

simplify135.0ms (1.3%)

prune623.0ms (5.9%)

regimes2.9s (27.6%)

bsearch20.0ms (0.2%)

simplify5.0ms (0%)

end734.0ms (7%)

Profiling