Details

analyze1.8s (22.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample262.0ms (3.3%)

Algorithm

1×

intervals

Symmetry

(sort y z t)

(sort a b)

Results

19.0ms	256×	body	128	valid
6.0ms	102×	body	128	invalid

Compiler

Compiled 53 to 41 computations (22.6% saved)

simplify71.0ms (0.9%)

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 (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
▶	2.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
✓	0.2b	(.f64 (.f64 a 27) b)
✓	0.4b	(.f64 (.f64 y 9) z)
✓	6.4b	(.f64 (.f64 (*.f64 y 9) z) t)

series52.0ms (0.7%)

Counts

4 → 156

Calls

4 calls:

31.0ms	(+.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)
7.0ms	(.f64 (.f64 a 27) b)
4.0ms	(.f64 (.f64 y 9) z)

rewrite21.0ms (0.3%)

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:

5.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
5.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
4.0ms	(.f64 (.f64 y 9) z)
4.0ms	(.f64 (.f64 a 27) b)

simplify104.0ms (1.3%)

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

prune170.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	132	6	138
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	134	6	140

Error

Counts

140 → 6

Alt Table

Status	Error	Program
▶	2.6b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))) (.f64 (.f64 a 27) b))
	3.4b	(+.f64 (.f64 x 2) (fma.f64 y (.f64 (.f64 t z) -9) (.f64 27 (*.f64 a b))))
	3.7b	(-.f64 (.f64 x 2) (fma.f64 a (.f64 b -27) (.f64 9 (.f64 y (*.f64 t z)))))
	36.6b	(.f64 (sqrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x)))) (sqrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (*.f64 a b) (+.f64 x x)))))
	16.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (*.f64 a 27) (sqrt.f64 b)) (sqrt.f64 b)))

Compiler

Compiled 3447 to 2110 computations (38.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
	0.2b	(.f64 (.f64 a 27) b)
✓	0.2b	(.f64 y (.f64 9 z))
✓	6.4b	(.f64 (.f64 y (*.f64 9 z)) t)

series53.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

34.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
14.0ms	(.f64 (.f64 y (*.f64 9 z)) t)
5.0ms	(.f64 y (.f64 9 z))

rewrite18.0ms (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)
4.0ms	(.f64 y (.f64 9 z))

simplify128.0ms (1.6%)

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

prune127.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	139	6	145

Error

Counts

145 → 6

Alt Table

Status	Error	Program
✓	2.6b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
▶	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))) (.f64 (.f64 a 27) b))
	3.4b	(+.f64 (.f64 x 2) (fma.f64 y (.f64 (.f64 t z) -9) (.f64 27 (*.f64 a b))))
	3.7b	(-.f64 (.f64 x 2) (fma.f64 a (.f64 b -27) (.f64 9 (.f64 y (*.f64 t z)))))
	36.6b	(.f64 (sqrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x)))) (sqrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (*.f64 a b) (+.f64 x x)))))
	16.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (*.f64 a 27) (sqrt.f64 b)) (sqrt.f64 b)))

Compiler

Compiled 3429 to 2107 computations (38.6% saved)

localize15.0ms (0.2%)

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)
✓	2.3b	(.f64 (.f64 (.f64 (.f64 y 9) z) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	4.4b	(.f64 (.f64 (.f64 y 9) z) (.f64 (cbrt.f64 t) (cbrt.f64 t)))

series902.0ms (11.3%)

Counts

4 → 96

Calls

4 calls:

810.0ms	(.f64 (.f64 (.f64 y 9) z) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
37.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
31.0ms	(cbrt.f64 t)
24.0ms	(.f64 (.f64 (.f64 (.f64 y 9) z) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))

rewrite42.0ms (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:

12.0ms	(.f64 (.f64 (.f64 (.f64 y 9) z) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
9.0ms	(.f64 (.f64 (.f64 y 9) z) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
4.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)

simplify134.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

642×	`fma-def_binary64`
614×	`unswap-sqr_binary64`
527×	`sqr-pow_binary64`
413×	`log-prod_binary64`
398×	`associate-l_binary64`

Counts

219 → 158

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	149	2899
1	317	2427
2	1378	2301
3	2019	2267
4	3852	2167
5	4244	2165
6	5233	2165

prune188.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	194	6	200

Error

Counts

200 → 6

Alt Table

Status	Error	Program
✓	2.6b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
✓	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))) (.f64 (.f64 a 27) b))
▶	3.4b	(+.f64 (.f64 x 2) (fma.f64 y (.f64 (.f64 t z) -9) (.f64 27 (*.f64 a b))))
	3.7b	(-.f64 (.f64 x 2) (fma.f64 a (.f64 b -27) (.f64 9 (.f64 y (*.f64 t z)))))
	36.6b	(.f64 (sqrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (.f64 a b) (+.f64 x x)))) (sqrt.f64 (fma.f64 y (.f64 (.f64 t z) -9) (fma.f64 27 (*.f64 a b) (+.f64 x x)))))
	16.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (*.f64 a 27) (sqrt.f64 b)) (sqrt.f64 b)))

Compiler

Compiled 5880 to 3115 computations (47% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x 2) (fma.f64 y (.f64 (.f64 t z) -9) (.f64 27 (*.f64 a b))))
✓	0.2b	(.f64 (.f64 t z) -9)
✓	0.2b	(.f64 27 (.f64 a b))
✓	3.3b	(fma.f64 y (.f64 (.f64 t z) -9) (.f64 27 (.f64 a b)))

series65.0ms (0.8%)

Counts

4 → 156

Calls

4 calls:

30.0ms	(+.f64 (.f64 x 2) (fma.f64 y (.f64 (.f64 t z) -9) (.f64 27 (*.f64 a b))))
23.0ms	(fma.f64 y (.f64 (.f64 t z) -9) (.f64 27 (.f64 a b)))
8.0ms	(.f64 (.f64 t z) -9)
4.0ms	(.f64 27 (.f64 a b))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
6×	`cbrt-unprod_binary64`
6×	`prod-exp_binary64`

Counts

4 → 65

Calls

4 calls:

4.0ms	(.f64 (.f64 t z) -9)
4.0ms	(.f64 27 (.f64 a b))
3.0ms	(+.f64 (.f64 x 2) (fma.f64 y (.f64 (.f64 t z) -9) (.f64 27 (*.f64 a b))))
0.0ms	(fma.f64 y (.f64 (.f64 t z) -9) (.f64 27 (.f64 a b)))

simplify130.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

637×	`associate-+l+_binary64`
403×	`*-commutative_binary64`
370×	`fma-neg_binary64`
337×	`exp-prod_binary64`
298×	`cancel-sign-sub-inv_binary64`

Counts

221 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	3656
1	316	3337
2	1008	3335
3	2303	3331
4	4773	3331
5	4972	3331

prune90.0ms (1.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	96	6	102

Error

Counts

102 → 6

Alt Table

Status	Error	Program
✓	2.6b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y (.f64 9 z)) t)) (.f64 (.f64 a 27) b))
	30.5b	(+.f64 (.f64 x 2) (fma.f64 y (.f64 (.f64 t z) -9) (.f64 (sqrt.f64 (.f64 27 (.f64 a b))) (sqrt.f64 (.f64 27 (.f64 a b))))))
✓	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))) (.f64 (.f64 a 27) b))
✓	3.4b	(+.f64 (.f64 x 2) (fma.f64 y (.f64 (.f64 t z) -9) (.f64 27 (*.f64 a b))))
	3.7b	(-.f64 (.f64 x 2) (fma.f64 a (.f64 b -27) (.f64 9 (.f64 y (*.f64 t z)))))
	16.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (*.f64 a 27) (sqrt.f64 b)) (sqrt.f64 b)))

Compiler

Compiled 2290 to 1232 computations (46.2% saved)

regimes1.2s (15.3%)

Accuracy

Total 0.5b remaining (94.6%)

Threshold costs 0.5b (94.6%)

Counts

61 → 2

Compiler

Compiled 21782 to 15876 computations (27.1% saved)

bsearch7.0ms (0.1%)

Steps

Iters	Range		Point
1	4066983.2623518775	34605200.74824929	12459616.618234916

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
9×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	54
1	42	54
2	58	54
3	74	54
4	84	54
5	89	54
6	90	54
7	89	54

end58.0ms (0.7%)

Compiler: Compiled 215 to 150 computations (30.2% saved)

sample2.3s (28.3%)

Algorithm

1×

intervals

Results

517.0ms	8000×	body	128	valid
198.0ms	2999×	body	128	invalid

Compiler

Compiled 227 to 163 computations (28.2% saved)

Details

analyze1.8s (22.5%)

sample262.0ms (3.3%)

simplify71.0ms (0.9%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

series52.0ms (0.7%)

rewrite21.0ms (0.3%)

simplify104.0ms (1.3%)

prune170.0ms (2.1%)

localize11.0ms (0.1%)

series53.0ms (0.7%)

rewrite18.0ms (0.2%)

simplify128.0ms (1.6%)

prune127.0ms (1.6%)

localize15.0ms (0.2%)

series902.0ms (11.3%)

rewrite42.0ms (0.5%)

simplify134.0ms (1.7%)

prune188.0ms (2.4%)

localize11.0ms (0.1%)

series65.0ms (0.8%)

rewrite13.0ms (0.2%)

simplify130.0ms (1.6%)

prune90.0ms (1.1%)

regimes1.2s (15.3%)

bsearch7.0ms (0.1%)

simplify4.0ms (0.1%)

end58.0ms (0.7%)

sample2.3s (28.3%)

Profiling