Details

analyze1.2s (12.7%)

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%	74.8%	25.2%	5
0%	74.8%	25.2%	6
0%	74.8%	25.2%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	62.3%	37.7%	10
0%	56.1%	43.9%	11
0%	56.1%	43.9%	12
1.6%	54.5%	43.9%	13
2.3%	53.7%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample1.9s (19.7%)

Symmetry

(sort x y)

Results

1.4s	8252×	body	128	valid
373.0ms	2339×	body	128	invalid
1.0ms	2×	body	1024	valid
1.0ms	1×	body	2048	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify285.0ms (3%)

Algorithm

1×	egg-herbie

Rules

5327×	`fma-def_binary64`
866×	`fma-neg_binary64`
705×	`sub-neg_binary64`
654×	`unsub-neg_binary64`
445×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	35	22
2	101	22
3	269	21
4	805	20
5	2079	20
6	2787	20
7	3848	20
8	4164	20
9	4306	20
10	4090	20
11	4094	20
12	4190	20
13	4488	20
14	4581	20
15	4587	20
16	4587	20
17	4593	20
18	4599	20
19	4599	20
20	4617	20
21	4601	20
22	4601	20
23	9364	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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))

Compiler

Compiled 120 to 79 computations (34.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (log.f64 t))
✓	0.0b	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))
✓	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

series221.0ms (2.4%)

Counts

3 → 128

Calls

3 calls:

189.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
20.0ms	(-.f64 1 (log.f64 t))
11.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
8×	`pow1_binary64`

Counts

3 → 59

Calls

3 calls:

4.0ms	(-.f64 1 (log.f64 t))
0.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
0.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

simplify124.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-neg_binary64`
593×	`exp-sum_binary64`
523×	`fma-def_binary64`
300×	`associate-+l+_binary64`
285×	`sub-neg_binary64`

Counts

187 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	2997
1	318	2754
2	918	2521
3	3268	2521
4	4379	2521
5	5221	2521

prune122.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	107	5	112

Error

0.0b

Counts

112 → 5

Alt Table

Status	Error	Program
	17.2b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(fma.f64 z (-.f64 (-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2)) (log.f64 (cbrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	30.9b	(fma.f64 z (+.f64 1 (*.f64 (neg.f64 (sqrt.f64 (log.f64 t))) (sqrt.f64 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
▶	0.1b	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 2385 to 1168 computations (51% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.0b	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))
✓	0.2b	(*.f64 z (log.f64 t))
✓	0.3b	(-.f64 z (*.f64 z (log.f64 t)))

series565.0ms (6%)

Counts

3 → 100

Calls

3 calls:

206.0ms	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
181.0ms	(-.f64 z (*.f64 z (log.f64 t)))
178.0ms	(*.f64 z (log.f64 t))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`log-prod_binary64`
10×	`add-log-exp_binary64`

Counts

3 → 78

Calls

3 calls:

4.0ms	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
3.0ms	(*.f64 z (log.f64 t))
3.0ms	(-.f64 z (*.f64 z (log.f64 t)))

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

504×	`distribute-rgt-in_binary64`
469×	`distribute-lft-in_binary64`
303×	`associate--l+_binary64`
285×	`fma-neg_binary64`
210×	`cancel-sign-sub-inv_binary64`

Counts

178 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	3072
1	428	2891
2	1358	2795
3	4579	2793
4	4960	2793

prune181.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	174	4	178
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	178	5	183

Error

Counts

183 → 5

Alt Table

Status	Error	Program
	17.2b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
▶	0.1b	(.f64 1 (+.f64 (.f64 (-.f64 1 (log.f64 t)) z) (fma.f64 b (-.f64 a 1/2) (+.f64 y x))))
	30.9b	(+.f64 (-.f64 z (.f64 (.f64 z (sqrt.f64 (log.f64 t))) (sqrt.f64 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 3877 to 1517 computations (60.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (-.f64 1 (log.f64 t)) z) (fma.f64 b (-.f64 a 1/2) (+.f64 y x)))
	0.0b	(-.f64 1 (log.f64 t))
✓	0.0b	(fma.f64 b (-.f64 a 1/2) (+.f64 y x))
✓	0.2b	(*.f64 (-.f64 1 (log.f64 t)) z)

series383.0ms (4.1%)

Counts

3 → 128

Calls

3 calls:

191.0ms	(*.f64 (-.f64 1 (log.f64 t)) z)
181.0ms	(+.f64 (*.f64 (-.f64 1 (log.f64 t)) z) (fma.f64 b (-.f64 a 1/2) (+.f64 y x)))
11.0ms	(fma.f64 b (-.f64 a 1/2) (+.f64 y x))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
7×	`associate-l_binary64`
6×	`pow1_binary64`
5×	`add-cube-cbrt_binary64`

Counts

3 → 51

Calls

3 calls:

7.0ms	(+.f64 (*.f64 (-.f64 1 (log.f64 t)) z) (fma.f64 b (-.f64 a 1/2) (+.f64 y x)))
5.0ms	(*.f64 (-.f64 1 (log.f64 t)) z)
0.0ms	(fma.f64 b (-.f64 a 1/2) (+.f64 y x))

simplify95.0ms (1%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-neg_binary64`
492×	`distribute-rgt-in_binary64`
467×	`distribute-lft-in_binary64`
465×	`fma-def_binary64`
375×	`associate-l_binary64`

Counts

179 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	3045
1	364	2891
2	1040	2776
3	4612	2775
4	5205	2775

prune186.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	158	4	162

Error

Counts

162 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(*.f64 1 (+.f64 (fma.f64 (-.f64 1 (log.f64 t)) z x) (fma.f64 b -1/2 (fma.f64 a b y))))
	30.9b	(+.f64 (-.f64 z (.f64 (.f64 z (sqrt.f64 (log.f64 t))) (sqrt.f64 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 3954 to 2122 computations (46.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))
✓	0.2b	(*.f64 (log.f64 (sqrt.f64 t)) z)
✓	0.3b	(-.f64 z (*.f64 (log.f64 (sqrt.f64 t)) z))
✓	0.3b	(-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z))

series590.0ms (6.3%)

Counts

3 → 24

Calls

3 calls:

204.0ms	(-.f64 z (*.f64 (log.f64 (sqrt.f64 t)) z))
197.0ms	(-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z))
189.0ms	(*.f64 (log.f64 (sqrt.f64 t)) z)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`
10×	`prod-diff_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 73

Calls

3 calls:

5.0ms	(-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z))
3.0ms	(*.f64 (log.f64 (sqrt.f64 t)) z)
2.0ms	(-.f64 z (*.f64 (log.f64 (sqrt.f64 t)) z))

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-neg_binary64`
543×	`cancel-sign-sub-inv_binary64`
453×	`associate-l_binary64`
394×	`associate-r_binary64`
334×	`fma-def_binary64`

Counts

97 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1521
1	245	1297
2	631	1229
3	2700	1222
4	4898	1222
5	4878	1222

prune149.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	161	4	165

Error

Counts

165 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(*.f64 1 (+.f64 (fma.f64 (-.f64 1 (log.f64 t)) z x) (fma.f64 b -1/2 (fma.f64 a b y))))
	30.9b	(+.f64 (-.f64 z (.f64 (.f64 z (sqrt.f64 (log.f64 t))) (sqrt.f64 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 4634 to 1324 computations (71.4% saved)

regimes3.1s (32.6%)

Accuracy

Total 0.0b remaining (69.4%)

Threshold costs 0.0b (69.4%)

Counts

175 → 1

Compiler

Compiled 52970 to 36732 computations (30.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`+-rgt-identity_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	25
1	28	25
2	29	25
3	27	25

end86.0ms (0.9%)

Remove: (sort x y)
Compiler: Compiled 199 to 135 computations (32.2% saved)

Details

analyze1.2s (12.7%)

sample1.9s (19.7%)

simplify285.0ms (3%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series221.0ms (2.4%)

rewrite7.0ms (0.1%)

simplify124.0ms (1.3%)

prune122.0ms (1.3%)

localize11.0ms (0.1%)

series565.0ms (6%)

rewrite13.0ms (0.1%)

simplify102.0ms (1.1%)

prune181.0ms (1.9%)

localize12.0ms (0.1%)

series383.0ms (4.1%)

rewrite15.0ms (0.2%)

simplify95.0ms (1%)

prune186.0ms (2%)

localize14.0ms (0.1%)

series590.0ms (6.3%)

rewrite16.0ms (0.2%)

simplify91.0ms (1%)

prune149.0ms (1.6%)

regimes3.1s (32.6%)

simplify2.0ms (0%)

end86.0ms (0.9%)

Profiling