Details

analyze1.4s (10.6%)

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
2.4%	53.7%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample52.0ms (0.4%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
3.0ms	44×	body	128	invalid
2.0ms	34×	body	128	nan

Compiler

Compiled 51 to 37 computations (27.5% saved)

simplify291.0ms (2.2%)

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

Compiler

Compiled 120 to 79 computations (34.2% saved)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series257.0ms (1.9%)

Counts

1 → 72

Calls

1 calls:

257.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

909×	`fma-def_binary64`
694×	`associate--l+_binary64`
549×	`exp-diff_binary64`
441×	`associate-+l-_binary64`
298×	`associate-+l+_binary64`

Counts

82 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	1752
1	183	1708
2	506	1547
3	1783	1535
4	4632	1535
5	5329	1535

prune39.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	41	3	44

Error

0.0b

Counts

44 → 3

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y))))) (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))))
✓	0.0b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 844 to 440 computations (47.9% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
✓	0.1b	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))
✓	0.3b	(*.f64 z (log.f64 t))

series599.0ms (4.5%)

Counts

3 → 128

Calls

3 calls:

230.0ms	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
226.0ms	(*.f64 z (log.f64 t))
142.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

13.0ms	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
7.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))
3.0ms	(*.f64 z (log.f64 t))

simplify111.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

643×	`associate-+r+_binary64`
371×	`associate--l+_binary64`
313×	`fma-neg_binary64`
230×	`cancel-sign-sub-inv_binary64`
159×	`distribute-rgt-in_binary64`

Counts

220 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	4206
1	608	3957
2	2271	3918
3	5140	3918

prune172.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	163	6	169

Error

Counts

169 → 6

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.3b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (log.f64 t)))) (.f64 (-.f64 a 1/2) b))
▶	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 z (log.f64 (cbrt.f64 t))))) (.f64 (-.f64 a 1/2) b))
	1.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t)))) (cbrt.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))))) (cbrt.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))))) (.f64 (-.f64 a 1/2) b))
	31.2b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 (sqrt.f64 (.f64 z (log.f64 t))) (sqrt.f64 (.f64 z (log.f64 t))))) (.f64 (-.f64 a 1/2) b))
	21.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (log.f64 t) (log.f64 t)) (log.f64 t))))) (.f64 (-.f64 a 1/2) b))

Compiler

Compiled 4504 to 1629 computations (63.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (log.f64 (cbrt.f64 t)))
✓	0.2b	(.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))
✓	0.3b	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.f64 t))))
✓	0.6b	(cbrt.f64 t)

series3.9s (29.1%)

Counts

4 → 84

Calls

4 calls:

1.4s	(*.f64 z (log.f64 (cbrt.f64 t)))
1.3s	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.f64 t))))
1.2s	(.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))
31.0ms	(cbrt.f64 t)

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`log-prod_binary64`
60×	`distribute-lft-in_binary64`
60×	`distribute-rgt-in_binary64`
39×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`

Counts

4 → 142

Calls

4 calls:

8.0ms	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.f64 t))))
5.0ms	(.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))
4.0ms	(*.f64 z (log.f64 (cbrt.f64 t)))
1.0ms	(cbrt.f64 t)

simplify123.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
475×	`fma-neg_binary64`
441×	`*-commutative_binary64`
440×	`cancel-sign-sub-inv_binary64`
306×	`distribute-rgt-in_binary64`

Counts

226 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3066
1	407	2725
2	1353	2500
3	3821	2492
4	4971	2492

prune349.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	246	2	248
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	249	5	254

Error

Counts

254 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 (.f64 z 1/3) (log.f64 t)))) (*.f64 (-.f64 a 1/2) b))
	31.2b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 (sqrt.f64 (.f64 z (log.f64 t))) (sqrt.f64 (.f64 z (log.f64 t))))) (.f64 (-.f64 a 1/2) b))
✓	0.0b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.2b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (+.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (log.f64 t) 2/3) (cbrt.f64 z))) (.f64 z (log.f64 (cbrt.f64 t))))) (.f64 (-.f64 a 1/2) b))
	21.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (log.f64 t) (log.f64 t)) (log.f64 t))))) (.f64 (-.f64 a 1/2) b))

Compiler

Compiled 7973 to 3245 computations (59.3% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 (.f64 z 1/3) (log.f64 t)))
✓	0.3b	(*.f64 z 1/3)
✓	0.4b	(.f64 (.f64 z 1/3) (log.f64 t))
	0.6b	(cbrt.f64 t)

series1.6s (11.9%)

Counts

3 → 60

Calls

3 calls:

1.4s	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 (.f64 z 1/3) (log.f64 t)))
224.0ms	(.f64 (.f64 z 1/3) (log.f64 t))
2.0ms	(*.f64 z 1/3)

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64`
30×	`distribute-lft-in_binary64`
30×	`distribute-rgt-in_binary64`
24×	`associate-+l+_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

3 → 91

Calls

3 calls:

7.0ms	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 (.f64 z 1/3) (log.f64 t)))
5.0ms	(.f64 (.f64 z 1/3) (log.f64 t))
3.0ms	(*.f64 z 1/3)

simplify115.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-def_binary64`
286×	`associate-l_binary64`
256×	`log-prod_binary64`
252×	`associate-r_binary64`
230×	`cancel-sign-sub-inv_binary64`

Counts

151 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2207
1	425	1837
2	1573	1403
3	4083	1403
4	4862	1403
5	4935	1403

prune249.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	179	5	184

Error

Counts

184 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 (.f64 z 1/3) (log.f64 t)))) (*.f64 (-.f64 a 1/2) b))
	31.2b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 (sqrt.f64 (.f64 z (log.f64 t))) (sqrt.f64 (.f64 z (log.f64 t))))) (.f64 (-.f64 a 1/2) b))
✓	0.0b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.2b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (+.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (log.f64 t) 2/3) (cbrt.f64 z))) (.f64 z (log.f64 (cbrt.f64 t))))) (.f64 (-.f64 a 1/2) b))
	21.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (log.f64 t) (log.f64 t)) (log.f64 t))))) (.f64 (-.f64 a 1/2) b))

Compiler

Compiled 5784 to 2762 computations (52.2% saved)

regimes2.4s (18.3%)

Accuracy

Total 0.0b remaining (61.4%)

Threshold costs 0.0b (61.4%)

Counts

101 → 1

Compiler

Compiled 32517 to 22002 computations (32.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	20
1	23	20
2	28	20
3	30	20
4	31	20
5	29	20

end7.0ms (0.1%)

Remove: (sort x y)
Compiler: Compiled 60 to 42 computations (30% saved)

sample1.4s (10.4%)

Algorithm

1×

intervals

Results

620.0ms	7995×	body	128	valid
100.0ms	1237×	body	128	invalid
74.0ms	1130×	body	128	nan
1.0ms	4×	body	512	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 200 to 134 computations (33% saved)

Details

analyze1.4s (10.6%)

sample52.0ms (0.4%)

simplify291.0ms (2.2%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series257.0ms (1.9%)

rewrite1.0ms (0%)

simplify86.0ms (0.7%)

prune39.0ms (0.3%)

localize12.0ms (0.1%)

series599.0ms (4.5%)

rewrite30.0ms (0.2%)

simplify111.0ms (0.8%)

prune172.0ms (1.3%)

localize16.0ms (0.1%)

series3.9s (29.1%)

rewrite29.0ms (0.2%)

simplify123.0ms (0.9%)

prune349.0ms (2.6%)

localize20.0ms (0.2%)

series1.6s (11.9%)

rewrite22.0ms (0.2%)

simplify115.0ms (0.9%)

prune249.0ms (1.9%)

regimes2.4s (18.3%)

simplify4.0ms (0%)

end7.0ms (0.1%)

sample1.4s (10.4%)

Profiling