Details

analyze260.0ms (2.7%)

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
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	25%	25.1%	8
49.9%	25%	25.1%	9
49.9%	25%	25.1%	10
49.9%	25%	25.1%	11
49.9%	12.5%	37.6%	12
49.9%	12.5%	37.6%	13
49.9%	12.5%	37.6%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.5s (15.3%)

Results

965.0ms	8256×	body	128	valid
257.0ms	2115×	body	128	invalid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify129.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-neg_binary64`
522×	`fma-def_binary64`
417×	`neg-sub0_binary64`
408×	`neg-mul-1_binary64`
378×	`prod-exp_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	51	25
3	102	25
4	219	25
5	464	25
6	1225	25
7	2416	25
8	3703	25
9	4714	25
10	4874	25
11	4224	25
12	4608	25
13	4555	25
14	4942	25

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

Compiler

Compiled 77 to 57 computations (26% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.2b	(sqrt.f64 (exp.f64 t))
✓	0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
✓	0.2b	(sqrt.f64 (*.f64 z 2))

series352.0ms (3.7%)

Counts

4 → 64

Calls

4 calls:

310.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
29.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
7.0ms	(sqrt.f64 (*.f64 z 2))
3.0ms	(sqrt.f64 (exp.f64 t))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64`
14×	`associate-r_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 85

Calls

4 calls:

12.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
9.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
8.0ms	(sqrt.f64 (*.f64 z 2))
1.0ms	(sqrt.f64 (exp.f64 t))

simplify241.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
658×	`fma-def_binary64`
291×	`associate-l_binary64`
267×	`associate-r_binary64`
256×	`distribute-rgt-in_binary64`

Counts

149 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	3764
1	498	3311
2	1785	3146
3	4592	3146
4	5135	3146

prune411.0ms (4.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	145	6	151

Error

0.0b

Counts

151 → 6

Alt Table

Status	Error	Program
	12.4b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 z)) 3))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
▶	0.2b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.1b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	30.6b	(.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	19.3b	(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 z)) (-.f64 (.f64 x (.f64 1/4 x)) (.f64 y y))) (+.f64 (*.f64 x 1/2) y)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

Compiler

Compiled 3964 to 2310 computations (41.7% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.1b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
	0.2b	(sqrt.f64 (exp.f64 t))
✓	0.3b	(.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

series1.1s (11%)

Counts

3 → 60

Calls

3 calls:

752.0ms

(*.f64 (*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))

294.0ms

(*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

11.0ms

(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

rewrite72.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`prod-exp_binary64`
19×	`add-cbrt-cube_binary64`
17×	`associate-r_binary64`

Counts

3 → 90

Calls

3 calls:

21.0ms

(*.f64 (*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))

15.0ms

(*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

12.0ms

(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

simplify300.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-neg_binary64`
524×	`cancel-sign-sub-inv_binary64`
408×	`associate-l_binary64`
371×	`associate-r_binary64`
291×	`distribute-rgt-in_binary64`

Counts

150 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	4875
1	622	3816
2	2407	3714
3	4506	3712
4	4994	3712
5	4975	3712

prune527.0ms (5.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	166	8	174

Error

0.0b

Counts

174 → 8

Alt Table

Status	Error	Program
	12.4b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 z)) 3))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.4b	(.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (*.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))
✓	0.2b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.1b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
▶	0.3b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))) (sqrt.f64 z))
	0.6b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) 3))) (sqrt.f64 z))

Compiler

Compiled 4849 to 2798 computations (42.3% saved)

localize37.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))) (sqrt.f64 z))
	0.2b	(sqrt.f64 (exp.f64 t))
✓	0.3b	(.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))
✓	0.5b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

series734.0ms (7.7%)

Counts

3 → 84

Calls

3 calls:

436.0ms

(*.f64 (*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))) (sqrt.f64 z))

284.0ms

(*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))

13.0ms

(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

rewrite103.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-exp-log_binary64`
37×	`prod-exp_binary64`
31×	`add-cbrt-cube_binary64`
19×	`cbrt-unprod_binary64`
19×	`pow1_binary64`

Counts

3 → 85

Calls

3 calls:

42.0ms

(*.f64 (*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))) (sqrt.f64 z))

23.0ms

(*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))

21.0ms

(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

simplify246.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

543×	`cancel-sign-sub-inv_binary64`
477×	`associate-l_binary64`
432×	`associate-r_binary64`
342×	`distribute-rgt-in_binary64`
311×	`fma-neg_binary64`

Counts

169 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	220	5744
1	633	4208
2	2559	4108
3	5014	4108

prune476.0ms (5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	176	8	184

Error

0.0b

Counts

184 → 8

Alt Table

Status	Error	Program
	12.4b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 z)) 3))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.4b	(.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (*.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))
✓	0.2b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.1b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
▶	0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))) (sqrt.f64 z))
	0.6b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) 3))) (sqrt.f64 z))

Compiler

Compiled 5684 to 3582 computations (37% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(sqrt.f64 (exp.f64 t))
	0.2b	(sqrt.f64 (*.f64 z 2))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))
✓	0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))

series350.0ms (3.6%)

Counts

2 → 56

Calls

2 calls:

266.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))
83.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`associate-r_binary64`
11×	`sqrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

2 → 53

Calls

2 calls:

24.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))
16.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))

simplify241.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

453×	`fma-def_binary64`
389×	`unsub-neg_binary64`
345×	`neg-mul-1_binary64`
342×	`neg-sub0_binary64`
273×	`*-commutative_binary64`

Counts

109 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	2720
1	256	2153
2	788	2063
3	1656	2063
4	3325	2063
5	4870	2063
6	4976	2063

prune517.0ms (5.4%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	158	8	166

Error

0.0b

Counts

166 → 8

Alt Table

Status	Error	Program
	12.4b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 z)) 3))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.4b	(.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (*.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))
✓	0.2b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.1b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))) (sqrt.f64 z))
	0.6b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) 3))) (sqrt.f64 z))

Compiler

Compiled 4773 to 3149 computations (34% saved)

regimes1.6s (16.8%)

Accuracy

Total 0.3b remaining (97%)

Threshold costs 0.3b (97%)

Counts

52 → 1

Compiler

Compiled 17576 to 13377 computations (23.9% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	22	25
2	27	25
3	29	25
4	30	25
5	30	25

end289.0ms (3%)

Compiler: Compiled 233 to 177 computations (24% saved)

Details

analyze260.0ms (2.7%)

sample1.5s (15.3%)

simplify129.0ms (1.3%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series352.0ms (3.7%)

rewrite37.0ms (0.4%)

simplify241.0ms (2.5%)

prune411.0ms (4.3%)

localize34.0ms (0.4%)

series1.1s (11%)

rewrite72.0ms (0.8%)

simplify300.0ms (3.1%)

prune527.0ms (5.5%)

localize37.0ms (0.4%)

series734.0ms (7.7%)

rewrite103.0ms (1.1%)

simplify246.0ms (2.6%)

prune476.0ms (5%)

localize32.0ms (0.3%)

series350.0ms (3.6%)

rewrite47.0ms (0.5%)

simplify241.0ms (2.5%)

prune517.0ms (5.4%)

regimes1.6s (16.8%)

simplify6.0ms (0.1%)

end289.0ms (3%)

Profiling