Details

analyze116.0ms (2.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample45.0ms (1%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify100.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

750×	`div-sub_binary64`
748×	`fma-neg_binary64`
599×	`fma-def_binary64`
502×	`associate-/l*_binary64`
423×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	37	29
2	82	27
3	201	27
4	526	27
5	991	25
6	1614	25
7	3273	25
8	3653	25
9	4694	25
10	4942	25

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 77 to 58 computations (24.7% saved)

localize21.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
✓	0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
✓	0.2b	(.f64 3 (.f64 v v))

rewrite68.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
26×	`associate-l_binary64`
23×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`

Counts

3 → 126

Calls

3 calls:

21.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
18.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
9.0ms	(.f64 3 (.f64 v v))

series73.0ms (1.6%)

Counts

3 → 36

Calls

3 calls:

31.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
22.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
19.0ms	(.f64 3 (.f64 v v))

simplify212.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

595×	`cancel-sign-sub-inv_binary64`
416×	`times-frac_binary64`
374×	`associate-l_binary64`
359×	`associate-r_binary64`
248×	`fma-neg_binary64`

Counts

162 → 275

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	306	4890
1	862	4558
2	3099	4490
3	4935	4490

prune403.0ms (9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	273	2	275
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	273	3	276

Error

Counts

276 → 3

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
▶	0.0b	(.f64 (cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))) 3) (.f64 (sqrt.f64 2) 1/32))) (-.f64 1 (.f64 v v)))

Compiler

Compiled 6821 to 5104 computations (25.2% saved)

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))) 3) (.f64 (sqrt.f64 2) 1/32))
✓	0.0b	(pow.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))) 3)
✓	0.0b	(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))) 3) (.f64 (sqrt.f64 2) 1/32)))
	0.2b	(.f64 3 (.f64 v v))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-l_binary64`
17×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 88

Calls

3 calls:

16.0ms

(*.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v)))) 3) (*.f64 (sqrt.f64 2) 1/32))

11.0ms

(cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v)))) 3) (*.f64 (sqrt.f64 2) 1/32)))

6.0ms

(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v)))) 3)

series102.0ms (2.3%)

Counts

3 → 36

Calls

3 calls:

50.0ms

(cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v)))) 3) (*.f64 (sqrt.f64 2) 1/32)))

34.0ms

(*.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v)))) 3) (*.f64 (sqrt.f64 2) 1/32))

18.0ms

(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v)))) 3)

simplify221.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-neg_binary64`
428×	`times-frac_binary64`
305×	`associate-r_binary64`
296×	`associate-l_binary64`
260×	`unswap-sqr_binary64`

Counts

124 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	3473
1	774	3304
2	2796	3230
3	4529	3228
4	5074	3228

prune423.0ms (9.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	289	3	292

Error

Counts

292 → 3

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
✓	0.0b	(.f64 (cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))) 3) (.f64 (sqrt.f64 2) 1/32))) (-.f64 1 (.f64 v v)))

Compiler

Compiled 6830 to 5323 computations (22.1% saved)

localize26.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))
	0.2b	(.f64 3 (.f64 v v))
✓	1.0b	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))))

rewrite96.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`sqrt-div_binary64`
59×	`add-sqr-sqrt_binary64`
58×	`frac-times_binary64`
38×	`associate-*r/_binary64`
37×	`sqrt-prod_binary64`

Counts

2 → 135

Calls

2 calls:

37.0ms

(*.f64 (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v)))

31.0ms

(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))))

series52.0ms (1.2%)

Counts

2 → 24

Calls

2 calls:

32.0ms

(*.f64 (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v)))

20.0ms

(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))))

simplify300.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

589×	`cancel-sign-sub-inv_binary64`
580×	`associate-l_binary64`
549×	`associate-r_binary64`
324×	`*-commutative_binary64`
277×	`times-frac_binary64`

Counts

159 → 309

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	6294
1	1002	5745
2	3546	5668
3	5253	5668

prune461.0ms (10.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	415	0	415
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	415	3	418

Error

Counts

418 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) 4)) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
✓	0.0b	(.f64 (cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))) 3) (.f64 (sqrt.f64 2) 1/32))) (-.f64 1 (.f64 v v)))

Compiler

Compiled 10453 to 8079 computations (22.7% saved)

regimes166.0ms (3.7%)

Accuracy

Total 0.0b remaining (75.7%)

Threshold costs 0.0b (75.7%)

Compiler

Compiled 1945 to 1548 computations (20.4% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`distribute-rgt-neg-in_binary64`
3×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	42	29
3	48	29
4	51	29
5	49	29

end3.0ms (0.1%)

Compiler: Compiled 20 to 15 computations (25% saved)

sample1.5s (33.9%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.0ms	7×	body	128	nan

Compiler

Compiled 112 to 87 computations (22.3% saved)

Details

analyze116.0ms (2.6%)

sample45.0ms (1%)

simplify100.0ms (2.2%)

prune6.0ms (0.1%)

localize21.0ms (0.5%)

rewrite68.0ms (1.5%)

series73.0ms (1.6%)

simplify212.0ms (4.7%)

prune403.0ms (9%)

localize25.0ms (0.6%)

rewrite43.0ms (1%)

series102.0ms (2.3%)

simplify221.0ms (4.9%)

prune423.0ms (9.4%)

localize26.0ms (0.6%)

rewrite96.0ms (2.1%)

series52.0ms (1.2%)

simplify300.0ms (6.7%)

prune461.0ms (10.3%)

regimes166.0ms (3.7%)

simplify7.0ms (0.2%)

end3.0ms (0.1%)

sample1.5s (33.9%)

Profiling