Details

analyze841.0ms (13.5%)

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
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	81.1%	0.2%	9
21.8%	78%	0.2%	10
25%	74.9%	0.2%	11
34.7%	64.9%	0.4%	12
47.2%	51.9%	0.9%	13
49%	49.2%	1.8%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample37.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
2.0ms	58×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`associate-/l*_binary64`
9×	`associate-/r/_binary64` `associate-*r/_binary64`
7×	`*-commutative_binary64`
6×	`associate-/r*_binary64`
4×	`times-frac_binary64` `associate-/l/_binary64` `associate-*l/_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	38	10
3	63	10
4	69	10
5	68	10
6	68	10

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

11.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	11.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

10.9b

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`prod-exp_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `cbrt-unprod_binary64`
1×	`pow1_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `frac-2neg_binary64` `times-frac_binary64` `-un-lft-identity_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/l_binary64` `associate-/r*_binary64`

Counts

1 → 21

Calls

1 calls:

5.0ms

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

Compiler

Compiled 295 to 77 computations (73.9% saved)

series43.0ms (0.7%)

Error

11.2b

Counts

1 → 12

Calls

1 calls:

42.0ms

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

Compiler

Compiled 275 to 175 computations (36.4% saved)

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-/r*_binary64`
393×	`associate-l_binary64`
381×	`associate-*l/_binary64`
297×	`associate-*r/_binary64`
271×	`associate-r_binary64`

Counts

33 → 11

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	475
1	155	370
2	779	370
3	3457	370
4	3762	370
5	4079	370
6	4763	370
7	5076	370

prune11.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	8	3	11
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	8	4	12

Error

0.1b

Counts

12 → 4

Alt Table

Status	Error	Program
✓	11.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	9.1b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	8.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	31.7b	(cbrt.f64 (pow.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2)) 3))

Compiler

Compiled 120 to 73 computations (39.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

4.6b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
6.2b	(/.f64 b1 (/.f64 a2 b2))

rewrite301.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

471×	`times-frac_binary64`
229×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
57×	`associate-/r*_binary64`
22×	`div-inv_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`

Counts

2 → 266

Calls

2 calls:

13.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
6.0ms	(/.f64 b1 (/.f64 a2 b2))

Compiler

Compiled 5189 to 1256 computations (75.8% saved)

series65.0ms (1%)

Error

0.1b

Counts

2 → 21

Calls

2 calls:

42.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
22.0ms	(/.f64 b1 (/.f64 a2 b2))

Compiler

Compiled 480 to 303 computations (36.9% saved)

simplify316.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

563×	`associate-/r/_binary64`
414×	`associate-/l/_binary64`
381×	`associate-*l/_binary64`
332×	`associate-*r/_binary64`
323×	`*-commutative_binary64`

Counts

287 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	6523
1	986	6310
2	3704	6307
3	3637	6307
4	4538	6307
5	4664	6307
6	4977	6307

prune174.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	215	8	223

Error

Counts

223 → 8

Alt Table

Status	Error	Program
✓	11.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	9.1b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	8.7b	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))
▶	8.7b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
	11.7b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	8.9b	(/.f64 1 (/.f64 b1 (*.f64 a1 (/.f64 a2 b2))))
	8.8b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	26.1b	(*.f64 (sqrt.f64 (/.f64 a2 b2)) (/.f64 a1 (/.f64 b1 (sqrt.f64 (/.f64 a2 b2)))))

Compiler

Compiled 3181 to 684 computations (78.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

4.6b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
6.4b	(*.f64 b1 (/.f64 b2 a2))

rewrite57.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`times-frac_binary64` `associate-r_binary64`
12×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
5×	`div-exp_binary64` `cbrt-undiv_binary64`

Counts

2 → 56

Calls

2 calls:

7.0ms	(*.f64 b1 (/.f64 b2 a2))
6.0ms	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))

Compiler

Compiled 731 to 209 computations (71.4% saved)

series64.0ms (1%)

Error

Counts

2 → 21

Calls

2 calls:

40.0ms	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
22.0ms	(*.f64 b1 (/.f64 b2 a2))

Compiler

Compiled 480 to 303 computations (36.9% saved)

simplify107.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

957×	`times-frac_binary64`
528×	`associate-/l*_binary64`
381×	`associate-/r*_binary64`
378×	`associate-*l/_binary64`
356×	`associate-*r/_binary64`

Counts

77 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	936
1	252	807
2	944	804
3	4089	804
4	4436	804
5	4880	804
6	4958	804

prune22.0ms (0.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	48	8	56

Error

Counts

56 → 8

Alt Table

Status	Error	Program
✓	11.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	9.1b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	8.7b	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))
✓	8.7b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
	11.7b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	8.9b	(/.f64 1 (/.f64 b1 (*.f64 a1 (/.f64 a2 b2))))
	8.8b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	26.1b	(*.f64 (sqrt.f64 (/.f64 a2 b2)) (/.f64 a1 (/.f64 b1 (sqrt.f64 (/.f64 a2 b2)))))

Compiler

Compiled 471 to 204 computations (56.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

4.0b	(*.f64 a1 (/.f64 a2 b2))
5.2b	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))

rewrite83.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

46×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
22×	`prod-exp_binary64` `add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

2 → 77

Calls

2 calls:

10.0ms	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))
7.0ms	(*.f64 a1 (/.f64 a2 b2))

Compiler

Compiled 1185 to 487 computations (58.9% saved)

series68.0ms (1.1%)

Error

Counts

2 → 21

Calls

2 calls:

41.0ms	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))
25.0ms	(*.f64 a1 (/.f64 a2 b2))

Compiler

Compiled 518 to 341 computations (34.2% saved)

simplify111.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

465×	`associate-/l*_binary64`
339×	`times-frac_binary64`
314×	`*-commutative_binary64`
242×	`unsub-neg_binary64`
231×	`sub-neg_binary64`

Counts

98 → 61

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	134	1236
1	312	1044
2	1164	1044
3	2873	1044
4	3606	1044
5	4719	1044
6	4969	1044

prune33.0ms (0.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	61	8	69

Error

Counts

69 → 8

Alt Table

Status	Error	Program
	11.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	9.1b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	8.7b	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))
	8.7b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
	11.7b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	8.9b	(/.f64 1 (/.f64 b1 (*.f64 a1 (/.f64 a2 b2))))
	8.8b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	26.1b	(*.f64 (sqrt.f64 (/.f64 a2 b2)) (/.f64 a1 (/.f64 b1 (sqrt.f64 (/.f64 a2 b2)))))

Compiler

Compiled 591 to 258 computations (56.3% saved)

regimes2.5s (40.5%)

Accuracy

Total 2.6b remaining (99.3%)

Threshold costs 0b (0%)

Compiler

Compiled 25430 to 14353 computations (43.6% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	122
1	36	122
2	36	122

end36.0ms (0.6%)

Compiler: Compiled 430 to 150 computations (65.1% saved)

sample1.2s (18.9%)

Algorithm

1×

intervals

Results

261.0ms	8000×	body	128	valid
56.0ms	1797×	body	128	invalid

Compiler

Compiled 200 to 104 computations (48% saved)

Details

analyze841.0ms (13.5%)

sample37.0ms (0.6%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite28.0ms (0.5%)

series43.0ms (0.7%)

simplify89.0ms (1.4%)

prune11.0ms (0.2%)

localize5.0ms (0.1%)

rewrite301.0ms (4.8%)

series65.0ms (1%)

simplify316.0ms (5.1%)

prune174.0ms (2.8%)

localize6.0ms (0.1%)

rewrite57.0ms (0.9%)

series64.0ms (1%)

simplify107.0ms (1.7%)

prune22.0ms (0.4%)

localize7.0ms (0.1%)

rewrite83.0ms (1.3%)

series68.0ms (1.1%)

simplify111.0ms (1.8%)

prune33.0ms (0.5%)

regimes2.5s (40.5%)

bsearch6.0ms (0.1%)

simplify5.0ms (0.1%)

end36.0ms (0.6%)

sample1.2s (18.9%)

Profiling