Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.0s (56.9%)

Infinites

100% of outputs are infinite.

Results

816.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify200.0ms (10.9%)

Algorithm

1×	egg-herbie

Rules

1115×	`distribute-rgt-neg-in_binary64`
788×	`distribute-rgt-out--_binary64`
692×	`unsub-neg_binary64`
492×	`fma-neg_binary64`
461×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	34	20
4	50	20
5	73	20
6	113	20
7	247	20
8	452	20
9	742	20
10	1560	20
11	2338	20
12	2392	20
13	2628	20
14	2776	20
15	2774	20
16	2851	20
17	3110	20
18	3673	20
19	4665	20
20	4910	20
21	4952	20
22	4963	20
23	4960	20
24	6208	20

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize8.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 x x))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
✓	0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

series24.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
4.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
2.0ms	(-.f64 1 (*.f64 x x))

rewrite48.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`*-un-lft-identity_binary64`
59×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
26×	`sqrt-prod_binary64`

Counts

4 → 141

Calls

4 calls:

15.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
15.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
2.0ms	(-.f64 1 (*.f64 x x))

simplify109.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

528×	`fma-def_binary64`
515×	`associate-/r*_binary64`
364×	`fma-neg_binary64`
289×	`cancel-sign-sub-inv_binary64`
279×	`times-frac_binary64`

Counts

189 → 238

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	3550
1	587	3366
2	1638	3325
3	4360	3290
4	4888	3290

prune152.0ms (8.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	237	2	239

Error

Counts

239 → 2

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 4938 to 3332 computations (32.5% saved)

localize8.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 1 (*.f64 x x))
✓	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

series8.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`sum-log_binary64`
3×	`associate-+r+_binary64`
3×	`distribute-neg-in_binary64`

Counts

1 → 27

Calls

1 calls:

4.0ms

(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

simplify67.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

466×	`fma-neg_binary64`
291×	`neg-mul-1_binary64`
290×	`sub-neg_binary64`
288×	`neg-sub0_binary64`
268×	`fma-def_binary64`

Counts

39 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	835
1	295	770
2	808	751
3	2584	743
4	4479	743
5	4993	743

prune53.0ms (2.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	92	2	94

Error

Counts

94 → 2

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 1649 to 1005 computations (39.1% saved)

regimes57.0ms (3.1%)

Accuracy

Total 0.0b remaining (93%)

Threshold costs 0.0b (93%)

Counts

19 → 1

Compiler

Compiled 667 to 508 computations (23.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	28	20
4	30	20
5	29	20

end45.0ms (2.4%)

Compiler: Compiled 54 to 39 computations (27.8% saved)

Details

analyze4.0ms (0.2%)

sample1.0s (56.9%)

simplify200.0ms (10.9%)

prune2.0ms (0.1%)

localize8.0ms (0.5%)

series24.0ms (1.3%)

rewrite48.0ms (2.6%)

simplify109.0ms (5.9%)

prune152.0ms (8.3%)

localize8.0ms (0.5%)

series8.0ms (0.4%)

rewrite6.0ms (0.3%)

simplify67.0ms (3.6%)

prune53.0ms (2.9%)

regimes57.0ms (3.1%)

simplify3.0ms (0.1%)

end45.0ms (2.4%)

Profiling