Details

analyze109.0ms (2.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample29.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	64×	body	1024	valid
6.0ms	133×	body	128	valid
4.0ms	37×	body	512	valid
1.0ms	7×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify92.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

prune2.0ms (0%)

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

30.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.4b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	2.7b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite155.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

1304×	`*-un-lft-identity_binary64`
1000×	`times-frac_binary64`
859×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
523×	`add-cube-cbrt_binary64`

Counts

2 → 748

Calls

2 calls:

46.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify837.0ms (21.3%)

Algorithm

1×	egg-herbie

Rules

552×	`fma-neg_binary64`
418×	`distribute-rgt-in_binary64`
361×	`unsub-neg_binary64`
255×	`fma-udef_binary64`
202×	`associate-+r-_binary64`

Counts

772 → 1534

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	521	54026
1	1234	30580
2	2848	22272
3	4495	22270
4	4718	22270

prune652.0ms (16.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1530	4	1534
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1531	4	1535

Error

0.0b

Counts

1535 → 4

Alt Table

Status	Error	Program
▶	30.4b	(log.f64 (/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
	32.5b	(fma.f64 3 x 1)
	62.1b	(+.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (neg.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
	31.1b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))

Compiler

Compiled 29165 to 21565 computations (26.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 x (+.f64 x 1)))
	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	0.0b	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	2.7b	(log.f64 (/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`*-un-lft-identity_binary64`
70×	`exp-prod_binary64`
65×	`times-frac_binary64`
46×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`

Counts

3 → 107

Calls

3 calls:

20.0ms	(log.f64 (/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
8.0ms	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
4.0ms	(exp.f64 (/.f64 x (+.f64 x 1)))

series14.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(log.f64 (/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
3.0ms	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
3.0ms	(exp.f64 (/.f64 x (+.f64 x 1)))

simplify126.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-neg_binary64`
423×	`times-frac_binary64`
373×	`fma-def_binary64`
256×	`cancel-sign-sub-inv_binary64`
214×	`associate-/l/_binary64`

Counts

143 → 264

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	232	2510
1	469	2367
2	1121	2258
3	2740	2242
4	4748	2232
5	5102	2232

prune180.0ms (4.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	396	1	397
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	397	4	401

Error

0.0b

Counts

401 → 4

Alt Table

Status	Error	Program
✓	30.4b	(log.f64 (/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
	32.5b	(fma.f64 3 x 1)
	62.1b	(+.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (neg.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
▶	31.1b	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))

Compiler

Compiled 6852 to 5191 computations (24.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 -1 (pow.f64 x 4))
✓	0.1b	(fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x))
✓	0.2b	(/.f64 1 (*.f64 x x))
✓	10.3b	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 109

Calls

4 calls:

8.0ms	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))
3.0ms	(/.f64 1 (*.f64 x x))
3.0ms	(/.f64 -1 (pow.f64 x 4))
0.0ms	(fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x))

series33.0ms (0.8%)

Counts

4 → 36

Calls

4 calls:

15.0ms	(/.f64 -1 (pow.f64 x 4))
7.0ms	(/.f64 1 (*.f64 x x))
7.0ms	(fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x))
4.0ms	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))

simplify105.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-neg_binary64`
349×	`times-frac_binary64`
282×	`associate-/r*_binary64`
268×	`associate-l_binary64`
265×	`fma-def_binary64`

Counts

145 → 251

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	2367
1	345	2153
2	942	2026
3	4122	1992
4	4939	1992

prune113.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	251	4	255

Error

0.0b

Counts

255 → 4

Alt Table

Status	Error	Program
✓	30.4b	(log.f64 (/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
▶	32.5b	(fma.f64 3 x 1)
	62.1b	(+.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (neg.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
✓	31.1b	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))

Compiler

Compiled 4490 to 3314 computations (26.2% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 x 1)

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 3 x 1)

series5.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(fma.f64 3 x 1)

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

483×	`associate-+l+_binary64`
481×	`associate-*l/_binary64`
464×	`unswap-sqr_binary64`
402×	`distribute-rgt-out_binary64`
368×	`fma-def_binary64`

Counts

22 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	142
1	21	130
2	44	130
3	102	130
4	266	130
5	932	130
6	1828	130
7	2069	130
8	2367	130
9	4354	130
10	5116	130

prune11.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	33	4	37

Error

0.0b

Counts

37 → 4

Alt Table

Status	Error	Program
✓	30.4b	(log.f64 (/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
✓	32.5b	(fma.f64 3 x 1)
	62.1b	(+.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (neg.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
✓	31.1b	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))

Compiler

Compiled 215 to 171 computations (20.5% saved)

regimes248.0ms (6.3%)

Accuracy

Total 0.1b remaining (76.4%)

Threshold costs 0.1b (76.4%)

Compiler

Compiled 6242 to 4642 computations (25.6% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	78
1	39	78
2	49	78
3	58	78
4	65	78
5	68	78
6	69	78
7	66	78

end1.0ms (0%)

Compiler: Compiled 53 to 40 computations (24.5% saved)

sample1.0s (26.2%)

Algorithm

1×

intervals

Results

337.0ms	2028×	body	1024	valid
184.0ms	4215×	body	128	valid
127.0ms	1048×	body	512	valid
41.0ms	488×	body	256	valid
41.0ms	221×	body	2048	valid

Compiler

Compiled 174 to 133 computations (23.6% saved)

Details

analyze109.0ms (2.8%)

sample29.0ms (0.7%)

simplify92.0ms (2.3%)

prune2.0ms (0%)

localize6.0ms (0.2%)

rewrite155.0ms (3.9%)

series7.0ms (0.2%)

simplify837.0ms (21.3%)

prune652.0ms (16.6%)

localize11.0ms (0.3%)

rewrite42.0ms (1.1%)

series14.0ms (0.4%)

simplify126.0ms (3.2%)

prune180.0ms (4.6%)

localize11.0ms (0.3%)

rewrite22.0ms (0.5%)

series33.0ms (0.8%)

simplify105.0ms (2.7%)

prune113.0ms (2.9%)

localize2.0ms (0.1%)

rewrite1.0ms (0%)

series5.0ms (0.1%)

simplify76.0ms (1.9%)

prune11.0ms (0.3%)

regimes248.0ms (6.3%)

bsearch5.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.0s (26.2%)

Profiling