Details

analyze669.0ms (8.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample138.0ms (1.7%)

Algorithm

1×

intervals

Results

68.0ms	79×	body	1024	valid
24.0ms	35×	body	2048	valid
17.0ms	37×	body	512	valid
8.0ms	76×	body	128	valid
7.0ms	28×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
3	13	9

prune5.0ms (0.1%)

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

45.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	1.4b	(+.f64 x (hypot.f64 1 x))
✓	3.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series21.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

10.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
5.0ms	(+.f64 x (hypot.f64 1 x))
5.0ms	(hypot.f64 1 x)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64`

Counts

3 → 44

Calls

3 calls:

5.0ms	(+.f64 x (hypot.f64 1 x))
5.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
1.0ms	(hypot.f64 1 x)

simplify138.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
469×	`cancel-sign-sub-inv_binary64`
426×	`associate-/r*_binary64`
376×	`fma-def_binary64`
361×	`sub-neg_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1089
1	394	1025
2	959	1013
3	2675	1013
4	4999	1013
5	5338	1013

prune112.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	109	5	114

Error

Counts

114 → 5

Alt Table

Status	Error	Program
	46.0b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	47.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
	47.9b	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
✓	45.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	31.2b	(fma.f64 (pow.f64 x 3) -1/6 x)

Compiler

Compiled 1633 to 1232 computations (24.6% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/6 x)

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(fma.f64 (pow.f64 x 3) -1/6 x)

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:

1.0ms

(fma.f64 (pow.f64 x 3) -1/6 x)

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

435×	`neg-mul-1_binary64`
394×	`associate-l_binary64`
372×	`associate-r_binary64`
317×	`distribute-rgt-out_binary64`
261×	`exp-prod_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	232
1	35	197
2	87	197
3	323	197
4	1659	197
5	4536	197
6	5201	197

prune19.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	16	5	21

Error

Counts

21 → 5

Alt Table

Status	Error	Program
▶	46.0b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	47.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
	47.9b	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
✓	45.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	31.2b	(fma.f64 (pow.f64 x 3) -1/6 x)

Compiler

Compiled 254 to 193 computations (24% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))
✓	0.3b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	1.4b	(+.f64 x (hypot.f64 1 x))
	3.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series35.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

27.0ms	(log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))
8.0ms	(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

1.0ms	(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
1.0ms	(log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))

simplify102.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

676×	`times-frac_binary64`
526×	`associate-/r*_binary64`
403×	`distribute-rgt-in_binary64`
386×	`distribute-lft-in_binary64`
379×	`fma-def_binary64`

Counts

46 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	1231
1	423	1137
2	1373	1129
3	4575	1127
4	5352	1127

prune170.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	154	5	159

Error

Counts

159 → 5

Alt Table

Status	Error	Program
✓	46.0b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
▶	47.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
	47.9b	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
✓	45.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	31.2b	(fma.f64 (pow.f64 x 3) -1/6 x)

Compiler

Compiled 3006 to 2413 computations (19.7% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1/16 (pow.f64 x 5))
✓	0.2b	(/.f64 1/8 (pow.f64 x 3))
✓	11.2b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
✓	17.9b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

series26.0ms (0.3%)

Counts

4 → 24

Calls

4 calls:

8.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
7.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
6.0ms	(/.f64 1/16 (pow.f64 x 5))
5.0ms	(/.f64 1/8 (pow.f64 x 3))

rewrite277.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

487×	`*-un-lft-identity_binary64`
369×	`times-frac_binary64`
245×	`add-sqr-sqrt_binary64`
219×	`add-cube-cbrt_binary64`
200×	`prod-diff_binary64`

Counts

4 → 412

Calls

4 calls:

70.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
69.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
10.0ms	(/.f64 1/16 (pow.f64 x 5))
7.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify669.0ms (8.4%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-neg_binary64`
326×	`unswap-sqr_binary64`
251×	`distribute-rgt-neg-in_binary64`
209×	`associate-l_binary64`
203×	`associate-r_binary64`

Counts

436 → 443

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	431	17011
1	810	13622
2	2988	10097
3	4811	10097
4	4893	10097

prune851.0ms (10.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	443	0	443
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	443	5	448

Error

Counts

448 → 5

Alt Table

Status	Error	Program
✓	46.0b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	47.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
	47.9b	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
✓	45.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	31.2b	(fma.f64 (pow.f64 x 3) -1/6 x)

Compiler

Compiled 17693 to 14430 computations (18.4% saved)

regimes172.0ms (2.2%)

Accuracy

Total 0.1b remaining (72.9%)

Threshold costs 0.1b (72.9%)

Counts

20 → 3

Compiler

Compiled 690 to 556 computations (19.4% saved)

bsearch60.0ms (0.8%)

Steps

Iters	Range		Point
9	3.946335256266931e-7	1.0923430863916905	0.0010396709414883317
10	-503.8715746736808	-5.4837533249068885e-8	-1.0229856676033233

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	64
1	48	64
2	62	64
3	88	64
4	103	64
5	110	64
6	112	64
7	107	64

end2.0ms (0%)

Compiler: Compiled 44 to 35 computations (20.5% saved)

sample4.3s (54.4%)

Algorithm

1×

intervals

Results

2.0s	2554×	body	1024	valid
847.0ms	1182×	body	2048	valid
552.0ms	1217×	body	512	valid
242.0ms	2337×	body	128	valid
174.0ms	681×	body	256	valid
29.0ms	29×	body	4096	valid

Compiler

Compiled 116 to 91 computations (21.6% saved)

Details

analyze669.0ms (8.4%)

sample138.0ms (1.7%)

simplify13.0ms (0.2%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

series21.0ms (0.3%)

rewrite13.0ms (0.2%)

simplify138.0ms (1.7%)

prune112.0ms (1.4%)

localize7.0ms (0.1%)

series6.0ms (0.1%)

rewrite1.0ms (0%)

simplify73.0ms (0.9%)

prune19.0ms (0.2%)

localize18.0ms (0.2%)

series35.0ms (0.4%)

rewrite3.0ms (0%)

simplify102.0ms (1.3%)

prune170.0ms (2.1%)

localize22.0ms (0.3%)

series26.0ms (0.3%)

rewrite277.0ms (3.5%)

simplify669.0ms (8.4%)

prune851.0ms (10.7%)

regimes172.0ms (2.2%)

bsearch60.0ms (0.8%)

simplify9.0ms (0.1%)

end2.0ms (0%)

sample4.3s (54.4%)

Profiling