Details

analyze295.0ms (5.5%)

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)

sample3.3s (62%)

Results

1.2s	2580×	body	1024	valid
1.1s	1339×	body	512	valid
560.0ms	1234×	body	2048	valid
225.0ms	2385×	body	128	valid
125.0ms	670×	body	256	valid
30.0ms	48×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify6.0ms (0.1%)

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

prune3.0ms (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

44.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	44.6b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	1.3b	(+.f64 x (hypot.f64 1 x))
✓	2.7b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series11.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

rewrite6.0ms (0.1%)

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:

2.0ms	(+.f64 x (hypot.f64 1 x))
2.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
0.0ms	(hypot.f64 1 x)

simplify72.0ms (1.3%)

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

prune69.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Error

0.0b

Counts

114 → 5

Alt Table

Status	Error	Program
	44.9b	(.f64 (.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
▶	33.6b	(fma.f64 (pow.f64 x 3) -1/6 x)
	45.8b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	45.0b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (hypot.f64 1 x)))))
	53.1b	(log.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))

Compiler

Compiled 1670 to 1255 computations (24.9% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(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:

0.0ms

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

simplify61.0ms (1.1%)

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

prune11.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	16	5	21

Error

0.0b

Counts

21 → 5

Alt Table

Status	Error	Program
▶	44.9b	(.f64 (.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	33.6b	(fma.f64 (pow.f64 x 3) -1/6 x)
	45.8b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	45.0b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (hypot.f64 1 x)))))
	53.1b	(log.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))

Compiler

Compiled 291 to 216 computations (25.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	0.2b	(cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))
	1.3b	(+.f64 x (hypot.f64 1 x))
	2.7b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series146.0ms (2.7%)

Counts

2 → 24

Calls

2 calls:

120.0ms	(*.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
26.0ms	(cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 61

Calls

2 calls:

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

simplify110.0ms (2%)

Algorithm

1×	egg-herbie

Rules

406×	`fma-def_binary64`
277×	`associate-r_binary64`
246×	`associate-+r+_binary64`
244×	`*-commutative_binary64`
239×	`associate-l_binary64`

Counts

85 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	397	4639
1	1203	4233
2	4524	4038
3	5079	4038

prune417.0ms (7.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	440	1	441
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	441	5	446

Error

0.0b

Counts

446 → 5

Alt Table

Status	Error	Program
✓	33.6b	(fma.f64 (pow.f64 x 3) -1/6 x)
▶	44.7b	(.f64 (cbrt.f64 (.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x))))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	45.8b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	45.0b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (hypot.f64 1 x)))))
	53.1b	(log.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))

Compiler

Compiled 18130 to 14365 computations (20.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))
✓	0.2b	(cbrt.f64 (*.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x)))))
	1.3b	(+.f64 x (hypot.f64 1 x))
	2.7b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series121.0ms (2.3%)

Counts

1 → 12

Calls

1 calls:

121.0ms

(cbrt.f64 (*.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`cbrt-prod_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

2.0ms

(cbrt.f64 (*.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x)))))

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

322×	`fma-def_binary64`
278×	`cancel-sign-sub-inv_binary64`
224×	`associate-+r+_binary64`
186×	`associate-r_binary64`
178×	`*-commutative_binary64`

Counts

23 → 36

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	280	2617
1	871	2423
2	3439	2421
3	4989	2421

prune293.0ms (5.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	318	0	318
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	318	5	323

Error

0.0b

Counts

323 → 5

Alt Table

Status	Error	Program
✓	33.6b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	44.7b	(.f64 (cbrt.f64 (.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) (log.f64 (+.f64 x (hypot.f64 1 x))))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	45.8b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	45.0b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (hypot.f64 1 x)))))
	53.1b	(log.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))

Compiler

Compiled 12671 to 9933 computations (21.6% saved)

regimes169.0ms (3.2%)

Accuracy

Total 0.2b remaining (75.7%)

Threshold costs 0.2b (75.7%)

Counts

44 → 3

Compiler

Compiled 1833 to 1402 computations (23.5% saved)

bsearch32.0ms (0.6%)

Steps

Iters	Range		Point
8	1.3266120546997035e-5	0.10507327391123435	0.000671786823788058
10	-2.8153387671547616	-4.882522986207836e-13	-1.0640612636644509

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	48
1	29	48
2	28	48

end99.0ms (1.9%)

Compiler: Compiled 140 to 105 computations (25% saved)

Details

analyze295.0ms (5.5%)

sample3.3s (62%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series11.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify72.0ms (1.3%)

prune69.0ms (1.3%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify61.0ms (1.1%)

prune11.0ms (0.2%)

localize7.0ms (0.1%)

series146.0ms (2.7%)

rewrite10.0ms (0.2%)

simplify110.0ms (2%)

prune417.0ms (7.8%)

localize9.0ms (0.2%)

series121.0ms (2.3%)

rewrite2.0ms (0%)

simplify74.0ms (1.4%)

prune293.0ms (5.5%)

regimes169.0ms (3.2%)

bsearch32.0ms (0.6%)

simplify3.0ms (0%)

end99.0ms (1.9%)

Profiling