Details

analyze116.0ms (2.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	1.5%	98.5%	0
0%	1.5%	98.5%	1
0%	1.5%	98.5%	2
0.8%	0.8%	98.5%	3
0.8%	0.8%	98.5%	4
1.2%	0.4%	98.5%	5
1.2%	0.4%	98.5%	6
1.4%	0.2%	98.5%	7
1.4%	0.2%	98.5%	8
1.4%	0.1%	98.5%	9
1.4%	0.1%	98.5%	10
1.5%	0%	98.5%	11
1.5%	0%	98.5%	12
1.5%	0%	98.5%	13
1.5%	0%	98.5%	14

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample1.7s (37.4%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 66 to 52 computations (21.2% saved)

simplify17.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

175×	`fma-neg_binary32`
152×	`fma-def_binary32`
46×	`cancel-sign-sub-inv_binary32`
46×	`sub-neg_binary32`
30×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11

Stop Event

1×

saturated

Counts

1 → 2

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))
	11.8b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))

Compiler

Compiled 61 to 49 computations (19.7% saved)

localize17.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))

series245.0ms (5.5%)

Counts

2 → 36

Calls

2 calls:

242.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))
2.0ms	(log1p.f32 (*.f32 u -4))

rewrite36.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

591×	`expm1-log1p-u_binary32`
590×	`log1p-expm1-u_binary32`
334×	`log-prod_binary32`
143×	`prod-diff_binary32`
125×	`expm1-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	162	15
2	1949	15

Stop Event

1×	node limit

Counts

2 → 42

Calls

2 calls:

35.0ms	(log1p.f32 (*.f32 u -4))
35.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))

simplify41.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-neg_binary32`
526×	`fma-def_binary32`
364×	`sub-neg_binary32`
212×	`associate-+l+_binary32`
186×	`unsub-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	726
1	336	675
2	1065	632
3	3590	624

Stop Event

1×	node limit

Counts

78 → 91

prune56.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	7	91
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Error

0.1b

Counts

93 → 9

Alt Table

Status	Error	Program
	3.3b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (*.f32 (pow.f32 u 3) -64/3)) (neg.f32 s))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))
▶	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	0.7b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2)) (neg.f32 s))
	12.0b	(.f32 (-.f32 (log.f32 (-.f32 1 (.f32 (.f32 u u) 16))) (log.f32 (-.f32 1 (.f32 u -4)))) (neg.f32 s))
	11.8b	(.f32 (-.f32 (log1p.f32 (pow.f32 (.f32 u -4) 3)) (log.f32 (+.f32 1 (-.f32 (.f32 (.f32 u u) 16) (*.f32 u -4))))) (neg.f32 s))
	2.6b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	3.3b	(fma.f32 4 (.f32 s u) (.f32 s (.f32 (.f32 u u) (+.f32 8 (*.f32 u 64/3)))))
	11.8b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))

Compiler

Compiled 1629 to 1173 computations (28% saved)

localize27.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.1b	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
✓	0.2b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
✓	0.7b	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)

series298.0ms (6.7%)

Counts

3 → 48

Calls

3 calls:

257.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
28.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)
13.0ms	(cbrt.f32 (log1p.f32 (*.f32 u -4)))

rewrite41.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

760×	`expm1-log1p-u_binary32`
759×	`log1p-expm1-u_binary32`
143×	`prod-diff_binary32`
99×	`add-sqr-sqrt_binary32`
93×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	224	23
2	2461	23

Stop Event

1×	node limit

Counts

3 → 59

Calls

3 calls:

40.0ms	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
40.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
40.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

372×	`fma-def_binary32`
275×	`associate-+r+_binary32`
228×	`+-commutative_binary32`
224×	`sub-neg_binary32`
222×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	305	2700
1	1037	2419
2	4050	2407

Stop Event

1×	node limit

Counts

107 → 132

prune142.0ms (3.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	175	10	185

Error

0.1b

Counts

185 → 10

Alt Table

Status	Error	Program
	3.3b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (*.f32 (pow.f32 u 3) -64/3)) (neg.f32 s))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))
	3.6b	(.f32 (pow.f32 (log.f32 (exp.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) 3) (neg.f32 s))
✓	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
▶	0.7b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2)) (neg.f32 s))
	12.0b	(.f32 (-.f32 (log.f32 (-.f32 1 (.f32 (.f32 u u) 16))) (log.f32 (-.f32 1 (.f32 u -4)))) (neg.f32 s))
	11.8b	(.f32 (-.f32 (log1p.f32 (pow.f32 (.f32 u -4) 3)) (log.f32 (+.f32 1 (-.f32 (.f32 (.f32 u u) 16) (*.f32 u -4))))) (neg.f32 s))
	3.3b	(fma.f32 4 (.f32 s u) (.f32 s (.f32 (.f32 u u) (+.f32 8 (*.f32 u 64/3)))))
	11.8b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
	2.6b	(fma.f32 8 (.f32 u (.f32 u s)) (fma.f32 (.f32 s 64/3) (pow.f32 u 3) (fma.f32 4 (.f32 u s) (.f32 s (.f32 (pow.f32 u 4) 64)))))

Compiler

Compiled 5344 to 4115 computations (23% saved)

localize39.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
✓	0.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2)) (neg.f32 s))
✓	0.4b	(.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2))
✓	0.5b	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)

series285.0ms (6.4%)

Counts

3 → 48

Calls

3 calls:

260.0ms

(*.f32 (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)) (neg.f32 s))

22.0ms

(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)

3.0ms

(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2))

rewrite42.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

800×	`expm1-log1p-u_binary32`
799×	`log1p-expm1-u_binary32`
143×	`prod-diff_binary32`
107×	`add-sqr-sqrt_binary32`
100×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	248	26
2	2643	26

Stop Event

1×	node limit

Counts

3 → 47

Calls

3 calls:

42.0ms

(*.f32 (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)) (neg.f32 s))

42.0ms

(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2))

42.0ms

(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

292×	`times-frac_binary32`
222×	`fma-def_binary32`
218×	`cancel-sign-sub-inv_binary32`
200×	`associate-*l/_binary32`
175×	`distribute-neg-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	1629
1	638	1428
2	2223	1287

Stop Event

1×	node limit

Counts

95 → 120

prune193.0ms (4.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	208	4	212
Fresh	4	3	7
Picked	1	0	1
Done	0	2	2
Total	213	9	222

Error

0.1b

Counts

222 → 9

Alt Table

Status	Error	Program
	3.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (log.f32 (exp.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) 2)) (neg.f32 s))
	3.6b	(.f32 (pow.f32 (log.f32 (exp.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) 3) (neg.f32 s))
✓	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	12.0b	(.f32 (-.f32 (log.f32 (-.f32 1 (.f32 (.f32 u u) 16))) (log.f32 (-.f32 1 (.f32 u -4)))) (neg.f32 s))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))
▶	0.4b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2))) (neg.f32 s))
	2.5b	(+.f32 (.f32 s (fma.f32 64 (pow.f32 u 4) (.f32 (pow.f32 u 3) 64/3))) (.f32 s (.f32 u (+.f32 (*.f32 8 u) 4))))
	0.9b	(.f32 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 3) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2)) (neg.f32 s))
	2.6b	(fma.f32 8 (.f32 u (.f32 u s)) (fma.f32 (.f32 s 64/3) (pow.f32 u 3) (fma.f32 4 (.f32 u s) (.f32 s (.f32 (pow.f32 u 4) 64)))))

Compiler

Compiled 6656 to 5262 computations (20.9% saved)

localize40.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
✓	0.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2))) (neg.f32 s))
✓	0.4b	(.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)))
✓	0.5b	(pow.f32 (log1p.f32 (*.f32 u -4)) 2)

series251.0ms (5.6%)

Counts

3 → 48

Calls

3 calls:

242.0ms

(*.f32 (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2))) (neg.f32 s))

6.0ms

(pow.f32 (log1p.f32 (*.f32 u -4)) 2)

3.0ms

(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)))

rewrite47.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

863×	`expm1-log1p-u_binary32`
862×	`log1p-expm1-u_binary32`
143×	`prod-diff_binary32`
116×	`add-sqr-sqrt_binary32`
112×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	264	24
2	2955	24

Stop Event

1×	node limit

Counts

3 → 52

Calls

3 calls:

46.0ms

(*.f32 (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2))) (neg.f32 s))

46.0ms

(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)))

46.0ms

(pow.f32 (log1p.f32 (*.f32 u -4)) 2)

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

286×	`cancel-sign-sub-inv_binary32`
282×	`fma-def_binary32`
243×	`sub-neg_binary32`
196×	`associate-l_binary32`
173×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	1385
1	671	1304
2	2372	1214

Stop Event

1×	node limit

Counts

100 → 124

prune144.0ms (3.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	170	9	179

Error

0.1b

Counts

179 → 9

Alt Table

Status	Error	Program
	3.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (log.f32 (exp.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) 2)) (neg.f32 s))
	3.6b	(.f32 (pow.f32 (log.f32 (exp.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) 3) (neg.f32 s))
	0.8b	(.f32 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 3) (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2))) (neg.f32 s))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))
✓	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	12.0b	(.f32 (-.f32 (log.f32 (-.f32 1 (.f32 (.f32 u u) 16))) (log.f32 (-.f32 1 (.f32 u -4)))) (neg.f32 s))
✓	0.4b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2))) (neg.f32 s))
	2.5b	(+.f32 (.f32 s (fma.f32 64 (pow.f32 u 4) (.f32 (pow.f32 u 3) 64/3))) (.f32 s (.f32 u (+.f32 (*.f32 8 u) 4))))
	2.6b	(fma.f32 8 (.f32 u (.f32 u s)) (fma.f32 (.f32 s 64/3) (pow.f32 u 3) (fma.f32 4 (.f32 u s) (.f32 s (.f32 (pow.f32 u 4) 64)))))

Compiler

Compiled 4652 to 3592 computations (22.8% saved)

regimes455.0ms (10.2%)

Accuracy

Total 0.2b remaining (71.9%)

Threshold costs 0.2b (71.9%)

Counts

67 → 1

Compiler

Compiled 8423 to 6785 computations (19.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
3×	`+-commutative_binary32`
3×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	24	11
3	30	11
4	33	11
5	34	11

Stop Event

1×

saturated

end118.0ms (2.6%)

Compiler: Compiled 184 to 145 computations (21.2% saved)

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11

Details

analyze116.0ms (2.6%)

sample1.7s (37.4%)

simplify17.0ms (0.4%)

prune6.0ms (0.1%)

localize17.0ms (0.4%)

series245.0ms (5.5%)

rewrite36.0ms (0.8%)

simplify41.0ms (0.9%)

prune56.0ms (1.3%)

localize27.0ms (0.6%)

series298.0ms (6.7%)

rewrite41.0ms (0.9%)

simplify58.0ms (1.3%)

prune142.0ms (3.2%)

localize39.0ms (0.9%)

series285.0ms (6.4%)

rewrite42.0ms (1%)

simplify42.0ms (0.9%)

prune193.0ms (4.3%)

localize40.0ms (0.9%)

series251.0ms (5.6%)

rewrite47.0ms (1.1%)

simplify39.0ms (0.9%)

prune144.0ms (3.2%)

regimes455.0ms (10.2%)

simplify2.0ms (0%)

end118.0ms (2.6%)

Profiling

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11