Details

analyze114.0ms (2.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	24.7%	75.3%	0
0%	24.7%	75.3%	1
0%	24.7%	75.3%	2
12.4%	12.4%	75.3%	3
12.4%	12.4%	75.3%	4
18.5%	6.2%	75.3%	5
18.5%	6.2%	75.3%	6
21.6%	3.1%	75.3%	7
21.6%	3.1%	75.3%	8
23.2%	1.5%	75.3%	9
23.2%	1.5%	75.3%	10
23.9%	0.8%	75.3%	11
23.9%	0.8%	75.3%	12
24.3%	0.4%	75.3%	13
24.3%	0.4%	75.3%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample1.3s (28%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 47 to 37 computations (21.3% saved)

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-neg_binary32`
518×	`unswap-sqr_binary32`
432×	`exp-prod_binary32`
340×	`times-frac_binary32`
333×	`associate-l_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	27	14
3	36	14
4	50	14
5	79	14
6	147	14
7	261	14
8	528	14
9	1676	14
10	3160	14
11	4121	14
12	4850	14

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

Compiler

Compiled 33 to 27 computations (18.2% saved)

localize24.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
✓	0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
✓	0.1b	(exp.f32 (/.f32 (neg.f32 x) s))

series34.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

23.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
6.0ms	(exp.f32 (/.f32 (neg.f32 x) s))
5.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary32`
42×	`times-frac_binary32`
34×	`exp-prod_binary32`
33×	`add-sqr-sqrt_binary32`
33×	`add-cube-cbrt_binary32`

Counts

3 → 102

Calls

3 calls:

6.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
5.0ms	(exp.f32 (/.f32 (neg.f32 x) s))
4.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))

simplify103.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-neg_binary32`
322×	`associate-/l/_binary32`
269×	`associate-/r/_binary32`
197×	`distribute-rgt-neg-in_binary32`
190×	`distribute-lft-neg-in_binary32`

Counts

174 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	2521
1	346	2365
2	806	2311
3	2414	2287
4	4850	2287
5	5089	2287

prune149.0ms (3.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	155	6	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	6	162

Error

0.0b

Counts

162 → 6

Alt Table

Status	Error	Program
	0.3b	(*.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (/.f32 (neg.f32 x) s)) (cbrt.f32 (/.f32 (neg.f32 x) s)))) (cbrt.f32 (/.f32 (neg.f32 x) s)))))
▶	0.1b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
	9.8b	(.f32 (/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -3))) (+.f32 (.f32 1 1) (-.f32 (.f32 (exp.f32 (/.f32 (neg.f32 x) s)) (exp.f32 (/.f32 (neg.f32 x) s))) (.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 2849 to 1533 computations (46.2% saved)

localize22.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
✓	0.1b	(exp.f32 (neg.f32 (/.f32 x s)))
✓	1.7b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series543.0ms (11.3%)

Counts

3 → 64

Calls

3 calls:

273.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
265.0ms	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))
5.0ms	(exp.f32 (neg.f32 (/.f32 x s)))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`exp-prod_binary32`
21×	`*-un-lft-identity_binary32`
21×	`add-sqr-sqrt_binary32`
21×	`add-cube-cbrt_binary32`
18×	`times-frac_binary32`

Counts

3 → 78

Calls

3 calls:

4.0ms	(exp.f32 (neg.f32 (/.f32 x s)))
2.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
0.0ms	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

simplify129.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

452×	`fma-neg_binary32`
354×	`distribute-neg-frac_binary32`
292×	`times-frac_binary32`
241×	`associate-/l*_binary32`
200×	`associate-/r*_binary32`

Counts

142 → 118

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	172	2142
1	367	1839
2	964	1802
3	3283	1774
4	4792	1772
5	4934	1772
6	4991	1772
7	4918	1772

prune131.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	119	5	124

Error

0.0b

Counts

124 → 5

Alt Table

Status	Error	Program
	0.3b	(*.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (/.f32 (neg.f32 x) s)) (cbrt.f32 (/.f32 (neg.f32 x) s)))) (cbrt.f32 (/.f32 (neg.f32 x) s)))))
▶	0.1b	(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
	9.8b	(.f32 (/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -3))) (+.f32 (.f32 1 1) (-.f32 (.f32 (exp.f32 (/.f32 (neg.f32 x) s)) (exp.f32 (/.f32 (neg.f32 x) s))) (.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 1945 to 918 computations (52.8% saved)

localize25.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.1b	(exp.f32 (neg.f32 (/.f32 x s)))
	1.7b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series536.0ms (11.1%)

Counts

1 → 24

Calls

1 calls:

536.0ms

(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow-unpow_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-sqr-sqrt_binary32`
5×	`add-cube-cbrt_binary32`
3×	`distribute-lft-neg-in_binary32`

Counts

1 → 29

Calls

1 calls:

2.0ms

(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

simplify89.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

481×	`associate-/l*_binary32`
463×	`times-frac_binary32`
362×	`fma-def_binary32`
329×	`fma-neg_binary32`
297×	`associate-*l/_binary32`

Counts

53 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	955
1	188	915
2	446	899
3	1429	881
4	4668	881
5	4873	881
6	4998	881
7	4898	881

prune155.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	120	5	125

Error

0.0b

Counts

125 → 5

Alt Table

Status	Error	Program
	0.3b	(*.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (/.f32 (neg.f32 x) s)) (cbrt.f32 (/.f32 (neg.f32 x) s)))) (cbrt.f32 (/.f32 (neg.f32 x) s)))))
✓	0.1b	(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
▶	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
	9.8b	(.f32 (/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -3))) (+.f32 (.f32 1 1) (-.f32 (.f32 (exp.f32 (/.f32 (neg.f32 x) s)) (exp.f32 (/.f32 (neg.f32 x) s))) (.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 2046 to 842 computations (58.8% saved)

localize31.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))
✓	0.0b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
✓	0.1b	(pow.f32 (exp.f32 -1) (/.f32 x s))

series40.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

27.0ms	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
7.0ms	(+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))
6.0ms	(pow.f32 (exp.f32 -1) (/.f32 x s))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary32`
22×	`add-sqr-sqrt_binary32`
22×	`add-cube-cbrt_binary32`
21×	`times-frac_binary32`
13×	`pow-unpow_binary32`

Counts

3 → 88

Calls

3 calls:

6.0ms	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
5.0ms	(pow.f32 (exp.f32 -1) (/.f32 x s))
4.0ms	(+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))

simplify119.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

717×	`fma-neg_binary32`
238×	`associate-r_binary32`
236×	`distribute-rgt-neg-in_binary32`
215×	`unswap-sqr_binary32`
212×	`fma-def_binary32`

Counts

160 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2396
1	348	2254
2	869	2200
3	3038	2188
4	4756	2188
5	4929	2188

prune209.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	145	6	151

Error

0.0b

Counts

151 → 6

Alt Table

Status	Error	Program
✓	0.1b	(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.1b	(/.f32 1 (+.f32 (pow.f32 (exp.f32 -1) (/.f32 x s)) 1))
	9.8b	(.f32 (/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (neg.f32 (/.f32 x s))) 3))) (+.f32 (.f32 1 1) (-.f32 (.f32 (pow.f32 (exp.f32 -1) (/.f32 x s)) (pow.f32 (exp.f32 -1) (/.f32 x s))) (.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))))
	9.8b	(.f32 (/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -3))) (+.f32 (.f32 1 1) (-.f32 (.f32 (exp.f32 (/.f32 (neg.f32 x) s)) (exp.f32 (/.f32 (neg.f32 x) s))) (.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
	0.3b	(*.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
	0.1b	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)))))

Compiler

Compiled 2615 to 1734 computations (33.7% saved)

regimes792.0ms (16.5%)

Accuracy

Total 0.0b remaining (60.4%)

Threshold costs 0.0b (60.4%)

Counts

127 → 1

Compiler

Compiled 14526 to 10979 computations (24.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	9	14
1	17	14
2	23	14
3	27	14
4	28	14
5	28	14

end100.0ms (2.1%)

Compiler: Compiled 163 to 119 computations (27% saved)

Details

analyze114.0ms (2.4%)

sample1.3s (28%)

simplify56.0ms (1.2%)

prune2.0ms (0%)

localize24.0ms (0.5%)

series34.0ms (0.7%)

rewrite21.0ms (0.4%)

simplify103.0ms (2.1%)

prune149.0ms (3.1%)

localize22.0ms (0.5%)

series543.0ms (11.3%)

rewrite10.0ms (0.2%)

simplify129.0ms (2.7%)

prune131.0ms (2.7%)

localize25.0ms (0.5%)

series536.0ms (11.1%)

rewrite3.0ms (0.1%)

simplify89.0ms (1.8%)

prune155.0ms (3.2%)

localize31.0ms (0.6%)

series40.0ms (0.8%)

rewrite21.0ms (0.4%)

simplify119.0ms (2.5%)

prune209.0ms (4.4%)

regimes792.0ms (16.5%)

simplify5.0ms (0.1%)

end100.0ms (2.1%)

Profiling