Details

analyze117.0ms (1.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0.1%	0.1%	99.8%	3
0.1%	0.1%	99.8%	4
0.1%	0%	99.8%	5
0.1%	0%	99.8%	6
0.1%	0%	99.8%	7
0.1%	0%	99.8%	8
0.2%	0%	99.8%	9
0.2%	0%	99.8%	10
0.2%	0%	99.8%	11
0.2%	0%	99.8%	12
0.2%	0%	99.8%	13
0.2%	0%	99.8%	14

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample1.9s (31.2%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

566×	`fma-def_binary32`
230×	`fma-neg_binary32`
88×	`cancel-sign-sub-inv_binary32`
79×	`distribute-rgt-in_binary32`
67×	`distribute-lft-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13

prune4.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.6b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
▶	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

Compiler

Compiled 61 to 42 computations (31.1% saved)

localize24.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

series295.0ms (4.9%)

Counts

2 → 36

Calls

2 calls:

292.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
3.0ms	(log1p.f32 (neg.f32 u0))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary32`
7×	`add-exp-log_binary32`
7×	`pow1_binary32`
3×	`associate-r_binary32`
3×	`*-un-lft-identity_binary32`

Counts

2 → 32

Calls

2 calls:

4.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
0.0ms	(log1p.f32 (neg.f32 u0))

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

588×	`fma-neg_binary32`
526×	`fma-def_binary32`
217×	`times-frac_binary32`
213×	`distribute-rgt-neg-out_binary32`
204×	`distribute-lft-neg-out_binary32`

Counts

68 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	1211
1	390	1075
2	1418	1024
3	4435	1014
4	4952	1014

prune72.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Error

0.0b

Counts

94 → 8

Alt Table

Status	Error	Program
	0.8b	(.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))
	1.7b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
▶	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	2.1b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 (neg.f32 alpha) (neg.f32 alpha)) (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))
	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	2.3b	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
	2.2b	(.f32 (.f32 alpha (neg.f32 alpha)) (neg.f32 (+.f32 u0 (+.f32 (.f32 1/3 (pow.f32 u0 3)) (.f32 1/2 (pow.f32 u0 2))))))

Compiler

Compiled 1812 to 871 computations (51.9% saved)

localize24.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.2b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
✓	0.3b	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))

series512.0ms (8.5%)

Counts

2 → 48

Calls

2 calls:

266.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
246.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`associate-l_binary32`
9×	`add-sqr-sqrt_binary32`
9×	`add-cbrt-cube_binary32`
9×	`add-exp-log_binary32`
9×	`pow1_binary32`

Counts

2 → 49

Calls

2 calls:

5.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
4.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary32`
338×	`fma-neg_binary32`
288×	`distribute-rgt-neg-out_binary32`
249×	`distribute-lft-neg-out_binary32`
230×	`times-frac_binary32`

Counts

97 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1675
1	436	1509
2	1377	1427
3	4367	1415
4	4977	1415

prune117.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	155	6	161
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	160	9	169

Error

Counts

169 → 9

Alt Table

Status	Error	Program
▶	0.3b	(expm1.f32 (log1p.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
	0.8b	(.f32 alpha (.f32 (.f32 (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))
	2.2b	(.f32 (.f32 alpha alpha) (+.f32 u0 (.f32 (.f32 u0 u0) (+.f32 (*.f32 1/3 u0) 1/2))))
	0.8b	(.f32 alpha (.f32 (.f32 (neg.f32 alpha) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))
	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	2.2b	(.f32 alpha (+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) alpha)) (+.f32 (.f32 u0 alpha) (.f32 1/2 (.f32 (pow.f32 u0 2) alpha)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.7b	(.f32 alpha (.f32 (sqrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))

Compiler

Compiled 2823 to 1284 computations (54.5% saved)

localize34.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.1b	(expm1.f32 (log1p.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
✓	0.1b	(log1p.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha))))
✓	0.3b	(.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))

series537.0ms (8.9%)

Counts

3 → 72

Calls

3 calls:

246.0ms

(expm1.f32 (log1p.f32 (*.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha)))))

244.0ms

(*.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha)))

47.0ms

(log1p.f32 (*.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary32`
8×	`add-exp-log_binary32`
8×	`pow1_binary32`
4×	`*-un-lft-identity_binary32`
4×	`add-sqr-sqrt_binary32`

Counts

3 → 43

Calls

3 calls:

4.0ms

(*.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha)))

0.0ms

(log1p.f32 (*.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha))))

0.0ms

(expm1.f32 (log1p.f32 (*.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha)))))

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

482×	`cancel-sign-sub-inv_binary32`
321×	`unswap-sqr_binary32`
274×	`associate-r_binary32`
241×	`unsub-neg_binary32`
224×	`fma-def_binary32`

Counts

115 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	3476
1	775	3105
2	3146	3093
3	5136	3093

prune140.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	156	9	165

Error

Counts

165 → 9

Alt Table

Status	Error	Program
✓	0.3b	(expm1.f32 (log1p.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
	0.8b	(.f32 alpha (.f32 (.f32 (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))
	2.2b	(.f32 (.f32 alpha alpha) (+.f32 u0 (.f32 (.f32 u0 u0) (+.f32 (*.f32 1/3 u0) 1/2))))
	0.8b	(.f32 alpha (.f32 (.f32 (neg.f32 alpha) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))
▶	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	2.2b	(.f32 alpha (+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) alpha)) (+.f32 (.f32 u0 alpha) (.f32 1/2 (.f32 (pow.f32 u0 2) alpha)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.7b	(.f32 alpha (.f32 (sqrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))

Compiler

Compiled 4484 to 2566 computations (42.8% saved)

localize34.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.2b	(sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))
	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
✓	0.5b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))

series542.0ms (9%)

Counts

2 → 40

Calls

2 calls:

276.0ms

(*.f32 (sqrt.f32 (*.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (*.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))

266.0ms

(sqrt.f32 (*.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

135×	`pow1_binary32`
74×	`pow-prod-down_binary32`
63×	`sqrt-pow1_binary32`
17×	`pow-prod-up_binary32`
13×	`pow1/2_binary32`

Counts

2 → 82

Calls

2 calls:

13.0ms

(*.f32 (sqrt.f32 (*.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (*.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))

3.0ms

(sqrt.f32 (*.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-def_binary32`
449×	`associate-/r*_binary32`
423×	`associate-/l*_binary32`
198×	`associate-*l/_binary32`
165×	`cancel-sign-sub-inv_binary32`

Counts

122 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	2656
1	423	2170
2	1498	2012
3	4725	2004
4	4965	2004

prune221.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	337	9	346

Error

Counts

346 → 9

Alt Table

Status	Error	Program
✓	0.3b	(expm1.f32 (log1p.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
	0.8b	(.f32 alpha (.f32 (.f32 (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))
	2.2b	(.f32 (.f32 alpha alpha) (+.f32 u0 (.f32 (.f32 u0 u0) (+.f32 (*.f32 1/3 u0) 1/2))))
	0.8b	(.f32 alpha (.f32 (.f32 (neg.f32 alpha) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))
✓	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	2.2b	(.f32 alpha (+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) alpha)) (+.f32 (.f32 u0 alpha) (.f32 1/2 (.f32 (pow.f32 u0 2) alpha)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.7b	(.f32 alpha (.f32 (sqrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))

Compiler

Compiled 9912 to 3424 computations (65.5% saved)

regimes945.0ms (15.7%)

Accuracy

Total 0.3b remaining (89.9%)

Threshold costs 0.3b (89.9%)

Counts

155 → 1

Compiler

Compiled 16344 to 10802 computations (33.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
8×	`neg-sub0_binary32`
8×	`neg-mul-1_binary32`
5×	`+-commutative_binary32`
5×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	22	13
2	36	13
3	43	13
4	48	13
5	51	13
6	52	13
7	50	13

end98.0ms (1.6%)

Compiler: Compiled 212 to 108 computations (49.1% saved)

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13

Details

analyze117.0ms (1.9%)

sample1.9s (31.2%)

simplify34.0ms (0.6%)

prune4.0ms (0.1%)

localize24.0ms (0.4%)

series295.0ms (4.9%)

rewrite6.0ms (0.1%)

simplify69.0ms (1.1%)

prune72.0ms (1.2%)

localize24.0ms (0.4%)

series512.0ms (8.5%)

rewrite11.0ms (0.2%)

simplify75.0ms (1.2%)

prune117.0ms (2%)

localize34.0ms (0.6%)

series537.0ms (8.9%)

rewrite8.0ms (0.1%)

simplify93.0ms (1.5%)

prune140.0ms (2.3%)

localize34.0ms (0.6%)

series542.0ms (9%)

rewrite26.0ms (0.4%)

simplify95.0ms (1.6%)

prune221.0ms (3.7%)

regimes945.0ms (15.7%)

simplify3.0ms (0.1%)

end98.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13