Details

analyze107.0ms (3.4%)

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)

sample1.5s (47.7%)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify24.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-def_binary32`
230×	`fma-neg_binary32`
87×	`cancel-sign-sub-inv_binary32`
81×	`distribute-rgt-in_binary32`
69×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	22	13
2	45	13
3	89	13
4	123	13
5	164	13
6	215	13
7	315	13
8	594	13
9	910	13
10	1174	13
11	1341	13
12	1511	13
13	1665	13
14	1692	13
15	1693	13

Stop Event

1×

saturated

Counts

1 → 2

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

Compiler

Compiled 39 to 26 computations (33.3% saved)

localize22.0ms (0.7%)

Local error

Found 1 expressions with local error:

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

series172.0ms (5.4%)

Counts

1 → 24

Calls

1 calls:

172.0ms

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

rewrite29.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`expm1-log1p-u_binary32`
521×	`log1p-expm1-u_binary32`
318×	`log-prod_binary32`
108×	`expm1-udef_binary32`
108×	`log1p-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	163	9
2	2117	9

Stop Event

1×	node limit

Counts

1 → 21

Calls

1 calls:

29.0ms

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

simplify26.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

352×	`times-frac_binary32`
297×	`fma-def_binary32`
250×	`associate-/l*_binary32`
219×	`distribute-rgt-out_binary32`
205×	`unswap-sqr_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	530
1	172	498
2	533	448
3	2050	434

Stop Event

1×	node limit

Counts

45 → 47

prune29.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	42	5	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	6	48

Error

0.1b

Counts

48 → 6

Alt Table

Status	Error	Program
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
▶	2.5b	(+.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)))))
	9.4b	(pow.f32 (*.f32 alpha (sqrt.f32 (log1p.f32 u0))) 2)
	9.4b	(pow.f32 (cbrt.f32 (.f32 alpha (.f32 alpha (log1p.f32 u0)))) 3)
	3.2b	(+.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 u0 (pow.f32 alpha 2))))
	4.5b	(.f32 alpha (.f32 alpha (fma.f32 1/2 (*.f32 u0 u0) u0)))

Compiler

Compiled 894 to 558 computations (37.6% saved)

localize65.0ms (2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f32 (pow.f32 u0 2) (pow.f32 alpha 2))
✓	0.3b	(*.f32 (pow.f32 u0 4) (pow.f32 alpha 2))
✓	0.4b	(.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2)))
✓	0.4b	(*.f32 (pow.f32 u0 3) (pow.f32 alpha 2))

series53.0ms (1.7%)

Counts

4 → 0

Calls

4 calls:

17.0ms	(.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2)))
13.0ms	(*.f32 (pow.f32 u0 4) (pow.f32 alpha 2))
12.0ms	(*.f32 (pow.f32 u0 3) (pow.f32 alpha 2))
11.0ms	(*.f32 (pow.f32 u0 2) (pow.f32 alpha 2))

rewrite53.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

636×	`log-prod_binary32`
227×	`expm1-udef_binary32`
227×	`log1p-udef_binary32`
208×	`log-pow_binary32`
136×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	318	40
2	3386	40

Stop Event

1×	node limit

Counts

4 → 71

Calls

4 calls:

52.0ms	(*.f32 (pow.f32 u0 2) (pow.f32 alpha 2))
52.0ms	(*.f32 (pow.f32 u0 4) (pow.f32 alpha 2))
52.0ms	(.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2)))
52.0ms	(*.f32 (pow.f32 u0 3) (pow.f32 alpha 2))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

71 → 71

prune106.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	71	6	77

Error

0.1b

Counts

77 → 6

Alt Table

Status	Error	Program
	9.4b	(pow.f32 (*.f32 alpha (sqrt.f32 (log1p.f32 u0))) 2)
	9.4b	(pow.f32 (cbrt.f32 (.f32 alpha (.f32 alpha (log1p.f32 u0)))) 3)
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
▶	3.1b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (cbrt.f32 (pow.f32 (pow.f32 (.f32 u0 alpha) 2) 3))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	3.2b	(+.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 u0 (pow.f32 alpha 2))))
	4.5b	(.f32 alpha (.f32 alpha (fma.f32 1/2 (*.f32 u0 u0) u0)))

Compiler

Compiled 2975 to 2198 computations (26.1% saved)

localize80.0ms (2.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2)))
	0.4b	(*.f32 (pow.f32 u0 3) (pow.f32 alpha 2))
✓	0.5b	(pow.f32 (*.f32 u0 alpha) 2)
✓	13.1b	(cbrt.f32 (pow.f32 (pow.f32 (*.f32 u0 alpha) 2) 3))

series17.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(cbrt.f32 (pow.f32 (pow.f32 (*.f32 u0 alpha) 2) 3))
7.0ms	(pow.f32 (*.f32 u0 alpha) 2)

rewrite43.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

636×	`log1p-expm1-u_binary32`
636×	`expm1-log1p-u_binary32`
330×	`log-prod_binary32`
126×	`expm1-udef_binary32`
126×	`log1p-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	186	14
2	1869	14

Stop Event

1×	node limit

Counts

2 → 65

Calls

2 calls:

42.0ms	(pow.f32 (*.f32 u0 alpha) 2)
42.0ms	(cbrt.f32 (pow.f32 (pow.f32 (*.f32 u0 alpha) 2) 3))

simplify81.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

719×	`associate-l_binary32`
564×	`sqr-pow_binary32`
505×	`associate-r_binary32`
482×	`*-commutative_binary32`
263×	`cube-prod_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	480
1	16	480
2	37	480
3	103	480
4	432	480
5	2343	480
6	2435	480
7	2636	480
8	2834	480
9	3072	480
10	3391	480
11	4063	480
12	4557	480

Stop Event

1×	node limit

Counts

113 → 37

prune94.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	71	6	77

Error

0.1b

Counts

77 → 6

Alt Table

Status	Error	Program
	9.4b	(pow.f32 (*.f32 alpha (sqrt.f32 (log1p.f32 u0))) 2)
	9.4b	(pow.f32 (cbrt.f32 (.f32 alpha (.f32 alpha (log1p.f32 u0)))) 3)
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
✓	3.1b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (cbrt.f32 (pow.f32 (pow.f32 (.f32 u0 alpha) 2) 3))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
▶	3.2b	(+.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 u0 (pow.f32 alpha 2))))
	4.5b	(.f32 alpha (.f32 alpha (fma.f32 1/2 (*.f32 u0 u0) u0)))

Compiler

Compiled 2939 to 2096 computations (28.7% saved)

localize51.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f32 u0 (pow.f32 alpha 2))
	0.3b	(*.f32 (pow.f32 u0 2) (pow.f32 alpha 2))
	0.4b	(.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2)))
	0.4b	(*.f32 (pow.f32 u0 3) (pow.f32 alpha 2))

series10.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

10.0ms

(*.f32 u0 (pow.f32 alpha 2))

rewrite29.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

461×	`log1p-expm1-u_binary32`
461×	`expm1-log1p-u_binary32`
320×	`unpow-prod-down_binary32`
254×	`log-prod_binary32`
142×	`pow2_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1336	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

1 calls:

28.0ms

(*.f32 u0 (pow.f32 alpha 2))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

17 → 17

prune76.0ms (2.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	70	6	76

Error

0.1b

Counts

76 → 6

Alt Table

Status	Error	Program
	3.4b	(+.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))) (sqrt.f32 (pow.f32 (*.f32 alpha (sqrt.f32 u0)) 4))))
✓	3.2b	(+.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 u0 (pow.f32 alpha 2))))
	3.6b	(+.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))) (pow.f32 (cbrt.f32 (.f32 u0 (.f32 alpha alpha))) 3)))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
✓	3.1b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (cbrt.f32 (pow.f32 (pow.f32 (.f32 u0 alpha) 2) 3))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	4.5b	(.f32 alpha (.f32 alpha (fma.f32 1/2 (*.f32 u0 u0) u0)))

Compiler

Compiled 2163 to 1528 computations (29.4% saved)

regimes382.0ms (12%)

Accuracy

Total 0.2b remaining (68.2%)

Threshold costs 0.2b (68.2%)

Counts

47 → 1

Compiler

Compiled 7658 to 5798 computations (24.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	28	13
3	39	13
4	44	13
5	47	13
6	48	13

Stop Event

1×

saturated

end101.0ms (3.2%)

Compiler: Compiled 166 to 125 computations (24.7% saved)

Details

analyze107.0ms (3.4%)

sample1.5s (47.7%)

simplify24.0ms (0.8%)

prune3.0ms (0.1%)

localize22.0ms (0.7%)

series172.0ms (5.4%)

rewrite29.0ms (0.9%)

simplify26.0ms (0.8%)

prune29.0ms (0.9%)

localize65.0ms (2%)

series53.0ms (1.7%)

rewrite53.0ms (1.7%)

simplify6.0ms (0.2%)

prune106.0ms (3.3%)

localize80.0ms (2.5%)

series17.0ms (0.5%)

rewrite43.0ms (1.3%)

simplify81.0ms (2.5%)

prune94.0ms (3%)

localize51.0ms (1.6%)

series10.0ms (0.3%)

rewrite29.0ms (0.9%)

simplify6.0ms (0.2%)

prune76.0ms (2.4%)

regimes382.0ms (12%)

simplify4.0ms (0.1%)

end101.0ms (3.2%)

Profiling