Details

analyze977.0ms (5.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
12.5%	78%	9.5%	6
20.3%	68.7%	11%	7
21.1%	62.4%	16.5%	8
25.4%	57%	17.7%	9
26%	52.1%	22%	10
28.3%	49%	22.7%	11
28.6%	47.2%	24.2%	12
29.8%	45.6%	24.7%	13
29.9%	43.9%	26.2%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample15.3s (82.6%)

Results

11.3s	4935×	body	8192	exit
1.9s	3339×	body	1024	invalid
1.1s	8256×	body	128	valid
585.0ms	1691×	body	512	invalid
204.0ms	903×	body	256	invalid
91.0ms	649×	body	128	invalid
7.0ms	2×	body	8192	invalid
5.0ms	1×	body	4096	invalid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess48.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

409×	`associate-l_binary64`
386×	`associate-/l*_binary64`
325×	`associate-r_binary64`
318×	`associate-/r*_binary64`
273×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	31	26
2	67	22
3	157	22
4	495	22
5	2153	22
6	3948	22
7	4105	22
8	4337	22
9	4787	22
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 10 to 7 computations (30% saved)

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

656×	`unswap-sqr_binary64`
607×	`times-frac_binary64`
203×	`associate-l_binary64`
192×	`associate-/l*_binary64`
177×	`sqr-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	38	11
3	85	11
4	260	11
5	1105	11
6	4055	11
7	4154	11
8	4278	11
9	4515	11
10	4958	11

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

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
	0.3b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
▶	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))

Compiler

Compiled 55 to 32 computations (41.8% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))
✓	0.3b	(pow.f64 l (exp.f64 w))

series232.0ms (1.3%)

Counts

2 → 44

Calls

12 calls:

44.0ms	(pow.f64 l (exp.f64 w))	w	inf
43.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))	w	-inf
42.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))	w	inf
41.0ms	(pow.f64 l (exp.f64 w))	w	-inf
11.0ms	(pow.f64 l (exp.f64 w))	l	inf

rewrite31.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

555×	`log1p-expm1-u_binary64`
555×	`expm1-log1p-u_binary64`
315×	`log-prod_binary64`
114×	`expm1-udef_binary64`
114×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	159	17
2	2031	17

Stop Event

1×	node limit

Counts

2 → 39

simplify28.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

832×	`fma-def_binary64`
433×	`associate-+l+_binary64`
421×	`associate-l_binary64`
321×	`associate-+r+_binary64`
313×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	76	694
1	255	663
2	913	588

Stop Event

1×	node limit

Counts

83 → 60

prune47.0ms (0.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	54	6	60
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	56	6	62

Error

0.1b

Counts

62 → 6

Alt Table

Status	Error	Program
▶	1.4b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (pow.f64 (cbrt.f64 l) 2) (exp.f64 w)) (pow.f64 (cbrt.f64 l) (exp.f64 w))))
	27.0b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (cbrt.f64 (pow.f64 l (exp.f64 w))) (cbrt.f64 (pow.f64 l (*.f64 2 (exp.f64 w))))))
	10.4b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
	8.5b	(.f64 (exp.f64 (neg.f64 w)) (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (.f64 (log.f64 l) 1/2))) (fma.f64 1/2 (.f64 (.f64 l (.f64 w w)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 2))) (.f64 l (+.f64 (.f64 1/6 (.f64 (pow.f64 w 3) (pow.f64 (log.f64 l) 3))) (*.f64 (log.f64 l) w)))))))
	5.1b	(.f64 (exp.f64 (neg.f64 w)) (exp.f64 (.f64 (log.f64 l) (exp.f64 w))))
	26.7b	(.f64 (exp.f64 (neg.f64 w)) (sqrt.f64 (pow.f64 l (.f64 2 (exp.f64 w)))))

Compiler

Compiled 1288 to 582 computations (54.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (cbrt.f64 l) (exp.f64 w))
✓	0.3b	(pow.f64 (pow.f64 (cbrt.f64 l) 2) (exp.f64 w))
✓	0.5b	(pow.f64 (cbrt.f64 l) 2)
✓	0.6b	(cbrt.f64 l)

series483.0ms (2.6%)

Counts

4 → 24

Calls

18 calls:

111.0ms	(pow.f64 (pow.f64 (cbrt.f64 l) 2) (exp.f64 w))	w	-inf
105.0ms	(pow.f64 (pow.f64 (cbrt.f64 l) 2) (exp.f64 w))	w	inf
82.0ms	(pow.f64 (cbrt.f64 l) (exp.f64 w))	w	-inf
82.0ms	(pow.f64 (cbrt.f64 l) (exp.f64 w))	w	inf
21.0ms	(pow.f64 (pow.f64 (cbrt.f64 l) 2) (exp.f64 w))	l	-inf

rewrite43.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
88×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	184	28
2	2081	28

Stop Event

1×	node limit

Counts

4 → 88

simplify35.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary64`
378×	`distribute-rgt-out_binary64`
368×	`*-commutative_binary64`
347×	`distribute-lft-out_binary64`
326×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	628
1	251	593
2	1052	529
3	3785	474

Stop Event

1×	node limit

Counts

112 → 107

prune80.0ms (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	129	6	135

Error

0.1b

Counts

135 → 6

Alt Table

Status	Error	Program
	5.1b	(.f64 (exp.f64 (neg.f64 w)) (exp.f64 (.f64 (log.f64 l) (exp.f64 w))))
▶	3.7b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (*.f64 (sqrt.f64 l) (pow.f64 l 1/6)) (exp.f64 w)) (pow.f64 (cbrt.f64 l) (exp.f64 w))))
	10.4b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
	8.5b	(.f64 (exp.f64 (neg.f64 w)) (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (.f64 (log.f64 l) 1/2))) (fma.f64 1/2 (.f64 (.f64 l (.f64 w w)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 2))) (.f64 l (+.f64 (.f64 1/6 (.f64 (pow.f64 w 3) (pow.f64 (log.f64 l) 3))) (*.f64 (log.f64 l) w)))))))
	4.5b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (pow.f64 (exp.f64 (log.f64 (cbrt.f64 l))) 2) (exp.f64 w)) (pow.f64 (cbrt.f64 l) (exp.f64 w))))
	28.6b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (pow.f64 (pow.f64 l 2) 1/3) (exp.f64 w)) (pow.f64 (cbrt.f64 l) (exp.f64 w))))

Compiler

Compiled 3479 to 1552 computations (55.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 (sqrt.f64 l) (pow.f64 l 1/6)) (exp.f64 w))
✓	0.4b	(*.f64 (sqrt.f64 l) (pow.f64 l 1/6))
	0.6b	(cbrt.f64 l)
✓	4.2b	(pow.f64 l 1/6)

series283.0ms (1.5%)

Counts

3 → 16

Calls

12 calls:

121.0ms	(pow.f64 (*.f64 (sqrt.f64 l) (pow.f64 l 1/6)) (exp.f64 w))	w	inf
114.0ms	(pow.f64 (*.f64 (sqrt.f64 l) (pow.f64 l 1/6)) (exp.f64 w))	w	-inf
9.0ms	(pow.f64 l 1/6)	l	-inf
7.0ms	(pow.f64 l 1/6)	l	inf
7.0ms	(pow.f64 (*.f64 (sqrt.f64 l) (pow.f64 l 1/6)) (exp.f64 w))	l	-inf

rewrite37.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

783×	`log1p-expm1-u_binary64`
783×	`expm1-log1p-u_binary64`
91×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`
85×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	188	25
2	2238	25

Stop Event

1×	node limit

Counts

3 → 52

simplify34.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

889×	`distribute-rgt-out_binary64`
675×	`associate-l_binary64`
575×	`associate-r_binary64`
343×	`fma-def_binary64`
162×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	426
1	146	399
2	556	325
3	3788	284

Stop Event

1×	node limit

Counts

68 → 64

prune55.0ms (0.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Error

0.0b

Counts

92 → 6

Alt Table

Status	Error	Program
	5.1b	(.f64 (exp.f64 (neg.f64 w)) (exp.f64 (.f64 (log.f64 l) (exp.f64 w))))
	3.8b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (*.f64 (sqrt.f64 l) (pow.f64 l 1/6)) (exp.f64 w)) (pow.f64 (exp.f64 (log.f64 (cbrt.f64 l))) (exp.f64 w))))
	10.4b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
	8.5b	(.f64 (exp.f64 (neg.f64 w)) (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (.f64 (log.f64 l) 1/2))) (fma.f64 1/2 (.f64 (.f64 l (.f64 w w)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 2))) (.f64 l (+.f64 (.f64 1/6 (.f64 (pow.f64 w 3) (pow.f64 (log.f64 l) 3))) (*.f64 (log.f64 l) w)))))))
▶	3.6b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (.f64 (sqrt.f64 l) (pow.f64 l 1/6)) (exp.f64 w)) (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 l)) (pow.f64 (cbrt.f64 (cbrt.f64 l)) 2)) (exp.f64 w))))
	28.6b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (pow.f64 (pow.f64 l 2) 1/3) (exp.f64 w)) (pow.f64 (cbrt.f64 l) (exp.f64 w))))

Compiler

Compiled 2435 to 1046 computations (57% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (cbrt.f64 l)) 2)
	0.6b	(cbrt.f64 l)
✓	0.6b	(cbrt.f64 (cbrt.f64 l))
	4.2b	(pow.f64 l 1/6)

series253.0ms (1.4%)

Counts

2 → 24

Calls

6 calls:

117.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 l)) 2)	l	-inf
106.0ms	(cbrt.f64 (cbrt.f64 l))	l	-inf
9.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 l)) 2)	l	0
8.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 l)) 2)	l	inf
7.0ms	(cbrt.f64 (cbrt.f64 l))	l	inf

rewrite34.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

404×	`log1p-expm1-u_binary64`
404×	`expm1-log1p-u_binary64`
356×	`pow1_binary64`
304×	`unpow-prod-down_binary64`
204×	`log-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	117	13
2	1211	12

Stop Event

1×	node limit

Counts

2 → 90

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

581×	`sqr-pow_binary64`
540×	`unswap-sqr_binary64`
352×	`fma-def_binary64`
345×	`*-commutative_binary64`
223×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	396
1	45	396
2	95	396
3	254	396
4	987	280
5	2061	280
6	2234	280
7	2517	280
8	2918	280
9	3361	280
10	3948	280
11	4691	280

Stop Event

1×	node limit

Counts

114 → 97

prune135.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	218	6	224

Error

0.0b

Counts

224 → 6

Alt Table

Status	Error	Program
	5.1b	(.f64 (exp.f64 (neg.f64 w)) (exp.f64 (.f64 (log.f64 l) (exp.f64 w))))
	3.8b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (*.f64 (sqrt.f64 l) (pow.f64 l 1/6)) (exp.f64 w)) (pow.f64 (exp.f64 (log.f64 (cbrt.f64 l))) (exp.f64 w))))
	10.4b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
	8.5b	(.f64 (exp.f64 (neg.f64 w)) (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (.f64 (log.f64 l) 1/2))) (fma.f64 1/2 (.f64 (.f64 l (.f64 w w)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 2))) (.f64 l (+.f64 (.f64 1/6 (.f64 (pow.f64 w 3) (pow.f64 (log.f64 l) 3))) (*.f64 (log.f64 l) w)))))))
✓	3.6b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (.f64 (sqrt.f64 l) (pow.f64 l 1/6)) (exp.f64 w)) (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 l)) (pow.f64 (cbrt.f64 (cbrt.f64 l)) 2)) (exp.f64 w))))
	28.6b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (pow.f64 (pow.f64 l 2) 1/3) (exp.f64 w)) (pow.f64 (cbrt.f64 l) (exp.f64 w))))

Compiler

Compiled 6864 to 3319 computations (51.6% saved)

regimes115.0ms (0.6%)

Accuracy

Total 0.2b remaining (73%)

Threshold costs 0.2b (73%)

Counts

40 → 1

Compiler

Compiled 2483 to 1582 computations (36.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	13	13
2	15	13
3	16	13

Stop Event

1×

saturated

end112.0ms (0.6%)

Stop Event

1×

fuel

Compiler

Compiled 169 to 111 computations (34.3% saved)

Details

analyze977.0ms (5.3%)

sample15.3s (82.6%)

preprocess48.0ms (0.3%)

simplify42.0ms (0.2%)

prune3.0ms (0%)

localize6.0ms (0%)

series232.0ms (1.3%)

rewrite31.0ms (0.2%)

simplify28.0ms (0.2%)

prune47.0ms (0.3%)

localize10.0ms (0.1%)

series483.0ms (2.6%)

rewrite43.0ms (0.2%)

simplify35.0ms (0.2%)

prune80.0ms (0.4%)

localize13.0ms (0.1%)

series283.0ms (1.5%)

rewrite37.0ms (0.2%)

simplify34.0ms (0.2%)

prune55.0ms (0.3%)

localize17.0ms (0.1%)

series253.0ms (1.4%)

rewrite34.0ms (0.2%)

simplify67.0ms (0.4%)

prune135.0ms (0.7%)

regimes115.0ms (0.6%)

simplify2.0ms (0%)

end112.0ms (0.6%)

Profiling