Details

analyze640.0ms (11.8%)

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
0%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample1.7s (31.2%)

Results

1.4s	8256×	body	128	valid
312.0ms	2021×	body	128	invalid

Compiler

Compiled 56 to 42 computations (25% saved)

preprocess42.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

864×	`fma-def_binary64`
536×	`fma-neg_binary64`
395×	`+-commutative_binary64`
348×	`associate--l+_binary64`
243×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	128
1	118	128
2	307	124
3	1011	120
4	2378	120
5	4733	120
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify32.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
568×	`fma-neg_binary64`
319×	`sub-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
235×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	32
1	43	32
2	100	31
3	294	30
4	666	30
5	1496	30
6	2874	30
7	4967	30

Stop Event

1×	node limit

Counts

1 → 2

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

7.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.4b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
▶	7.3b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))

Status

Error

Program

7.4b

(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))

▶

7.3b

(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))

Compiler

Compiled 150 to 107 computations (28.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)
✓	0.1b	(-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x))
✓	0.2b	(fma.f64 (log.f64 x) (-.f64 1/2 x) x)
✓	6.8b	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)

series63.0ms (1.2%)

Counts

4 → 84

Calls

21 calls:

7.0ms	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)	x	-inf
6.0ms	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)	x	inf
5.0ms	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)	z	0
4.0ms	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)	x	0
4.0ms	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)	y	-inf

rewrite76.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

272×	`prod-diff_binary64`
190×	`add-sqr-sqrt_binary64`
182×	`log1p-expm1-u_binary64`
182×	`expm1-log1p-u_binary64`
181×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	50
1	380	50
2	4797	50

Stop Event

1×	node limit

Counts

4 → 109

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

448×	`fma-neg_binary64`
372×	`cancel-sign-sub-inv_binary64`
353×	`sub-neg_binary64`
259×	`fma-def_binary64`
238×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1866
1	260	1816
2	778	1619
3	2503	1180

Stop Event

1×	node limit

Counts

193 → 154

prune271.0ms (5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	138	16	154
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	140	16	156

Error

0.8b

Counts

156 → 16

Alt Table

Status	Error	Program
	22.8b	(+.f64 (/.f64 1 (/.f64 (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000) (-.f64 8444480278083503881401098089/10000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.9b	(+.f64 (-.f64 91893853320467/100000000000000 (*.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	10.4b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (/.f64 (pow.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) 2) x))
	22.8b	(+.f64 (*.f64 (-.f64 8444480278083503881401098089/10000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)) (/.f64 1 (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	21.9b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (neg.f64 (/.f64 z (/.f64 x (+.f64 13888888888889/5000000000000000 (*.f64 z (-.f64 -7936500793651/10000000000000000 y)))))))
	29.0b	(+.f64 (.f64 (-.f64 775995832041781888678988180190112618287563/1000000000000000000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 3)) (/.f64 1 (+.f64 8444480278083503881401098089/10000000000000000000000000000 (.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000))))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	7.7b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (cbrt.f64 x))))
	21.4b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (.f64 (/.f64 z x) (.f64 z (+.f64 7936500793651/10000000000000000 y))))
	12.5b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (*.f64 (/.f64 (cbrt.f64 (pow.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) 2)) 1) (/.f64 (cbrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
	10.7b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (/.f64 (fma.f64 z -13888888888889/5000000000000000 83333333333333/1000000000000000) x))
▶	7.3b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (+.f64 (/.f64 (.f64 y (pow.f64 z 2)) x) (.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (.f64 13888888888889/5000000000000000 (/.f64 z x))))
	7.8b	(+.f64 (-.f64 91893853320467/100000000000000 (pow.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) 3)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	7.5b	(+.f64 (pow.f64 (sqrt.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x))) 2) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.8b	(+.f64 (-.f64 91893853320467/100000000000000 (/.f64 (-.f64 (.f64 (.f64 (log.f64 x) (-.f64 1/2 x)) (.f64 (log.f64 x) (-.f64 1/2 x))) (.f64 x x)) (-.f64 (*.f64 (log.f64 x) (-.f64 1/2 x)) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	10.2b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) 1) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
	7.3b	(+.f64 (-.f64 91893853320467/100000000000000 (-.f64 (+.f64 (.f64 1/2 (log.f64 x)) x) (.f64 (log.f64 x) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))

Compiler

Compiled 5164 to 3456 computations (33.1% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 83333333333333/1000000000000000 (/.f64 1 x))
✓	7.9b	(/.f64 (*.f64 y (pow.f64 z 2)) x)
✓	8.1b	(*.f64 y (pow.f64 z 2))
✓	10.0b	(/.f64 (pow.f64 z 2) x)

series44.0ms (0.8%)

Counts

4 → 12

Calls

24 calls:

5.0ms	(/.f64 (*.f64 y (pow.f64 z 2)) x)	x	-inf
4.0ms	(*.f64 y (pow.f64 z 2))	z	0
3.0ms	(/.f64 (*.f64 y (pow.f64 z 2)) x)	y	-inf
3.0ms	(/.f64 (*.f64 y (pow.f64 z 2)) x)	y	0
2.0ms	(/.f64 (*.f64 y (pow.f64 z 2)) x)	y	inf

rewrite61.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`log-prod_binary64`
219×	`expm1-udef_binary64`
219×	`log1p-udef_binary64`
197×	`log-pow_binary64`
142×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	28
1	271	28
2	3291	28

Stop Event

1×	node limit

Counts

4 → 126

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48

Stop Event

1×

saturated

Counts

138 → 126

prune312.0ms (5.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	126	16	142

Error

0.1b

Counts

142 → 16

Alt Table

Status	Error	Program
	22.8b	(+.f64 (/.f64 1 (/.f64 (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000) (-.f64 8444480278083503881401098089/10000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
▶	6.3b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (+.f64 (.f64 y (/.f64 z (/.f64 x z))) (.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (.f64 13888888888889/5000000000000000 (/.f64 z x))))
	22.9b	(+.f64 (-.f64 91893853320467/100000000000000 (*.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	10.4b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (/.f64 (pow.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) 2) x))
	22.8b	(+.f64 (*.f64 (-.f64 8444480278083503881401098089/10000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)) (/.f64 1 (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	21.9b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (neg.f64 (/.f64 z (/.f64 x (+.f64 13888888888889/5000000000000000 (*.f64 z (-.f64 -7936500793651/10000000000000000 y)))))))
	29.0b	(+.f64 (.f64 (-.f64 775995832041781888678988180190112618287563/1000000000000000000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 3)) (/.f64 1 (+.f64 8444480278083503881401098089/10000000000000000000000000000 (.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000))))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	7.7b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (cbrt.f64 x))))
	21.4b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (.f64 (/.f64 z x) (.f64 z (+.f64 7936500793651/10000000000000000 y))))
	10.7b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (/.f64 (fma.f64 z -13888888888889/5000000000000000 83333333333333/1000000000000000) x))
✓	7.3b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (+.f64 (/.f64 (.f64 y (pow.f64 z 2)) x) (.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (.f64 13888888888889/5000000000000000 (/.f64 z x))))
	7.8b	(+.f64 (-.f64 91893853320467/100000000000000 (pow.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) 3)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	7.5b	(+.f64 (pow.f64 (sqrt.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x))) 2) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.8b	(+.f64 (-.f64 91893853320467/100000000000000 (/.f64 (-.f64 (.f64 (.f64 (log.f64 x) (-.f64 1/2 x)) (.f64 (log.f64 x) (-.f64 1/2 x))) (.f64 x x)) (-.f64 (*.f64 (log.f64 x) (-.f64 1/2 x)) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	10.2b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) 1) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
	7.3b	(+.f64 (-.f64 91893853320467/100000000000000 (-.f64 (+.f64 (.f64 1/2 (log.f64 x)) x) (.f64 (log.f64 x) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))

Compiler

Compiled 6259 to 3817 computations (39% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 (log.f64 x) (-.f64 1/2 x) x)
	0.4b	(*.f64 83333333333333/1000000000000000 (/.f64 1 x))
✓	4.7b	(*.f64 y (/.f64 z (/.f64 x z)))
	10.0b	(/.f64 (pow.f64 z 2) x)

series22.0ms (0.4%)

Counts

1 → 36

Calls

9 calls:

4.0ms	(*.f64 y (/.f64 z (/.f64 x z)))	z	0
3.0ms	(*.f64 y (/.f64 z (/.f64 x z)))	y	-inf
3.0ms	(*.f64 y (/.f64 z (/.f64 x z)))	y	0
3.0ms	(*.f64 y (/.f64 z (/.f64 x z)))	x	-inf
2.0ms	(*.f64 y (/.f64 z (/.f64 x z)))	y	inf

rewrite39.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

798×	`log1p-expm1-u_binary64`
798×	`expm1-log1p-u_binary64`
78×	`add-sqr-sqrt_binary64`
72×	`add-log-exp_binary64`
71×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	151	10
2	2175	10

Stop Event

1×	node limit

Counts

1 → 25

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

541×	`associate-*l/_binary64`
335×	`associate-*r/_binary64`
303×	`*-commutative_binary64`
271×	`sqr-pow_binary64`
249×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	360
1	16	360
2	33	360
3	71	360
4	198	360
5	685	360
6	1778	360
7	2700	360
8	2807	360
9	2944	360
10	3117	360
11	3381	360
12	3698	360
13	4851	360

Stop Event

1×	node limit

Counts

61 → 27

prune245.0ms (4.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	5	9	14
Picked	1	0	1
Done	0	1	1
Total	119	14	133

Error

0.1b

Counts

133 → 14

Alt Table

Status	Error	Program
	22.8b	(+.f64 (/.f64 1 (/.f64 (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000) (-.f64 8444480278083503881401098089/10000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.9b	(+.f64 (-.f64 91893853320467/100000000000000 (*.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.8b	(+.f64 (*.f64 (-.f64 8444480278083503881401098089/10000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)) (/.f64 1 (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	21.9b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (neg.f64 (/.f64 z (/.f64 x (+.f64 13888888888889/5000000000000000 (*.f64 z (-.f64 -7936500793651/10000000000000000 y)))))))
	6.3b	(+.f64 (-.f64 91893853320467/100000000000000 (+.f64 (.f64 (log.f64 x) (-.f64 1/2 x)) x)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (+.f64 (.f64 y (/.f64 z (/.f64 x z))) (.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (*.f64 13888888888889/5000000000000000 (/.f64 z x))))
▶	0.3b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (pow.f64 (/.f64 z (/.f64 x z)) 1)) (+.f64 (.f64 y (/.f64 z (/.f64 x z))) (.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (.f64 13888888888889/5000000000000000 (/.f64 z x))))
	29.0b	(+.f64 (.f64 (-.f64 775995832041781888678988180190112618287563/1000000000000000000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 3)) (/.f64 1 (+.f64 8444480278083503881401098089/10000000000000000000000000000 (.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000))))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	7.7b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (cbrt.f64 x))))
	6.7b	(+.f64 (-.f64 91893853320467/100000000000000 (pow.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) 3)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (+.f64 (.f64 y (/.f64 z (/.f64 x z))) (.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (.f64 13888888888889/5000000000000000 (/.f64 z x))))
	7.5b	(+.f64 (pow.f64 (sqrt.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x))) 2) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.8b	(+.f64 (-.f64 91893853320467/100000000000000 (/.f64 (-.f64 (.f64 (.f64 (log.f64 x) (-.f64 1/2 x)) (.f64 (log.f64 x) (-.f64 1/2 x))) (.f64 x x)) (-.f64 (*.f64 (log.f64 x) (-.f64 1/2 x)) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	10.2b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) 1) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
✓	7.3b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (+.f64 (/.f64 (.f64 y (pow.f64 z 2)) x) (.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (.f64 13888888888889/5000000000000000 (/.f64 z x))))
	6.5b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (+.f64 (.f64 y (/.f64 z (/.f64 x z))) (pow.f64 (cbrt.f64 (/.f64 83333333333333/1000000000000000 x)) 3))) (*.f64 13888888888889/5000000000000000 (/.f64 z x))))

Compiler

Compiled 5828 to 3358 computations (42.4% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 13888888888889/5000000000000000 (/.f64 z x))
	0.2b	(fma.f64 (log.f64 x) (-.f64 1/2 x) x)
	0.4b	(*.f64 83333333333333/1000000000000000 (/.f64 1 x))
	4.7b	(*.f64 y (/.f64 z (/.f64 x z)))

series6.0ms (0.1%)

Counts

1 → 0

Calls

6 calls:

1.0ms	(*.f64 13888888888889/5000000000000000 (/.f64 z x))	z	0
1.0ms	(*.f64 13888888888889/5000000000000000 (/.f64 z x))	z	inf
1.0ms	(*.f64 13888888888889/5000000000000000 (/.f64 z x))	z	-inf
1.0ms	(*.f64 13888888888889/5000000000000000 (/.f64 z x))	x	inf
1.0ms	(*.f64 13888888888889/5000000000000000 (/.f64 z x))	x	-inf

rewrite36.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

607×	`log1p-expm1-u_binary64`
607×	`expm1-log1p-u_binary64`
317×	`log-prod_binary64`
116×	`expm1-udef_binary64`
116×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	127	7
2	1622	7

Stop Event

1×	node limit

Counts

1 → 25

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

25 → 25

prune219.0ms (4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	104	13	117

Error

0.0b

Counts

117 → 13

Alt Table

Status	Error	Program
	0.3b	(+.f64 (-.f64 91893853320467/100000000000000 (+.f64 (.f64 (log.f64 x) (-.f64 1/2 x)) x)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (pow.f64 (/.f64 z (/.f64 x z)) 1)) (+.f64 (.f64 y (/.f64 z (/.f64 x z))) (.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (*.f64 13888888888889/5000000000000000 (/.f64 z x))))
	7.5b	(+.f64 (pow.f64 (sqrt.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x))) 2) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	0.8b	(+.f64 (-.f64 91893853320467/100000000000000 (pow.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) 3)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (pow.f64 (/.f64 z (/.f64 x z)) 1)) (+.f64 (.f64 y (/.f64 z (/.f64 x z))) (.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (.f64 13888888888889/5000000000000000 (/.f64 z x))))
	22.8b	(+.f64 (/.f64 1 (/.f64 (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000) (-.f64 8444480278083503881401098089/10000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.9b	(+.f64 (-.f64 91893853320467/100000000000000 (*.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.8b	(+.f64 (*.f64 (-.f64 8444480278083503881401098089/10000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 2)) (/.f64 1 (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	21.9b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (neg.f64 (/.f64 z (/.f64 x (+.f64 13888888888889/5000000000000000 (*.f64 z (-.f64 -7936500793651/10000000000000000 y)))))))
	29.0b	(+.f64 (.f64 (-.f64 775995832041781888678988180190112618287563/1000000000000000000000000000000000000000000 (pow.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 3)) (/.f64 1 (+.f64 8444480278083503881401098089/10000000000000000000000000000 (.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) (+.f64 (fma.f64 (log.f64 x) (-.f64 1/2 x) x) 91893853320467/100000000000000))))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	7.7b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (cbrt.f64 x))))
	22.8b	(+.f64 (-.f64 91893853320467/100000000000000 (/.f64 (-.f64 (.f64 (.f64 (log.f64 x) (-.f64 1/2 x)) (.f64 (log.f64 x) (-.f64 1/2 x))) (.f64 x x)) (-.f64 (*.f64 (log.f64 x) (-.f64 1/2 x)) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	10.2b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) 1) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
✓	7.3b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (+.f64 (/.f64 (.f64 y (pow.f64 z 2)) x) (.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (.f64 13888888888889/5000000000000000 (/.f64 z x))))
	6.5b	(+.f64 (-.f64 91893853320467/100000000000000 (fma.f64 (log.f64 x) (-.f64 1/2 x) x)) (-.f64 (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (+.f64 (.f64 y (/.f64 z (/.f64 x z))) (pow.f64 (cbrt.f64 (/.f64 83333333333333/1000000000000000 x)) 3))) (*.f64 13888888888889/5000000000000000 (/.f64 z x))))

Compiler

Compiled 4882 to 2654 computations (45.6% saved)

regimes1.1s (20.6%)

Accuracy

Total 0.4b remaining (85.8%)

Threshold costs 0.4b (85.8%)

Counts

122 → 1

Compiler

Compiled 29103 to 20761 computations (28.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
9×	`*-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	55
1	47	55
2	62	55
3	72	55
4	79	55
5	82	55
6	83	55

Stop Event

1×

saturated

end279.0ms (5.1%)

Stop Event

1×

fuel

Compiler

Compiled 574 to 395 computations (31.2% saved)

Details

analyze640.0ms (11.8%)

sample1.7s (31.2%)

preprocess42.0ms (0.8%)

simplify32.0ms (0.6%)

prune4.0ms (0.1%)

localize14.0ms (0.3%)

series63.0ms (1.2%)

rewrite76.0ms (1.4%)

simplify61.0ms (1.1%)

prune271.0ms (5%)

localize24.0ms (0.4%)

series44.0ms (0.8%)

rewrite61.0ms (1.1%)

simplify8.0ms (0.2%)

prune312.0ms (5.7%)

localize23.0ms (0.4%)

series22.0ms (0.4%)

rewrite39.0ms (0.7%)

simplify67.0ms (1.2%)

prune245.0ms (4.5%)

localize22.0ms (0.4%)

series6.0ms (0.1%)

rewrite36.0ms (0.7%)

simplify7.0ms (0.1%)

prune219.0ms (4%)

regimes1.1s (20.6%)

simplify4.0ms (0.1%)

end279.0ms (5.1%)

Profiling