Details

analyze629.0ms (8.6%)

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)

sample108.0ms (1.5%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
4.0ms	46×	body	128	invalid
1.0ms	19×	body	128	nan

Compiler

Compiled 58 to 44 computations (24.1% saved)

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
691×	`associate-/l*_binary64`
673×	`sub-neg_binary64`
568×	`fma-neg_binary64`
439×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	32
1	43	32
2	99	31
3	223	30
4	529	30
5	1016	30
6	1917	30
7	3001	30
8	3396	30
9	4830	30
10	5110	30

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

6.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.4b	(+.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))
▶	6.4b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))

Status

Error

Program

6.4b

(+.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))

▶

6.4b

(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) 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)

localize15.0ms (0.2%)

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)
✓	0.2b	(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)
✓	0.3b	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
✓	6.0b	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)

series119.0ms (1.6%)

Counts

4 → 84

Calls

4 calls:

92.0ms	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)
9.0ms	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
9.0ms	(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)
8.0ms	(fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
9×	`times-frac_binary64`

Counts

4 → 80

Calls

4 calls:

4.0ms	(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)
2.0ms	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)
0.0ms	(fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)
0.0ms	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)

simplify212.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

646×	`times-frac_binary64`
501×	`fma-neg_binary64`
456×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
375×	`cancel-sign-sub-inv_binary64`

Counts

164 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	3470
1	445	3008
2	1616	2849
3	4650	2833
4	4993	2833
5	4990	2833
6	4904	2833

prune261.0ms (3.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	164	12	176
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	166	12	178

Error

0.1b

Counts

178 → 12

Alt Table

Status	Error	Program
	21.9b	(+.f64 (/.f64 (-.f64 (.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (.f64 x x)) (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	11.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 x (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)))))
	6.8b	(+.f64 (*.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.9b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (fma.f64 z (/.f64 (.f64 z (+.f64 7936500793651/10000000000000000 y)) x) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	11.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
	6.9b	(+.f64 (.f64 -1 (.f64 (+.f64 1 (log.f64 (/.f64 1 x))) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	6.8b	(+.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	6.4b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) 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))))
	6.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
▶	0.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.5b	(+.f64 (fma.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	6.5b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x)) (sqrt.f64 x)))

Compiler

Compiled 6047 to 3843 computations (36.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
	0.3b	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
✓	0.3b	(/.f64 83333333333333/1000000000000000 x)
✓	5.3b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series40.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

30.0ms	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
7.0ms	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
2.0ms	(/.f64 83333333333333/1000000000000000 x)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
6.0ms	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
2.0ms	(/.f64 83333333333333/1000000000000000 x)

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-def_binary64`
596×	`associate-*l/_binary64`
452×	`associate-*r/_binary64`
331×	`distribute-rgt-in_binary64`
326×	`distribute-lft-in_binary64`

Counts

153 → 140

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	191	1847
1	449	1683
2	1343	1683
3	4491	1683
4	4985	1683

prune350.0ms (4.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	162	6	168
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	165	15	180

Error

0.0b

Counts

180 → 15

Alt Table

Status	Error	Program
	21.9b	(+.f64 (/.f64 (-.f64 (.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (.f64 x x)) (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	11.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 x (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)))))
	0.8b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 (.f64 z (/.f64 z x)) (.f64 (cbrt.f64 (+.f64 7936500793651/10000000000000000 y)) (cbrt.f64 (+.f64 7936500793651/10000000000000000 y)))) (cbrt.f64 (+.f64 7936500793651/10000000000000000 y)))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.8b	(+.f64 (*.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.9b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (fma.f64 z (/.f64 (.f64 z (+.f64 7936500793651/10000000000000000 y)) x) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.9b	(+.f64 (.f64 -1 (.f64 (+.f64 1 (log.f64 (/.f64 1 x))) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	4.1b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (/.f64 (.f64 z z) x) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.8b	(+.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	1.1b	(+.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.5b	(+.f64 (fma.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	10.4b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (sqrt.f64 (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (sqrt.f64 (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
▶	0.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (.f64 (sqrt.f64 83333333333333/1000000000000000) (/.f64 (sqrt.f64 83333333333333/1000000000000000) x)) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.4b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (/.f64 (.f64 y (pow.f64 z 2)) x))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.5b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x)) (sqrt.f64 x)))

Compiler

Compiled 7064 to 3976 computations (43.7% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
	0.3b	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
✓	0.3b	(*.f64 (sqrt.f64 83333333333333/1000000000000000) (/.f64 (sqrt.f64 83333333333333/1000000000000000) x))
	5.3b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series9.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(*.f64 (sqrt.f64 83333333333333/1000000000000000) (/.f64 (sqrt.f64 83333333333333/1000000000000000) x))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
22×	`times-frac_binary64`
17×	`sqrt-prod_binary64`
16×	`*-un-lft-identity_binary64`

Counts

1 → 50

Calls

1 calls:

8.0ms

(*.f64 (sqrt.f64 83333333333333/1000000000000000) (/.f64 (sqrt.f64 83333333333333/1000000000000000) x))

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

907×	`fma-neg_binary64`
403×	`associate-/r*_binary64`
384×	`associate-/r/_binary64`
377×	`unswap-sqr_binary64`
213×	`associate-/l*_binary64`

Counts

62 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	732
1	177	615
2	554	599
3	1345	583
4	2197	583
5	2810	583
6	4562	583
7	5163	583

prune410.0ms (5.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	201	15	216

Error

0.0b

Counts

216 → 15

Alt Table

Status	Error	Program
	21.9b	(+.f64 (/.f64 (-.f64 (.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (.f64 x x)) (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	0.8b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 (.f64 z (/.f64 z x)) (.f64 (cbrt.f64 (+.f64 7936500793651/10000000000000000 y)) (cbrt.f64 (+.f64 7936500793651/10000000000000000 y)))) (cbrt.f64 (+.f64 7936500793651/10000000000000000 y)))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.8b	(+.f64 (*.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.9b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (fma.f64 z (/.f64 (.f64 z (+.f64 7936500793651/10000000000000000 y)) x) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.9b	(+.f64 (.f64 -1 (.f64 (+.f64 1 (log.f64 (/.f64 1 x))) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	4.1b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (/.f64 (.f64 z z) x) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.8b	(+.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	1.1b	(+.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.5b	(+.f64 (fma.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	10.4b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (sqrt.f64 (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (sqrt.f64 (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
▶	0.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (.f64 (sqrt.f64 (sqrt.f64 83333333333333/1000000000000000)) (/.f64 (pow.f64 (sqrt.f64 83333333333333/1000000000000000) 3/2) x)) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
✓	0.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (.f64 (sqrt.f64 83333333333333/1000000000000000) (/.f64 (sqrt.f64 83333333333333/1000000000000000) x)) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.4b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (/.f64 (.f64 y (pow.f64 z 2)) x))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.5b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x)) (sqrt.f64 x)))

Compiler

Compiled 9016 to 5428 computations (39.8% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
	0.3b	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 83333333333333/1000000000000000)) (/.f64 (pow.f64 (sqrt.f64 83333333333333/1000000000000000) 3/2) x))
	5.3b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series10.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(*.f64 (sqrt.f64 (sqrt.f64 83333333333333/1000000000000000)) (/.f64 (pow.f64 (sqrt.f64 83333333333333/1000000000000000) 3/2) x))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
42×	`times-frac_binary64`
36×	`sqrt-prod_binary64`
34×	`associate-r_binary64`
24×	`unpow-prod-down_binary64`

Counts

1 → 76

Calls

1 calls:

13.0ms

(*.f64 (sqrt.f64 (sqrt.f64 83333333333333/1000000000000000)) (/.f64 (pow.f64 (sqrt.f64 83333333333333/1000000000000000) 3/2) x))

simplify135.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

516×	`associate-/l*_binary64`
403×	`associate-l_binary64`
390×	`fma-neg_binary64`
384×	`associate-r_binary64`
375×	`associate-*l/_binary64`

Counts

88 → 97

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	130	1906
1	280	1712
2	961	1676
3	3405	1460
4	3946	1370
5	4521	1355
6	4915	1355
7	4833	1355

prune532.0ms (7.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	232	15	247

Error

0.0b

Counts

247 → 15

Alt Table

Status	Error	Program
	21.9b	(+.f64 (/.f64 (-.f64 (.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (.f64 x x)) (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	0.8b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 (.f64 z (/.f64 z x)) (.f64 (cbrt.f64 (+.f64 7936500793651/10000000000000000 y)) (cbrt.f64 (+.f64 7936500793651/10000000000000000 y)))) (cbrt.f64 (+.f64 7936500793651/10000000000000000 y)))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.8b	(+.f64 (*.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	22.9b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (fma.f64 z (/.f64 (.f64 z (+.f64 7936500793651/10000000000000000 y)) x) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.9b	(+.f64 (.f64 -1 (.f64 (+.f64 1 (log.f64 (/.f64 1 x))) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	4.1b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (/.f64 (.f64 z z) x) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.8b	(+.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	1.1b	(+.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.5b	(+.f64 (fma.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	10.4b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (sqrt.f64 (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (sqrt.f64 (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
✓	0.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (.f64 (sqrt.f64 (sqrt.f64 83333333333333/1000000000000000)) (/.f64 (pow.f64 (sqrt.f64 83333333333333/1000000000000000) 3/2) x)) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
✓	0.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (.f64 (sqrt.f64 83333333333333/1000000000000000) (/.f64 (sqrt.f64 83333333333333/1000000000000000) x)) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.4b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (+.f64 (.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (/.f64 (.f64 y (pow.f64 z 2)) x))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.5b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x)) (sqrt.f64 x)))

Compiler

Compiled 10555 to 6642 computations (37.1% saved)

regimes2.5s (33.9%)

Accuracy

Total 0.4b remaining (88.9%)

Threshold costs 0.4b (88.9%)

Counts

200 → 1

Compiler

Compiled 48850 to 34209 computations (30% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	55
1	40	55
2	46	55
3	48	55
4	49	55
5	48	55

end1.0ms (0%)

Compiler: Compiled 39 to 28 computations (28.2% saved)

sample1.6s (21.8%)

Algorithm

1×

intervals

Results

743.0ms	8000×	body	128	valid
111.0ms	1212×	body	128	invalid
59.0ms	730×	body	128	nan

Compiler

Compiled 662 to 447 computations (32.5% saved)

Details

analyze629.0ms (8.6%)

sample108.0ms (1.5%)

simplify75.0ms (1%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

series119.0ms (1.6%)

rewrite10.0ms (0.1%)

simplify212.0ms (2.9%)

prune261.0ms (3.6%)

localize20.0ms (0.3%)

series40.0ms (0.5%)

rewrite19.0ms (0.3%)

simplify92.0ms (1.3%)

prune350.0ms (4.8%)

localize21.0ms (0.3%)

series9.0ms (0.1%)

rewrite15.0ms (0.2%)

simplify85.0ms (1.2%)

prune410.0ms (5.6%)

localize25.0ms (0.3%)

series10.0ms (0.1%)

rewrite22.0ms (0.3%)

simplify135.0ms (1.9%)

prune532.0ms (7.3%)

regimes2.5s (33.9%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.6s (21.8%)

Profiling