Details

analyze683.0ms (8.5%)

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)

sample1.6s (20.4%)

Results

1.3s	8256×	body	128	valid
299.0ms	1988×	body	128	invalid

Compiler

Compiled 83 to 62 computations (25.3% saved)

simplify77.0ms (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

6.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.1b	(+.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))
▶	6.1b	(+.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

6.1b

(+.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))

▶

6.1b

(+.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)
✓	5.7b	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)

series83.0ms (1%)

Counts

4 → 84

Calls

4 calls:

40.0ms	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)
27.0ms	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
8.0ms	(fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)
8.0ms	(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)

rewrite11.0ms (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 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)
3.0ms	(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)
0.0ms	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
0.0ms	(fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)

simplify154.0ms (1.9%)

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

prune266.0ms (3.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	163	13	176
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	164	14	178

Error

0.0b

Counts

178 → 14

Alt Table

Status	Error	Program
	11.1b	(+.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)))))
	10.2b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (-.f64 (+.f64 83333333333333/1000000000000000 (.f64 7936500793651/10000000000000000 (pow.f64 z 2))) (.f64 13888888888889/5000000000000000 z)) x))
	11.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))) x))
	20.4b	(+.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)))
	19.8b	(+.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))
	6.2b	(+.f64 (-.f64 (*.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))) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	11.1b	(+.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)))
	6.1b	(+.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))
	6.6b	(+.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 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	6.1b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 1 (/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))))
▶	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)))
	7.3b	(+.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))
	6.2b	(+.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))
	6.5b	(+.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))

Compiler

Compiled 6071 to 3891 computations (35.9% saved)

localize16.0ms (0.2%)

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)
✓	0.4b	(/.f64 83333333333333/1000000000000000 x)
✓	4.4b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series39.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

31.0ms	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
6.0ms	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
1.0ms	(/.f64 83333333333333/1000000000000000 x)

rewrite18.0ms (0.2%)

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))
4.0ms	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
2.0ms	(/.f64 83333333333333/1000000000000000 x)

simplify81.0ms (1%)

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

prune293.0ms (3.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	168	14	182

Error

0.0b

Counts

182 → 14

Alt Table

Status	Error	Program
	11.1b	(+.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)))))
	10.2b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (-.f64 (+.f64 83333333333333/1000000000000000 (.f64 7936500793651/10000000000000000 (pow.f64 z 2))) (.f64 13888888888889/5000000000000000 z)) x))
	11.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))) x))
	20.4b	(+.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)))
	19.8b	(+.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))
	6.2b	(+.f64 (-.f64 (*.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))) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	11.1b	(+.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)))
	6.1b	(+.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))
	6.6b	(+.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 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
▶	6.1b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 1 (/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))))
✓	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)))
	7.3b	(+.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))
	6.2b	(+.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))
	6.5b	(+.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))

Compiler

Compiled 6784 to 3825 computations (43.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)
✓	0.2b	(/.f64 1 (/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)))
	0.3b	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
✓	5.6b	(/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))

series208.0ms (2.6%)

Counts

2 → 72

Calls

2 calls:

163.0ms

(/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))

45.0ms

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

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms

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

2.0ms

(/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))

simplify140.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

391×	`distribute-rgt-in_binary64`
386×	`cancel-sign-sub-inv_binary64`
206×	`unswap-sqr_binary64`
160×	`sub-neg_binary64`
159×	`associate-/r*_binary64`

Counts

179 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	303	6149
1	788	5564
2	2919	5376
3	5048	5376

prune536.0ms (6.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	290	2	292
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	293	13	306

Error

0.0b

Counts

306 → 13

Alt Table

Status	Error	Program
	11.1b	(+.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)))))
	10.2b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (-.f64 (+.f64 83333333333333/1000000000000000 (.f64 7936500793651/10000000000000000 (pow.f64 z 2))) (.f64 13888888888889/5000000000000000 z)) x))
	11.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))) x))
	20.4b	(+.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)))
	19.8b	(+.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))
	6.2b	(+.f64 (-.f64 (*.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))) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	6.6b	(+.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 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	6.1b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (/.f64 1 x) (/.f64 1 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))))
✓	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)))
	7.3b	(+.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))
▶	6.1b	(+.f64 (-.f64 (+.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000) x) (/.f64 1 (/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))))
	6.2b	(+.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))
	6.5b	(+.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))

Compiler

Compiled 11464 to 7643 computations (33.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (+.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000) x)
✓	0.2b	(+.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000)
	0.2b	(/.f64 1 (/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)))
	5.6b	(/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))

series25.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

13.0ms	(+.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000)
11.0ms	(-.f64 (+.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000) x)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`prod-diff_binary64`
26×	`associate-+l+_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`

Counts

2 → 72

Calls

2 calls:

10.0ms	(+.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000)
7.0ms	(-.f64 (+.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000) x)

simplify104.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
621×	`distribute-rgt-in_binary64`
583×	`distribute-lft-in_binary64`
457×	`fma-neg_binary64`
260×	`cancel-sign-sub-inv_binary64`

Counts

96 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	1762
1	383	1211
2	1256	1152
3	4713	1152
4	4993	1152
5	4886	1152

prune580.0ms (7.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	342	2	344
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	345	12	357

Error

0.0b

Counts

357 → 12

Alt Table

Status	Error	Program
	11.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))) x))
	20.4b	(+.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)))
	6.2b	(+.f64 (-.f64 (*.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))) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	10.1b	(+.f64 (-.f64 (+.f64 (.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000) x) (/.f64 1 (/.f64 x (-.f64 (+.f64 83333333333333/1000000000000000 (.f64 7936500793651/10000000000000000 (pow.f64 z 2))) (*.f64 13888888888889/5000000000000000 z)))))
	6.6b	(+.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 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	6.1b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (/.f64 1 x) (/.f64 1 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))))
	11.1b	(+.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)))))
	6.2b	(+.f64 (-.f64 (+.f64 (.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (.f64 1/2 1))) (log.f64 x)) 91893853320467/100000000000000) x) (/.f64 1 (/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))))
✓	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)))
	7.3b	(+.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))
	6.2b	(+.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))
	6.5b	(+.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))

Compiler

Compiled 13296 to 8988 computations (32.4% saved)

regimes2.8s (34.6%)

Accuracy

Total 0.4b remaining (87.1%)

Threshold costs 0.4b (87.1%)

Counts

255 → 1

Compiler

Compiled 60087 to 43485 computations (27.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
4×	`*-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	22	43
1	34	43
2	40	43
3	42	43
4	43	43
5	42	43

end236.0ms (2.9%)

Compiler: Compiled 460 to 324 computations (29.6% saved)

Details

analyze683.0ms (8.5%)

sample1.6s (20.4%)

simplify77.0ms (1%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

series83.0ms (1%)

rewrite11.0ms (0.1%)

simplify154.0ms (1.9%)

prune266.0ms (3.3%)

localize16.0ms (0.2%)

series39.0ms (0.5%)

rewrite18.0ms (0.2%)

simplify81.0ms (1%)

prune293.0ms (3.6%)

localize14.0ms (0.2%)

series208.0ms (2.6%)

rewrite17.0ms (0.2%)

simplify140.0ms (1.7%)

prune536.0ms (6.6%)

localize15.0ms (0.2%)

series25.0ms (0.3%)

rewrite21.0ms (0.3%)

simplify104.0ms (1.3%)

prune580.0ms (7.2%)

regimes2.8s (34.6%)

simplify3.0ms (0%)

end236.0ms (2.9%)

Profiling