Details

analyze1.0s (13.8%)

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)

sample1.8s (23.9%)

Results

1.4s	8256×	body	128	valid
343.0ms	1954×	body	128	invalid

Compiler

Compiled 83 to 62 computations (25.3% saved)

simplify73.0ms (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

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

5.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.5b	(+.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

▶

5.5b

(+.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 96 to 67 computations (30.2% saved)

localize14.0ms (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)
✓	5.2b	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)

series69.0ms (0.9%)

Counts

4 → 84

Calls

4 calls:

42.0ms	(/.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)
9.0ms	(fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)

rewrite9.0ms (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:

3.0ms	(-.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 (-.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)

simplify163.0ms (2.2%)

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 (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	165	11	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	11	177

Error

0.0b

Counts

177 → 11

Alt Table

Status	Error	Program
	6.1b	(+.f64 (-.f64 (.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))) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	6.5b	(+.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))
	27.5b	(+.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) 3) (pow.f64 x 3)) (+.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 (.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))
	8.5b	(+.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)))
	20.3b	(+.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)))
	8.5b	(+.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)))))
▶	0.6b	(+.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)))
	5.8b	(+.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))))
	5.7b	(+.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))
	5.7b	(+.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))
	5.7b	(+.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 5931 to 3787 computations (36.1% 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)
✓	5.5b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series37.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

28.0ms	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
8.0ms	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
1.0ms	(/.f64 83333333333333/1000000000000000 x)

rewrite17.0ms (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:

6.0ms	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
4.0ms	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
2.0ms	(/.f64 83333333333333/1000000000000000 x)

simplify92.0ms (1.2%)

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

prune303.0ms (4.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	163	5	168
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	167	12	179

Error

0.0b

Counts

179 → 12

Alt Table

Status	Error	Program
	0.8b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 z (.f64 (/.f64 z x) (+.f64 7936500793651/10000000000000000 y)))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	20.3b	(+.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)))
	6.5b	(+.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))
	13.8b	(+.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 (.f64 7936500793651/10000000000000000 7936500793651/10000000000000000) (.f64 y y))) (-.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	8.5b	(+.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)))))
	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)))
	5.7b	(+.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))
	0.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (.f64 83333333333333/1000000000000000 (/.f64 1 x)) (.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 83333333333333/1000000000000000) (/.f64 (sqrt.f64 83333333333333/1000000000000000) x)) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	27.5b	(+.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) 3) (pow.f64 x 3)) (+.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 (.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))
	5.7b	(+.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))
	5.7b	(+.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 6760 to 3790 computations (43.9% 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	(*.f64 (sqrt.f64 83333333333333/1000000000000000) (/.f64 (sqrt.f64 83333333333333/1000000000000000) x))
	0.3b	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
	5.5b	(.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))

rewrite11.0ms (0.1%)

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))

simplify89.0ms (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

prune1.3s (17.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	201	12	213

Error

0.0b

Counts

213 → 12

Alt Table

Status	Error	Program
	0.8b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 z (.f64 (/.f64 z x) (+.f64 7936500793651/10000000000000000 y)))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	20.3b	(+.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)))
	6.5b	(+.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))
	13.8b	(+.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 (.f64 7936500793651/10000000000000000 7936500793651/10000000000000000) (.f64 y y))) (-.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	8.5b	(+.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)))))
	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)))
	5.7b	(+.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))
▶	0.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (.f64 83333333333333/1000000000000000 (/.f64 1 x)) (.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 83333333333333/1000000000000000) (/.f64 (sqrt.f64 83333333333333/1000000000000000) x)) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	27.5b	(+.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) 3) (pow.f64 x 3)) (+.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 (.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))
	5.7b	(+.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))
	5.7b	(+.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 8706 to 5238 computations (39.8% 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)
✓	0.4b	(*.f64 83333333333333/1000000000000000 (/.f64 1 x))
	5.5b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(*.f64 83333333333333/1000000000000000 (/.f64 1 x))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 38

Calls

1 calls:

5.0ms

(*.f64 83333333333333/1000000000000000 (/.f64 1 x))

simplify77.0ms (1%)

Algorithm

1×	egg-herbie

Rules

429×	`unswap-sqr_binary64`
384×	`*-commutative_binary64`
363×	`fma-def_binary64`
273×	`fma-neg_binary64`
262×	`associate-l_binary64`

Counts

50 → 56

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	60	351
1	112	306
2	199	306
3	312	306
4	498	306
5	743	306
6	1677	306
7	2209	306
8	4008	306
9	4690	306
10	4907	306

prune363.0ms (4.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	191	12	203

Error

0.0b

Counts

203 → 12

Alt Table

Status	Error	Program
	0.8b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 z (.f64 (/.f64 z x) (+.f64 7936500793651/10000000000000000 y)))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	20.3b	(+.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)))
	6.5b	(+.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))
	13.8b	(+.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 (.f64 7936500793651/10000000000000000 7936500793651/10000000000000000) (.f64 y y))) (-.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	8.5b	(+.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)))))
	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)))
	5.7b	(+.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))
✓	0.6b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (.f64 83333333333333/1000000000000000 (/.f64 1 x)) (.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 83333333333333/1000000000000000) (/.f64 (sqrt.f64 83333333333333/1000000000000000) x)) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	27.5b	(+.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) 3) (pow.f64 x 3)) (+.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 (.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))
	5.7b	(+.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))
	5.7b	(+.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 7489 to 4297 computations (42.6% saved)

regimes1.4s (19.4%)

Accuracy

Total 0.4b remaining (87.8%)

Threshold costs 0.4b (87.8%)

Counts

149 → 1

Compiler

Compiled 34404 to 24276 computations (29.4% saved)

simplify3.0ms (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	24	50
1	37	50
2	43	50
3	45	50
4	46	50
5	45	50

end254.0ms (3.4%)

Compiler: Compiled 509 to 350 computations (31.2% saved)

Details

analyze1.0s (13.8%)

sample1.8s (23.9%)

simplify73.0ms (1%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

series69.0ms (0.9%)

rewrite9.0ms (0.1%)

simplify163.0ms (2.2%)

prune261.0ms (3.5%)

localize16.0ms (0.2%)

series37.0ms (0.5%)

rewrite17.0ms (0.2%)

simplify92.0ms (1.2%)

prune303.0ms (4.1%)

localize20.0ms (0.3%)

series9.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify89.0ms (1.2%)

prune1.3s (17.3%)

localize21.0ms (0.3%)

series2.0ms (0%)

rewrite7.0ms (0.1%)

simplify77.0ms (1%)

prune363.0ms (4.9%)

regimes1.4s (19.4%)

simplify3.0ms (0%)

end254.0ms (3.4%)

Profiling