Details

analyze609.0ms (8.1%)

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)

sample2.1s (27.2%)

Results

1.6s	8256×	body	128	valid
420.0ms	1980×	body	128	invalid

Compiler

Compiled 83 to 62 computations (25.3% saved)

simplify79.0ms (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

5.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.8b	(+.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

▶

5.8b

(+.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)

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)
✓	5.4b	(/.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:

43.0ms	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)
10.0ms	(fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)
9.0ms	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
8.0ms	(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)

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 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)

simplify166.0ms (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

prune264.0ms (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

0.1b

Counts

177 → 11

Alt Table

Status	Error	Program
	6.8b	(+.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))
	5.8b	(+.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))))
	26.2b	(+.f64 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000) 3)) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	11.3b	(+.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)))
	5.8b	(+.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) (/.f64 1 x)))
	5.9b	(+.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))
	11.5b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (sqrt.f64 x))))
	6.2b	(+.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))
	22.4b	(+.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 (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))
▶	0.3b	(+.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)))

Compiler

Compiled 5867 to 3747 computations (36.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
✓	0.3b	(/.f64 83333333333333/1000000000000000 x)
	0.3b	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
✓	2.9b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series36.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

27.0ms	(.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))
4.0ms	(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
2.0ms	(/.f64 83333333333333/1000000000000000 x)

simplify84.0ms (1.1%)

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

prune320.0ms (4.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	166	13	179

Error

0.0b

Counts

179 → 13

Alt Table

Status	Error	Program
	6.8b	(+.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))
	5.8b	(+.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))))
	10.5b	(+.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)))
	26.2b	(+.f64 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000) 3)) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
	11.3b	(+.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)))
	5.8b	(+.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) (/.f64 1 x)))
	0.8b	(+.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)))
▶	0.4b	(+.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (sqrt.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)))
	13.7b	(+.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)) (sqrt.f64 (+.f64 7936500793651/10000000000000000 y))) (sqrt.f64 (+.f64 7936500793651/10000000000000000 y)))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	11.5b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (sqrt.f64 x))))
	6.2b	(+.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))
	22.4b	(+.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 (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))

Compiler

Compiled 6830 to 3842 computations (43.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 83333333333333/1000000000000000 x)
✓	0.3b	(fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)
✓	0.5b	(*.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)))
	2.9b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series17.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

9.0ms

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

8.0ms

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

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
17×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 63

Calls

2 calls:

5.0ms

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

0.0ms

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

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

472×	`fma-def_binary64`
460×	`fma-neg_binary64`
446×	`unswap-sqr_binary64`
434×	`times-frac_binary64`
298×	`unsub-neg_binary64`

Counts

87 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1430
1	156	1139
2	391	1092
3	1280	1006
4	2781	1006
5	4149	1006
6	4949	1006

prune406.0ms (5.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	155	5	160
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	157	16	173

Error

0.0b

Counts

173 → 16

Alt Table

Status	Error	Program
	0.8b	(+.f64 (-.f64 (.f64 (.f64 (sqrt.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)))) (sqrt.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))))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (sqrt.f64 (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)))
	5.8b	(+.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) (/.f64 1 x)))
	6.8b	(+.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))
	5.8b	(+.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))))
	10.5b	(+.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)))
	11.3b	(+.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)))
	0.9b	(+.f64 (-.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 4) (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)))
	11.5b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (sqrt.f64 x))))
✓	0.4b	(+.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (sqrt.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)))
	13.7b	(+.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)) (sqrt.f64 (+.f64 7936500793651/10000000000000000 y))) (sqrt.f64 (+.f64 7936500793651/10000000000000000 y)))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	0.6b	(+.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (sqrt.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)))
	6.2b	(+.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))
	22.4b	(+.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)))
	0.8b	(+.f64 (-.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 5) (cbrt.f64 (sqrt.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)))
	6.2b	(+.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))
▶	0.6b	(+.f64 (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3)) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))

Compiler

Compiled 8363 to 5064 computations (39.4% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3))
✓	0.6b	(pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3)
	2.9b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series198.0ms (2.6%)

Counts

2 → 24

Calls

2 calls:

189.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3)

9.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`sqrt-prod_binary64`
64×	`add-sqr-sqrt_binary64`
27×	`cube-prod_binary64`
27×	`unpow-prod-down_binary64`
24×	`associate-r_binary64`

Counts

2 → 114

Calls

2 calls:

13.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3))

3.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3)

simplify174.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

372×	`times-frac_binary64`
316×	`associate-r_binary64`
255×	`associate-l_binary64`
253×	`associate-/l*_binary64`
249×	`associate-/r*_binary64`

Counts

138 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	305	6225
1	945	5658
2	4609	5531
3	4969	5520
4	4949	5520

prune544.0ms (7.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	3	11	14
Picked	1	0	1
Done	0	1	1
Total	193	16	209

Error

Counts

209 → 16

Alt Table

Status	Error	Program
	6.8b	(+.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))
	5.8b	(+.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 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3))) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	0.6b	(+.f64 (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3))) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	10.5b	(+.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)))
	11.3b	(+.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)))
	0.8b	(+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (pow.f64 (sqrt.f64 (fabs.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)))) 3)) (pow.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)))) 3)) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	0.6b	(+.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (sqrt.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)))
	1.6b	(+.f64 (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3)) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 z (.f64 (+.f64 7936500793651/10000000000000000 y) (/.f64 z x)))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	11.5b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (sqrt.f64 x))))
	5.8b	(+.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) (/.f64 1 x)))
✓	0.4b	(+.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (sqrt.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)))
	13.7b	(+.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)) (sqrt.f64 (+.f64 7936500793651/10000000000000000 y))) (sqrt.f64 (+.f64 7936500793651/10000000000000000 y)))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	6.2b	(+.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))
	0.8b	(+.f64 (-.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 5) (cbrt.f64 (sqrt.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)))
	6.2b	(+.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))

Compiler

Compiled 13580 to 9233 computations (32% saved)

regimes1.9s (25.1%)

Accuracy

Total 0.4b remaining (90%)

Threshold costs 0.4b (90%)

Counts

183 → 1

Compiler

Compiled 49855 to 34892 computations (30% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	50
1	42	50
2	53	50
3	59	50
4	63	50
5	64	50
6	63	50

end404.0ms (5.4%)

Compiler: Compiled 759 to 524 computations (31% saved)

Details

analyze609.0ms (8.1%)

sample2.1s (27.2%)

simplify79.0ms (1%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

series69.0ms (0.9%)

rewrite9.0ms (0.1%)

simplify166.0ms (2.2%)

prune264.0ms (3.5%)

localize18.0ms (0.2%)

series36.0ms (0.5%)

rewrite19.0ms (0.3%)

simplify84.0ms (1.1%)

prune320.0ms (4.2%)

localize20.0ms (0.3%)

series17.0ms (0.2%)

rewrite9.0ms (0.1%)

simplify88.0ms (1.2%)

prune406.0ms (5.4%)

localize23.0ms (0.3%)

series198.0ms (2.6%)

rewrite26.0ms (0.3%)

simplify174.0ms (2.3%)

prune544.0ms (7.2%)

regimes1.9s (25.1%)

simplify4.0ms (0%)

end404.0ms (5.4%)

Profiling