Details

analyze107.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
49.9%	49.9%	0.1%	2
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	25%	25.1%	5
49.9%	25%	25.1%	6
49.9%	25%	25.1%	7
49.9%	12.5%	37.6%	8
49.9%	12.5%	37.6%	9
49.9%	12.5%	37.6%	10
49.9%	6.2%	43.8%	11
49.9%	6.2%	43.8%	12
49.9%	6.2%	43.8%	13
49.9%	3.1%	47%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample1.3s (20.1%)

Infinites

68.9% of outputs are infinite.

Results

1.1s	8256×	body	128	valid
67.0ms	553×	body	128	invalid

Compiler

Compiled 83 to 62 computations (25.3% saved)

simplify75.0ms (1.2%)

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

prune5.0ms (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

3.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.3b	(+.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))
▶	3.3b	(+.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

3.3b

(+.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))

▶

3.3b

(+.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)
✓	0.1b	(-.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)
✓	3.3b	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)

series70.0ms (1.1%)

Counts

4 → 84

Calls

4 calls:

43.0ms	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)
8.0ms	(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 (0.2%)

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 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)

simplify165.0ms (2.5%)

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

prune270.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	168	8	176
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	170	8	178

Error

0.0b

Counts

178 → 8

Alt Table

Status	Error	Program
	3.6b	(+.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))
	3.9b	(+.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))
	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)))
	3.3b	(+.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))
	11.3b	(+.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)))))
	18.2b	(+.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)))
	3.3b	(+.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))
▶	3.2b	(+.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 5679 to 3613 computations (36.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
✓	0.3b	(/.f64 83333333333333/1000000000000000 x)
✓	2.4b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
✓	2.6b	(+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000))

series79.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

49.0ms

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

28.0ms

(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

1.0ms

(/.f64 83333333333333/1000000000000000 x)

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 84

Calls

3 calls:

9.0ms

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

7.0ms

(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

2.0ms

(/.f64 83333333333333/1000000000000000 x)

simplify111.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

266×	`associate-l_binary64`
238×	`cancel-sign-sub-inv_binary64`
225×	`associate-r_binary64`
225×	`fma-neg_binary64`
221×	`associate-/l*_binary64`

Counts

156 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	3156
1	706	2906
2	2550	2583
3	4664	2583
4	5039	2583

prune262.0ms (4.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	163	8	171

Error

0.0b

Counts

171 → 8

Alt Table

Status	Error	Program
	3.3b	(+.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))
	3.7b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (pow.f64 (.f64 z (.f64 (/.f64 z x) (+.f64 7936500793651/10000000000000000 y))) 1)) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	3.6b	(+.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))
	3.9b	(+.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))
	12.9b	(+.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 62988044847622952881909801/100000000000000000000000000000000 (.f64 y y))) (-.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)))
	11.3b	(+.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)))))
▶	3.3b	(+.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)))

Compiler

Compiled 6672 to 3855 computations (42.2% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 83333333333333/1000000000000000 x)
✓	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)))
	2.4b	(.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
	2.6b	(+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000))

series8.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

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

25×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
16×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 53

Calls

1 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)))

simplify85.0ms (1.3%)

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

65 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	1095
1	155	896
2	390	851
3	1280	774
4	2781	774
5	4149	774
6	4949	774

prune432.0ms (6.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	199	11	210

Error

0.0b

Counts

210 → 11

Alt Table

Status	Error	Program
	3.5b	(+.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)))
	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)))
▶	3.3b	(+.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))
	3.7b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (pow.f64 (.f64 z (.f64 (/.f64 z x) (+.f64 7936500793651/10000000000000000 y))) 1)) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	3.6b	(+.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))
	3.9b	(+.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))
	12.9b	(+.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 62988044847622952881909801/100000000000000000000000000000000 (.f64 y y))) (-.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	3.6b	(+.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)))
	3.4b	(+.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)))) (.f64 (sqrt.f64 (cbrt.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)))
	11.3b	(+.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)))))
✓	3.3b	(+.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)))

Compiler

Compiled 10172 to 6128 computations (39.8% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(-.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)
✓	0.5b	(*.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)))
	3.3b	(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)

series9.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(*.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)))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
30×	`sqrt-prod_binary64`
23×	`*-un-lft-identity_binary64`
16×	`pow1_binary64`
12×	`swap-sqr_binary64`

Counts

1 → 69

Calls

1 calls:

19.0ms

(*.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)))

simplify121.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

461×	`associate-+l+_binary64`
238×	`associate-+l-_binary64`
235×	`associate--l+_binary64`
232×	`associate-l_binary64`
221×	`sub-neg_binary64`

Counts

81 → 93

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	121	2138
1	247	1914
2	712	1757
3	2106	1666
4	4592	1650
5	5025	1650

prune775.0ms (12%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	317	1	318
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	317	12	329

Error

Counts

329 → 12

Alt Table

Status	Error	Program
	3.5b	(+.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)))
	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)))
✓	3.3b	(+.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))
	3.7b	(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (pow.f64 (.f64 z (.f64 (/.f64 z x) (+.f64 7936500793651/10000000000000000 y))) 1)) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	3.6b	(+.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))
	3.9b	(+.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))
	12.9b	(+.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 62988044847622952881909801/100000000000000000000000000000000 (.f64 y y))) (-.f64 7936500793651/10000000000000000 y))) (.f64 (/.f64 z x) -13888888888889/5000000000000000)))
	3.6b	(+.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)))
	3.4b	(+.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)))) (.f64 (sqrt.f64 (cbrt.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)))
	11.3b	(+.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)))))
✓	3.3b	(+.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)))
	3.3b	(+.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (sqrt.f64 x)))) (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (sqrt.f64 x)))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))

Compiler

Compiled 13844 to 8869 computations (35.9% saved)

regimes2.1s (32.9%)

Accuracy

Total 0.4b remaining (87.7%)

Threshold costs 0.4b (87.7%)

Counts

214 → 2

Compiler

Compiled 51528 to 36622 computations (28.9% saved)

bsearch28.0ms (0.4%)

Steps

Iters	Range		Point
2	2.7459805274957443e+67	1.0357461845557803e+68	4.0281667929952995e+67

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`mul-1-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	64
1	44	64
2	46	64
3	47	64
4	48	64
5	45	64

end293.0ms (4.5%)

Compiler: Compiled 589 to 405 computations (31.2% saved)

Details

analyze107.0ms (1.7%)

sample1.3s (20.1%)

simplify75.0ms (1.2%)

prune5.0ms (0.1%)

localize15.0ms (0.2%)

series70.0ms (1.1%)

rewrite11.0ms (0.2%)

simplify165.0ms (2.5%)

prune270.0ms (4.2%)

localize18.0ms (0.3%)

series79.0ms (1.2%)

rewrite24.0ms (0.4%)

simplify111.0ms (1.7%)

prune262.0ms (4.1%)

localize20.0ms (0.3%)

series8.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify85.0ms (1.3%)

prune432.0ms (6.7%)

localize19.0ms (0.3%)

series9.0ms (0.1%)

rewrite29.0ms (0.4%)

simplify121.0ms (1.9%)

prune775.0ms (12%)

regimes2.1s (32.9%)

bsearch28.0ms (0.4%)

simplify4.0ms (0.1%)

end293.0ms (4.5%)

Profiling