Details

analyze656.0ms (4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	74.9%	25.1%	6
0%	56.1%	43.9%	7
0%	42.1%	57.9%	8
0%	31.6%	68.4%	9
0%	26.3%	73.7%	10
0%	21.9%	78.1%	11
0%	18.3%	81.7%	12
0%	15.2%	84.8%	13
0%	13.7%	86.3%	14

Compiler

Compiled 36 to 28 computations (22.2% saved)

sample7.4s (44.5%)

Symmetry

(sort x y z t)

Results

2.6s	4442×	body	512	valid
2.4s	10202×	body	128	invalid
1.6s	1833×	body	1024	valid
451.0ms	1131×	body	256	valid
194.0ms	850×	body	128	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify43.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-def_binary64`
529×	`associate-+r-_binary64`
510×	`associate-+l-_binary64`
481×	`associate--r+_binary64`
355×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	50
1	54	50
2	166	50
3	893	50
4	4070	50
5	4939	50
6	5040	50

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

4.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 136 to 100 computations (26.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	1.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	4.7b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
✓	5.4b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series65.0ms (0.4%)

Counts

4 → 4

Calls

4 calls:

17.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
17.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
16.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
16.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite66.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`sqrt-prod_binary64`
208×	`*-un-lft-identity_binary64`
168×	`prod-diff_binary64`
156×	`add-sqr-sqrt_binary64`
124×	`add-cube-cbrt_binary64`

Counts

4 → 300

Calls

4 calls:

13.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
8.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
8.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
7.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

simplify298.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

784×	`times-frac_binary64`
760×	`fma-neg_binary64`
360×	`exp-prod_binary64`
312×	`*-commutative_binary64`
308×	`fabs-mul_binary64`

Counts

304 → 253

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	9256
1	583	4524
2	1602	3684
3	3485	3684
4	4297	3684
5	4453	3684
6	4714	3684
7	4774	3684
8	5084	3684

prune658.0ms (4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	241	12	253
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	242	12	254

Error

0.9b

Counts

254 → 12

Alt Table

Status	Error	Program
	17.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 y 1))) (sqrt.f64 (sqrt.f64 (+.f64 y 1))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 y)) (.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 y))) (.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y))) (.f64 (cbrt.f64 (sqrt.f64 y)) (*.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y))))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	41.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))) (sqrt.f64 (cbrt.f64 (+.f64 z 1))) (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)) (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.4b	(+.f64 (+.f64 (+.f64 (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	3.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	4.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) 3))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (sqrt.f64 z))) (-.f64 (sqrt.f64 (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	3.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	2.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 12971 to 7384 computations (43.1% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	1.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	4.7b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
	5.4b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series14.0ms (0.1%)

Counts

1 → 1

Calls

1 calls:

13.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`distribute-lft-out_binary64`
16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

1 → 47

Calls

1 calls:

12.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

837×	`div-sub_binary64`
502×	`associate-+l+_binary64`
423×	`associate-+r+_binary64`
330×	`associate-+l-_binary64`
310×	`times-frac_binary64`

Counts

48 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	845
1	100	785
2	197	785
3	383	785
4	949	785
5	2306	785
6	4846	785
7	5785	785

prune783.0ms (4.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	229	6	235
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	234	13	247

Error

0.1b

Counts

247 → 13

Alt Table

Status	Error	Program
	3.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	2.4b	(+.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	2.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) 3))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	2.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	1.0b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	17.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 y 1))) (sqrt.f64 (sqrt.f64 (+.f64 y 1))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 y)) (.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 y))) (.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y))) (.f64 (cbrt.f64 (sqrt.f64 y)) (*.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y))))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	41.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))) (sqrt.f64 (cbrt.f64 (+.f64 z 1))) (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)) (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	2.4b	(+.f64 (+.f64 (+.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	2.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (sqrt.f64 z))) (-.f64 (sqrt.f64 (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	3.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 12402 to 7478 computations (39.7% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
	1.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	5.4b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series13.0ms (0.1%)

Counts

1 → 1

Calls

1 calls:

13.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`distribute-lft-out_binary64`
16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

1 → 47

Calls

1 calls:

8.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

837×	`div-sub_binary64`
502×	`associate-+l+_binary64`
423×	`associate-+r+_binary64`
330×	`associate-+l-_binary64`
310×	`times-frac_binary64`

Counts

48 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	845
1	100	785
2	197	785
3	383	785
4	949	785
5	2306	785
6	4846	785
7	5785	785

prune581.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	214	3	217
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	222	8	230

Error

0.0b

Counts

230 → 8

Alt Table

Status	Error	Program
	1.0b	(+.f64 (+.f64 (+.f64 (.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	1.0b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 3))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	0.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	2.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	2.4b	(+.f64 (+.f64 (+.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	2.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (sqrt.f64 z))) (-.f64 (sqrt.f64 (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 11105 to 7048 computations (36.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
	1.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series15.0ms (0.1%)

Counts

1 → 1

Calls

1 calls:

15.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`distribute-lft-out_binary64`
16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

1 → 47

Calls

1 calls:

7.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

837×	`div-sub_binary64`
502×	`associate-+l+_binary64`
423×	`associate-+r+_binary64`
330×	`associate-+l-_binary64`
310×	`times-frac_binary64`

Counts

48 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	845
1	100	785
2	197	785
3	383	785
4	949	785
5	2306	785
6	4846	785
7	5785	785

prune501.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	194	4	198
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	198	8	206

Error

0.0b

Counts

206 → 8

Alt Table

Status	Error	Program
	0.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (log.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	1.0b	(+.f64 (+.f64 (+.f64 (.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	0.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	2.4b	(+.f64 (+.f64 (+.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	0.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 3))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	2.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	0.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 9840 to 6577 computations (33.2% saved)

regimes4.1s (24.7%)

Accuracy

Total 0.0b remaining (20.4%)

Threshold costs 0.0b (20.4%)

Counts

249 → 1

Compiler

Compiled 158452 to 119467 computations (24.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	62
1	42	62
2	41	62

end983.0ms (5.9%)

Compiler: Compiled 561 to 443 computations (21% saved)

Details

analyze656.0ms (4%)

sample7.4s (44.5%)

simplify43.0ms (0.3%)

prune9.0ms (0.1%)

localize20.0ms (0.1%)

series65.0ms (0.4%)

rewrite66.0ms (0.4%)

simplify298.0ms (1.8%)

prune658.0ms (4%)

localize21.0ms (0.1%)

series14.0ms (0.1%)

rewrite15.0ms (0.1%)

simplify99.0ms (0.6%)

prune783.0ms (4.7%)

localize23.0ms (0.1%)

series13.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify97.0ms (0.6%)

prune581.0ms (3.5%)

localize23.0ms (0.1%)

series15.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify93.0ms (0.6%)

prune501.0ms (3%)

regimes4.1s (24.7%)

simplify3.0ms (0%)

end983.0ms (5.9%)

Profiling