Details

analyze346.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample1.4s (27.5%)

Results

1.2s	7946×	body	128	valid
138.0ms	972×	body	128	invalid
82.0ms	310×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1220×	`fma-neg_binary64`
367×	`fma-def_binary64`
351×	`times-frac_binary64`
266×	`associate-/l*_binary64`
254×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	69	22
3	160	22
4	264	22
5	433	22
6	744	22
7	1341	22
8	2769	22
9	4702	22

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

27.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
	27.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 111 to 75 computations (32.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 a (.f64 c -3))
✓	0.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	27.2b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b)

series96.0ms (1.8%)

Counts

4 → 64

Calls

4 calls:

53.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
37.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b)
4.0ms	(.f64 a (.f64 c -3))
1.0ms	(/.f64 1/3 a)

rewrite65.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

737×	`prod-diff_binary64`
143×	`egg-rr`
140×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`
133×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	282	47
2	3646	47

Stop Event

1×	node limit

Counts

4 → 143

Calls

4 calls:

62.0ms	(.f64 a (.f64 c -3))
62.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
62.0ms	(/.f64 1/3 a)
62.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b)

simplify40.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
459×	`associate-/l*_binary64`
392×	`associate-/r*_binary64`
316×	`fma-def_binary64`
174×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1538
1	369	1520
2	1302	1491

Stop Event

1×	node limit

Counts

207 → 192

prune139.0ms (2.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	175	17	192
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	177	17	194

Error

1.0b

Counts

194 → 17

Alt Table

Status	Error	Program
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (sqrt.f64 (/.f64 1/3 a)) 2))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 -3 (*.f64 c a)))) b) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (cbrt.f64 (/.f64 1/3 a)) 3))
▶	6.7b	(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a)) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	27.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (pow.f64 (/.f64 1/3 a) 3) 1/3))
	6.7b	(neg.f64 (+.f64 (.f64 9/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 135/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (.f64 3/8 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b 3))) (*.f64 1/2 (/.f64 c b))))))
	28.7b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
	7.0b	(.f64 (-.f64 (.f64 (/.f64 -3/2 b) (.f64 c a)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	29.3b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	7.0b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -3)))) b) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 1/3 (pow.f64 a -1)))
	28.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (-.f64 (exp.f64 (log1p.f64 (/.f64 1/3 a))) 1))
	28.6b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 -1 b b)) (/.f64 1/3 a))
	9.0b	(.f64 (fma.f64 -3/2 (.f64 (/.f64 c b) a) (fma.f64 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) -9/8 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) -27/16))) (/.f64 1/3 a))
	9.1b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (exp.f64 (log.f64 (/.f64 1/3 a))))

Compiler

Compiled 5707 to 3691 computations (35.3% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3))
✓	0.4b	(/.f64 (*.f64 c c) (pow.f64 b 3))
✓	0.4b	(/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a))
✓	0.4b	(/.f64 (pow.f64 c 4) (pow.f64 b 7))

series222.0ms (4.2%)

Counts

4 → 96

Calls

4 calls:

84.0ms	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3))
73.0ms	(/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a))
37.0ms	(/.f64 (pow.f64 c 4) (pow.f64 b 7))
28.0ms	(/.f64 (*.f64 c c) (pow.f64 b 3))

rewrite35.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

205×	`add-sqr-sqrt_binary64`
203×	`log1p-expm1-u_binary64`
203×	`expm1-log1p-u_binary64`
197×	`add-cbrt-cube_binary64`
194×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	49
1	449	49

Stop Event

1×	node limit

Counts

4 → 107

Calls

4 calls:

34.0ms	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3))
34.0ms	(/.f64 (*.f64 c c) (pow.f64 b 3))
34.0ms	(/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a))
34.0ms	(/.f64 (pow.f64 c 4) (pow.f64 b 7))

simplify61.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

855×	`associate-/l*_binary64`
424×	`associate-l_binary64`
418×	`associate-/r*_binary64`
363×	`associate-r_binary64`
200×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	1284
1	59	1284
2	177	1284
3	809	1284
4	4886	1284
5	4988	1284

Stop Event

1×	node limit

Counts

203 → 112

prune238.0ms (4.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	110	19	129

Error

1.0b

Counts

129 → 19

Alt Table

Status	Error	Program
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (sqrt.f64 (/.f64 1/3 a)) 2))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 -3 (*.f64 c a)))) b) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (cbrt.f64 (/.f64 1/3 a)) 3))
✓	6.7b	(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a)) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	27.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (pow.f64 (/.f64 1/3 a) 3) 1/3))
▶	6.7b	(neg.f64 (+.f64 (.f64 9/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 135/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (.f64 3/8 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b 3))) (*.f64 1/2 (/.f64 c b))))))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 1/3 (pow.f64 a -1)))
	7.0b	(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a)) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (pow.f64 c 4) (pow.f64 b -7)) (pow.f64 a 3)))) 1) (.f64 3/8 (.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a)))))
	15.9b	(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a)) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (log.f64 (+.f64 1 (expm1.f64 (.f64 (*.f64 c c) (pow.f64 b -3))))) a)))))
	28.7b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
	7.0b	(.f64 (-.f64 (.f64 (/.f64 -3/2 b) (.f64 c a)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	29.3b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	7.0b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -3)))) b) (/.f64 1/3 a))
	28.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (-.f64 (exp.f64 (log1p.f64 (/.f64 1/3 a))) 1))
	28.6b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 -1 b b)) (/.f64 1/3 a))
	9.0b	(.f64 (fma.f64 -3/2 (.f64 (/.f64 c b) a) (fma.f64 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) -9/8 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) -27/16))) (/.f64 1/3 a))
	9.1b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (exp.f64 (log.f64 (/.f64 1/3 a))))

Compiler

Compiled 6566 to 4416 computations (32.7% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (pow.f64 c 3) (pow.f64 a 2))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))

series231.0ms (4.4%)

Counts

4 → 0

Calls

4 calls:

86.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
75.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))
56.0ms	(/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3))
14.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 2))

rewrite32.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

225×	`log1p-expm1-u_binary64`
225×	`expm1-log1p-u_binary64`
224×	`add-sqr-sqrt_binary64`
216×	`add-cbrt-cube_binary64`
215×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	515	55

Stop Event

1×	node limit

Counts

4 → 72

Calls

4 calls:

31.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 2))
31.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
31.0ms	(/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3))
31.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

72 → 72

prune172.0ms (3.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	2	15	17
Picked	1	0	1
Done	0	1	1
Total	72	19	91

Error

1.0b

Counts

91 → 19

Alt Table

Status	Error	Program
	7.9b	(neg.f64 (+.f64 (.f64 9/16 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b -5)))) 1)) (+.f64 (.f64 135/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (.f64 3/8 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b 3))) (*.f64 1/2 (/.f64 c b))))))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -3)))) b) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (sqrt.f64 (/.f64 1/3 a)) 2))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 -3 (*.f64 c a)))) b) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (cbrt.f64 (/.f64 1/3 a)) 3))
✓	6.7b	(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a)) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	28.7b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
	7.0b	(.f64 (-.f64 (.f64 (/.f64 -3/2 b) (.f64 c a)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	29.3b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
▶	7.0b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/3 a))
	9.0b	(.f64 (fma.f64 -3/2 (.f64 (/.f64 c b) a) (fma.f64 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) -9/8 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) -27/16))) (/.f64 1/3 a))
	12.6b	(neg.f64 (+.f64 (.f64 9/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 135/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (.f64 3/8 (log.f64 (+.f64 1 (expm1.f64 (.f64 (.f64 a (.f64 c c)) (pow.f64 b -3)))))) (*.f64 1/2 (/.f64 c b))))))
	27.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (pow.f64 (/.f64 1/3 a) 3) 1/3))
	12.0b	(neg.f64 (+.f64 (.f64 9/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 135/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (.f64 3/8 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 a (.f64 c c)) (pow.f64 b -3)))) 1)) (*.f64 1/2 (/.f64 c b))))))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 1/3 (pow.f64 a -1)))
	28.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (-.f64 (exp.f64 (log1p.f64 (/.f64 1/3 a))) 1))
	28.6b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 -1 b b)) (/.f64 1/3 a))
	9.1b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (exp.f64 (log.f64 (/.f64 1/3 a))))

Compiler

Compiled 4862 to 3497 computations (28.1% saved)

localize34.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/3 a))
✓	0.4b	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
	0.4b	(/.f64 1/3 a)

series165.0ms (3.1%)

Counts

3 → 36

Calls

3 calls:

87.0ms

(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))

61.0ms

(*.f64 (neg.f64 (+.f64 (*.f64 3/2 (/.f64 (*.f64 c a) b)) (+.f64 (*.f64 9/8 (/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (*.f64 405/128 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (*.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/3 a))

16.0ms

(*.f64 (pow.f64 c 3) (pow.f64 a 3))

rewrite40.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

431×	`log1p-expm1-u_binary64`
431×	`expm1-log1p-u_binary64`
404×	`add-log-exp_binary64`
392×	`pow1_binary64`
133×	`unpow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	86
1	954	86

Stop Event

1×	node limit

Counts

3 → 44

Calls

3 calls:

38.0ms

(*.f64 (neg.f64 (+.f64 (*.f64 3/2 (/.f64 (*.f64 c a) b)) (+.f64 (*.f64 9/8 (/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (*.f64 405/128 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (*.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/3 a))

38.0ms

(*.f64 (pow.f64 c 3) (pow.f64 a 3))

38.0ms

(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary64`
390×	`distribute-rgt-neg-in_binary64`
285×	`unswap-sqr_binary64`
262×	`distribute-neg-frac_binary64`
227×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	48	1446
1	152	1446
2	521	1392
3	2938	1392

Stop Event

1×	node limit

Counts

80 → 57

prune140.0ms (2.7%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	5	12	17
Picked	1	0	1
Done	0	1	1
Total	77	21	98

Error

1.0b

Counts

98 → 21

Alt Table

Status	Error	Program
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (sqrt.f64 (/.f64 1/3 a)) 2))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 -3 (*.f64 c a)))) b) (/.f64 1/3 a))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (cbrt.f64 (/.f64 1/3 a)) 3))
✓	6.7b	(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a)) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	27.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (pow.f64 (/.f64 1/3 a) 3) 1/3))
	7.1b	(cbrt.f64 (pow.f64 (.f64 (neg.f64 (fma.f64 3/2 (/.f64 c (/.f64 b a)) (fma.f64 9/8 (.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b -3)) (fma.f64 (.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b -7)) 405/128 (/.f64 (.f64 27/16 (pow.f64 (*.f64 c a) 3)) (pow.f64 b 5)))))) (/.f64 1/3 a)) 3))
	25.6b	(log.f64 (+.f64 1 (expm1.f64 (.f64 (neg.f64 (fma.f64 3/2 (/.f64 c (/.f64 b a)) (fma.f64 9/8 (.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b -3)) (fma.f64 (.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b -7)) 405/128 (/.f64 (.f64 27/16 (pow.f64 (*.f64 c a) 3)) (pow.f64 b 5)))))) (/.f64 1/3 a)))))
	12.0b	(neg.f64 (+.f64 (.f64 9/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 135/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (.f64 3/8 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 a (.f64 c c)) (pow.f64 b -3)))) 1)) (*.f64 1/2 (/.f64 c b))))))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 1/3 (pow.f64 a -1)))
	7.4b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (log.f64 (exp.f64 (.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b -7))))) (.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/3 a))
	28.6b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 -1 b b)) (/.f64 1/3 a))
	7.0b	(/.f64 (.f64 (neg.f64 (fma.f64 3/2 (/.f64 c (/.f64 b a)) (fma.f64 9/8 (.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b -3)) (fma.f64 (.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b -7)) 405/128 (/.f64 (.f64 27/16 (pow.f64 (*.f64 c a) 3)) (pow.f64 b 5)))))) 1/3) a)
	29.3b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	10.2b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (-.f64 (exp.f64 (log1p.f64 (/.f64 1/3 a))) 1))
	7.7b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (exp.f64 (log.f64 (/.f64 1/3 a))))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -3)))) b) (/.f64 1/3 a))
	28.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (-.f64 (exp.f64 (log1p.f64 (/.f64 1/3 a))) 1))
	28.7b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
	7.5b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (pow.f64 (cbrt.f64 (/.f64 1/3 a)) 3))
	7.0b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (pow.f64 (.f64 a 3) -1))
	27.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (exp.f64 (log.f64 (/.f64 1/3 a))))

Compiler

Compiled 4760 to 3353 computations (29.6% saved)

regimes1.0s (19.7%)

Accuracy

Total 4.3b remaining (84.8%)

Threshold costs 0b (0%)

Counts

116 → 2

Compiler

Compiled 25721 to 19231 computations (25.2% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 20 to 14 computations (30% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	127
1	77	125
2	97	125
3	106	125
4	112	125
5	114	125

Stop Event

1×

saturated

end544.0ms (10.4%)

Compiler: Compiled 1001 to 721 computations (28% saved)

Details

analyze346.0ms (6.6%)

sample1.4s (27.5%)

simplify31.0ms (0.6%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series96.0ms (1.8%)

rewrite65.0ms (1.2%)

simplify40.0ms (0.8%)

prune139.0ms (2.7%)

localize27.0ms (0.5%)

series222.0ms (4.2%)

rewrite35.0ms (0.7%)

simplify61.0ms (1.2%)

prune238.0ms (4.5%)

localize29.0ms (0.5%)

series231.0ms (4.4%)

rewrite32.0ms (0.6%)

simplify7.0ms (0.1%)

prune172.0ms (3.3%)

localize34.0ms (0.6%)

series165.0ms (3.1%)

rewrite40.0ms (0.8%)

simplify44.0ms (0.8%)

prune140.0ms (2.7%)

regimes1.0s (19.7%)

bsearch7.0ms (0.1%)

simplify5.0ms (0.1%)

end544.0ms (10.4%)

Profiling