Details

analyze198.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 43 to 28 computations (34.9% saved)

sample49.0ms (0.2%)

Algorithm

1×

intervals

Results

18.0ms	205×	body	128	valid
6.0ms	256×	pre	128	true
6.0ms	22×	body	512	valid
5.0ms	19×	body	1024	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 78 to 51 computations (34.6% saved)

simplify45.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64`
817×	`distribute-rgt-in_binary64`
748×	`distribute-lft-in_binary64`
537×	`div-sub_binary64`
535×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	39
2	110	37
3	435	37
4	1672	37
5	2494	37
6	3358	37
7	5392	37

prune5.0ms (0%)

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

21.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	21.3b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
	26.2b	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

Status

Error

Program

▶

21.3b

(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)

26.2b

(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

Compiler

Compiled 180 to 106 computations (41.1% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	13.8b	(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
✓	19.4b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series829.0ms (3.9%)

Counts

3 → 108

Calls

3 calls:

505.0ms

(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

304.0ms

(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

20.0ms

(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

12.0ms

(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

5.0ms

(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))

0.0ms

(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

simplify211.0ms (1%)

Algorithm

1×	egg-herbie

Rules

561×	`+-commutative_binary64`
490×	`fma-def_binary64`
487×	`associate-+r+_binary64`
392×	`*-commutative_binary64`
294×	`associate-*r/_binary64`

Counts

175 → 205

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1400	19973
1	5450	19973

prune470.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	201	4	205
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	203	4	207

Error

0.2b

Counts

207 → 4

Alt Table

Status	Error	Program
	22.5b	(/.f64 (-.f64 (+.f64 1 (/.f64 beta (+.f64 beta (+.f64 2 alpha)))) (/.f64 alpha (+.f64 beta (+.f64 2 alpha)))) 2)
	53.2b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)))))))))))))))))))))))) 2)
	48.1b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
▶	13.7b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)

Compiler

Compiled 25129 to 16228 computations (35.4% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.3b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	13.8b	(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

series901.0ms (4.2%)

Counts

3 → 108

Calls

3 calls:

511.0ms

(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

340.0ms

(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))

49.0ms

(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
24×	`associate-/l*_binary64`

Counts

3 → 169

Calls

3 calls:

9.0ms

(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))

5.0ms

(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))

0.0ms

(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

simplify246.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-def_binary64`
477×	`associate-+r+_binary64`
326×	`associate-*r/_binary64`
177×	`associate-/l*_binary64`
171×	`associate-/r*_binary64`

Counts

277 → 298

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1591	25853
1	5046	25853

prune546.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	297	1	298
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	298	4	302

Error

0.2b

Counts

302 → 4

Alt Table

Status	Error	Program
▶	13.7b	(/.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) 2)
	22.5b	(/.f64 (-.f64 (+.f64 1 (/.f64 beta (+.f64 beta (+.f64 2 alpha)))) (/.f64 alpha (+.f64 beta (+.f64 2 alpha)))) 2)
	53.2b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)))))))))))))))))))))))) 2)
	48.1b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

Compiler

Compiled 30717 to 19033 computations (38% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
	0.3b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	3.9b	(log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))
	13.8b	(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

series586.0ms (2.7%)

Counts

1 → 36

Calls

1 calls:

585.0ms

(log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log-prod_binary64`
4×	`log-pow_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`exp-prod_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

(log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))

simplify134.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-def_binary64`
441×	`associate-*l/_binary64`
266×	`+-commutative_binary64`
241×	`*-commutative_binary64`
229×	`associate-+r+_binary64`

Counts

54 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	795	9427
1	3051	9078
2	5369	9078

prune950.0ms (4.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	373	2	375
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	375	4	379

Error

0.2b

Counts

379 → 4

Alt Table

Status	Error	Program
	22.5b	(/.f64 (-.f64 (+.f64 1 (/.f64 beta (+.f64 beta (+.f64 2 alpha)))) (/.f64 alpha (+.f64 beta (+.f64 2 alpha)))) 2)
	48.1b	(/.f64 (/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha) 2)
	53.2b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)))))))))))))))))))))))) 2)
▶	13.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))) (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))))) 2)

Compiler

Compiled 42840 to 27164 computations (36.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f64 (.f64 (.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))) (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))))
	0.3b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
	3.9b	(log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))
	13.8b	(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

series538.0ms (2.5%)

Counts

1 → 36

Calls

1 calls:

537.0ms

(cbrt.f64 (*.f64 (*.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))) (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`rem-cbrt-cube_binary64`
1×	`pow3_binary64`
1×	`cbrt-prod_binary64`

Counts

1 → 12

Calls

1 calls:

5.0ms

(cbrt.f64 (*.f64 (*.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))) (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))))

simplify588.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
439×	`associate-*l/_binary64`
266×	`+-commutative_binary64`
240×	`*-commutative_binary64`
229×	`associate-+r+_binary64`

Counts

48 → 65

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	780	9787
1	3034	8854
2	5327	8854

prune2.7s (12.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	712	1	713
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	713	4	717

Error

0.2b

Counts

717 → 4

Alt Table

Status	Error	Program
	22.5b	(/.f64 (-.f64 (+.f64 1 (/.f64 beta (+.f64 beta (+.f64 2 alpha)))) (/.f64 alpha (+.f64 beta (+.f64 2 alpha)))) 2)
	48.1b	(/.f64 (/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha) 2)
	53.2b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)))))))))))))))))))))))) 2)
	13.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))) (.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)) (log.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)))))))) 2)

Compiler

Compiled 127264 to 76561 computations (39.8% saved)

regimes10.3s (48.3%)

Accuracy

Total 1.2b remaining (91.5%)

Threshold costs 0b (0%)

Counts

652 → 2

Compiler

Compiled 365266 to 212927 computations (41.7% saved)

bsearch67.0ms (0.3%)

Compiler: Compiled 28 to 16 computations (42.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	97
1	41	97
2	45	97
3	47	97
4	48	97
5	47	97

end1.0ms (0%)

Compiler: Compiled 70 to 41 computations (41.4% saved)

sample1.9s (8.7%)

Algorithm

1×

intervals

Results

557.0ms	6490×	body	128	valid
239.0ms	650×	body	1024	valid
200.0ms	8000×	pre	128	true
111.0ms	502×	body	512	valid
45.0ms	309×	body	256	valid
19.0ms	49×	body	2048	valid

Compiler

Compiled 585 to 353 computations (39.7% saved)

Details

analyze198.0ms (0.9%)

sample49.0ms (0.2%)

simplify45.0ms (0.2%)

prune5.0ms (0%)

localize11.0ms (0.1%)

series829.0ms (3.9%)

rewrite21.0ms (0.1%)

simplify211.0ms (1%)

prune470.0ms (2.2%)

localize13.0ms (0.1%)

series901.0ms (4.2%)

rewrite39.0ms (0.2%)

simplify246.0ms (1.1%)

prune546.0ms (2.5%)

localize16.0ms (0.1%)

series586.0ms (2.7%)

rewrite3.0ms (0%)

simplify134.0ms (0.6%)

prune950.0ms (4.4%)

localize18.0ms (0.1%)

series538.0ms (2.5%)

rewrite7.0ms (0%)

simplify588.0ms (2.7%)

prune2.7s (12.6%)

regimes10.3s (48.3%)

bsearch67.0ms (0.3%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.9s (8.7%)

Profiling