Details

analyze1.2s (18.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample3.9s (60.1%)

Results

2.4s	4121×	body	2048	valid
918.0ms	2113×	body	1024	valid
364.0ms	972×	body	512	valid
109.0ms	502×	body	256	valid
67.0ms	546×	body	128	valid
2.0ms	2×	body	4096	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

378×	`fma-neg_binary64`
198×	`fma-def_binary64`
192×	`rules-11_binary64`
174×	`rules-43_binary64`
173×	`rules-40_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	65	19
2	175	19
3	679	19
4	35	19

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))

Compiler

Compiled 56 to 38 computations (32.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 5 (.f64 v v))
✓	0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))
2.0ms	(.f64 5 (.f64 v v))

rewrite67.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

774×	`fma-neg_binary64`
534×	`prod-diff_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`
110×	`add-sqr-sqrt_binary64`

Counts

2 → 77

Calls

2 calls:

65.0ms	(.f64 5 (.f64 v v))
65.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	259	26
2	2954	26
3	5100	26
0	0	0
1	0	0

simplify26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

279×	`fma-neg_binary64`
152×	`rules-11_binary64`
144×	`rules-43_binary64`
143×	`rules-40_binary64`
143×	`rules-41_binary64`

Counts

101 → 81

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	312
1	68	312
2	161	312
3	584	312
4	36	312

prune70.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Error

0.5b

Counts

82 → 5

Alt Table

Status	Error	Program
	2.4b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))))))
▶	0.5b	(acos.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 v v) 1/5)) (fma.f64 v v -1)))
	2.0b	(fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (*.f64 v v))) (fma.f64 v v -1)))))
	1.4b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3))
	1.5b	(pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) 3)

Compiler

Compiled 2571 to 1776 computations (30.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 v v) 1/5)
✓	0.5b	(acos.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 v v) 1/5)) (fma.f64 v v -1)))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(acos.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 v v) 1/5)) (fma.f64 v v -1)))
2.0ms	(/.f64 (*.f64 v v) 1/5)

rewrite67.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

714×	`fma-neg_binary64`
406×	`fma-def_binary64`
374×	`prod-diff_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`

Counts

2 → 82

Calls

2 calls:

65.0ms	(/.f64 (*.f64 v v) 1/5)
65.0ms	(acos.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 v v) 1/5)) (fma.f64 v v -1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	256	26
2	2895	26
3	5125	26
0	0	0
1	0	0

simplify26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

279×	`fma-neg_binary64`
152×	`rules-11_binary64`
144×	`rules-43_binary64`
143×	`rules-40_binary64`
143×	`rules-41_binary64`

Counts

106 → 86

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	312
1	68	312
2	161	312
3	584	312
4	36	312

prune68.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	86	5	91

Error

0.5b

Counts

91 → 5

Alt Table

Status	Error	Program
	2.4b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))))))
✓	0.5b	(acos.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 v v) 1/5)) (fma.f64 v v -1)))
	2.0b	(fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (*.f64 v v))) (fma.f64 v v -1)))))
▶	1.4b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3))
	1.5b	(pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) 3)

Compiler

Compiled 2622 to 1813 computations (30.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 5 (.f64 v v))
	0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))
✓	1.0b	(pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3)
✓	1.0b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3))

series27.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

24.0ms	(pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3)
3.0ms	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3))

rewrite77.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

568×	`prod-diff_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
126×	`add-sqr-sqrt_binary64`
120×	`log1p-expm1-u_binary64`

Counts

2 → 92

Calls

2 calls:

74.0ms	(pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3)
74.0ms	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	306	41
2	3390	41
3	5028	41
0	0	0
1	0	0

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

321×	`fma-neg_binary64`
184×	`rules-11_binary64`
177×	`rules-43_binary64`
176×	`rules-40_binary64`
176×	`rules-41_binary64`

Counts

116 → 94

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	456
1	81	456
2	198	456
3	700	456
4	25	456

prune140.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	172	3	175
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	175	5	180

Error

0.5b

Counts

180 → 5

Alt Table

Status	Error	Program
	2.4b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))))))
▶	0.5b	(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3))))
	1.5b	(pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) 3)
	0.5b	(exp.f64 (.f64 (.f64 3 (log.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))) 1/3))
	1.4b	(.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (pow.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (*.f64 v v))) (fma.f64 v v -1))) 2) 1/3))

Compiler

Compiled 6580 to 4632 computations (29.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))
	1.0b	(pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3)
✓	1.0b	(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3))))
✓	1.0b	(expm1.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3)))

series27.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

24.0ms

(expm1.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (fma.f64 v v -1))) 3)))

3.0ms

(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (fma.f64 v v -1))) 3))))

rewrite113.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

716×	`prod-diff_binary64`
135×	`add-sqr-sqrt_binary64`
129×	`expm1-log1p-u_binary64`
128×	`log1p-expm1-u_binary64`
127×	`add-cbrt-cube_binary64`

Counts

2 → 97

Calls

2 calls:

101.0ms

(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (fma.f64 v v -1))) 3))))

101.0ms

(expm1.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (fma.f64 v v -1))) 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	330	41
2	3637	41
3	4958	41
0	0	0
1	0	0

simplify31.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

321×	`fma-neg_binary64`
184×	`rules-11_binary64`
177×	`rules-43_binary64`
176×	`rules-40_binary64`
176×	`rules-41_binary64`

Counts

121 → 99

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	528
1	81	528
2	198	528
3	700	528
4	25	528

prune202.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	191	6	197

Error

0.5b

Counts

197 → 6

Alt Table

Status	Error	Program
	2.4b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))))))
✓	0.5b	(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))) 3))))
	2.0b	(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) 3) 3))))
	1.5b	(pow.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) 3)
	0.5b	(exp.f64 (.f64 (.f64 3 (log.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1))))) 1/3))
	1.4b	(.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (fma.f64 v v -1)))) (pow.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (*.f64 v v))) (fma.f64 v v -1))) 2) 1/3))

Compiler

Compiled 8073 to 5715 computations (29.2% saved)

regimes149.0ms (2.3%)

Accuracy

Total 0.0b remaining (1.7%)

Threshold costs 0.0b (1.7%)

Counts

41 → 1

Compiler

Compiled 4466 to 3300 computations (26.1% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	18	28
2	17	28

end179.0ms (2.8%)

Compiler: Compiled 299 to 220 computations (26.4% saved)

Details

analyze1.2s (18.6%)

sample3.9s (60.1%)

simplify20.0ms (0.3%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series5.0ms (0.1%)

rewrite67.0ms (1%)

simplify26.0ms (0.4%)

prune70.0ms (1.1%)

localize8.0ms (0.1%)

series5.0ms (0.1%)

rewrite67.0ms (1%)

simplify26.0ms (0.4%)

prune68.0ms (1.1%)

localize11.0ms (0.2%)

series27.0ms (0.4%)

rewrite77.0ms (1.2%)

simplify30.0ms (0.5%)

prune140.0ms (2.2%)

localize15.0ms (0.2%)

series27.0ms (0.4%)

rewrite113.0ms (1.7%)

simplify31.0ms (0.5%)

prune202.0ms (3.1%)

regimes149.0ms (2.3%)

simplify1.0ms (0%)

end179.0ms (2.8%)

Profiling