Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.5s (41.6%)

Results

601.0ms	2083×	body	1024	valid
399.0ms	4382×	body	128	valid
233.0ms	1021×	body	512	valid
85.0ms	245×	body	2048	valid
77.0ms	525×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify43.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

550×	`fma-neg_binary64`
303×	`rules-6-rev_binary64`
266×	`rules-5-rev_binary64`
262×	`rules-42_binary64`
262×	`rules-43_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	40	11
2	94	11
3	213	11
4	458	11
5	1173	11
6	523	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series18.0ms (0.5%)

Counts

1 → 1

Calls

1 calls:

18.0ms

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

rewrite58.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

687×	`log1p-expm1-u_binary64`
687×	`expm1-log1p-u_binary64`
499×	`prod-diff_binary64`
87×	`egg-rr`
67×	`add-sqr-sqrt_binary64`

Counts

1 → 87

Calls

1 calls:

56.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	165	11
2	1969	11
3	5350	11
0	0	0
1	0	0

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-neg_binary64`
21×	`rules-13_binary64`
18×	`rules-40_binary64`
18×	`rules-41_binary64`
18×	`rules-42_binary64`

Counts

88 → 88

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	8	1
2	16	1
3	22	1
4	35	1
5	58	1
6	76	1
7	88	1
8	97	1
9	101	1
10	114	1
11	5	1

prune109.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Error

29.9b

Counts

89 → 9

Alt Table

Status	Error	Program
	31.1b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))
	32.2b	1
	31.3b	(/.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x)))))
	30.9b	(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
	31.5b	(+.f64 (fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))
	31.0b	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
▶	30.9b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) (fma.f64 -1 (sqrt.f64 x) (sqrt.f64 x)))
	30.9b	(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)
	31.5b	(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))

Compiler

Compiled 2449 to 1387 computations (43.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))
✓	0.3b	(pow.f64 (cbrt.f64 (+.f64 x 1)) 2)
✓	0.3b	(cbrt.f64 (+.f64 x 1))
✓	30.7b	(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))

series32.0ms (0.9%)

Counts

4 → 37

Calls

4 calls:

12.0ms	(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
8.0ms	(pow.f64 (cbrt.f64 (+.f64 x 1)) 2)
6.0ms	(cbrt.f64 (+.f64 x 1))
5.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))

rewrite77.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

887×	`log1p-expm1-u_binary64`
887×	`expm1-log1p-u_binary64`
309×	`prod-diff_binary64`
181×	`egg-rr`
97×	`add-sqr-sqrt_binary64`

Counts

4 → 181

Calls

4 calls:

73.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))
73.0ms	(pow.f64 (cbrt.f64 (+.f64 x 1)) 2)
73.0ms	(cbrt.f64 (+.f64 x 1))
73.0ms	(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	251	32
2	2636	32
3	6301	32
0	0	0
1	0	0

simplify53.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

695×	`rules-40_binary64`
695×	`rules-42_binary64`
693×	`rules-41_binary64`
693×	`rules-43_binary64`
296×	`rules-21_binary64`

Counts

218 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	94	1076
1	654	1048
2	2632	778
3	4974	778

prune364.0ms (10.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	247	2	249
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	249	9	258

Error

29.9b

Counts

258 → 9

Alt Table

Status	Error	Program
	31.3b	(/.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x)))))
	31.3b	(+.f64 (fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) (fma.f64 -1 (sqrt.f64 x) (sqrt.f64 x)))
	31.1b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))
	32.2b	1
	31.0b	(+.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (+.f64 1 (/.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))) (fma.f64 -1 (sqrt.f64 x) (sqrt.f64 x)))
▶	30.9b	(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
	31.5b	(+.f64 (fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))
	31.0b	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
	31.5b	(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))

Compiler

Compiled 8673 to 5770 computations (33.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
	0.3b	(cbrt.f64 (+.f64 x 1))
✓	30.9b	(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))

series18.0ms (0.5%)

Counts

2 → 13

Calls

2 calls:

13.0ms	(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
4.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x 1)))

rewrite58.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

824×	`log1p-expm1-u_binary64`
824×	`expm1-log1p-u_binary64`
311×	`prod-diff_binary64`
87×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`

Counts

2 → 65

Calls

2 calls:

57.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
57.0ms	(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	221	20
2	2437	20
3	5952	20
0	0	0
1	0	0

simplify36.0ms (1%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-neg_binary64`
374×	`rules-40_binary64`
374×	`rules-42_binary64`
372×	`rules-41_binary64`
372×	`rules-43_binary64`

Counts

78 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	56	357
1	375	349
2	1435	269
3	4895	269

prune223.0ms (6.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	164	9	173

Error

29.9b

Counts

173 → 9

Alt Table

Status	Error	Program
	31.3b	(/.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x)))))
	31.3b	(+.f64 (fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) (fma.f64 -1 (sqrt.f64 x) (sqrt.f64 x)))
▶	31.0b	(*.f64 (neg.f64 (sqrt.f64 x)) (+.f64 1 (/.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))
	31.5b	(+.f64 (fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))
	31.1b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))
	32.2b	1
✓	30.9b	(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
	31.0b	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
	31.5b	(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))

Compiler

Compiled 3979 to 2750 computations (30.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))
✓	0.2b	(*.f64 (neg.f64 (sqrt.f64 x)) (+.f64 1 (/.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))
✓	3.0b	(+.f64 1 (/.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))

series63.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

35.0ms

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

17.0ms

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

11.0ms

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

rewrite98.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

908×	`fma-neg_binary64`
512×	`prod-diff_binary64`
253×	`egg-rr`
169×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`

Counts

3 → 253

Calls

3 calls:

91.0ms

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

91.0ms

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

91.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	238	42
2	2869	42
3	5079	42
0	0	0
1	0	0

simplify84.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

658×	`rules-21_binary64`
376×	`fma-neg_binary64`
290×	`rules-11_binary64`
289×	`rules-18-rev_binary64`
277×	`rules-15-rev_binary64`

Counts

262 → 267

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	122
1	227	122
2	884	107
3	4765	107
4	4562	107
5	4848	107

prune182.0ms (5.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	265	2	267
Fresh	6	1	7
Picked	0	1	1
Done	1	0	1
Total	272	4	276

Error

0.2b

Counts

276 → 4

Alt Table

Status	Error	Program
	31.1b	(*.f64 (neg.f64 (sqrt.f64 x)) (+.f64 (-.f64 (/.f64 (+.f64 -1/2 (/.f64 1/8 x)) x) (/.f64 1/16 (pow.f64 x 3))) (/.f64 5/128 (pow.f64 x 4))))
✓	31.0b	(*.f64 (neg.f64 (sqrt.f64 x)) (+.f64 1 (/.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))
	31.1b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))
	30.9b	(+.f64 (sqrt.f64 (+.f64 1 x)) (neg.f64 (sqrt.f64 x)))

Compiler

Compiled 6721 to 3923 computations (41.6% saved)

regimes365.0ms (10.4%)

Accuracy

Total 0.0b remaining (3.7%)

Threshold costs 0.0b (3.7%)

Counts

152 → 2

Compiler

Compiled 5688 to 4195 computations (26.2% saved)

bsearch20.0ms (0.6%)

Steps

Iters	Range		Point
9	0.013401816907784322	10537.71196967466	896.2978944243135

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	59
1	33	59
2	32	59

end100.0ms (2.8%)

Compiler: Compiled 153 to 113 computations (26.1% saved)

Details

analyze3.0ms (0.1%)

sample1.5s (41.6%)

simplify43.0ms (1.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series18.0ms (0.5%)

rewrite58.0ms (1.7%)

simplify11.0ms (0.3%)

prune109.0ms (3.1%)

localize12.0ms (0.3%)

series32.0ms (0.9%)

rewrite77.0ms (2.2%)

simplify53.0ms (1.5%)

prune364.0ms (10.4%)

localize8.0ms (0.2%)

series18.0ms (0.5%)

rewrite58.0ms (1.7%)

simplify36.0ms (1%)

prune223.0ms (6.3%)

localize7.0ms (0.2%)

series63.0ms (1.8%)

rewrite98.0ms (2.8%)

simplify84.0ms (2.4%)

prune182.0ms (5.2%)

regimes365.0ms (10.4%)

bsearch20.0ms (0.6%)

simplify2.0ms (0%)

end100.0ms (2.8%)

Profiling