Details

analyze923.0ms (10.5%)

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%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	74.9%	25.1%	8
6.2%	68.6%	25.1%	9
7.8%	67.1%	25.1%	10
10.1%	64.7%	25.1%	11
14.8%	47.6%	37.6%	12
15.8%	36.8%	47.4%	13
16.6%	35.1%	48.3%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample2.9s (32.6%)

Results

1.6s	11100×	body	128	invalid
1.2s	8256×	body	128	valid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify27.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
314×	`associate-l_binary64`
304×	`*-commutative_binary64`
272×	`fma-neg_binary64`
248×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	52	25
3	116	25
4	286	25
5	632	25
6	1793	25
7	3725	25

Stop Event

1×	node limit

Counts

1 → 2

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

Compiler

Compiled 77 to 57 computations (26% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

series180.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

159.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
21.0ms	(.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

rewrite56.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
161×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`
151×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	333	37
2	4103	37

Stop Event

1×	node limit

Counts

2 → 36

Calls

2 calls:

55.0ms	(.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
55.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

688×	`associate-l_binary64`
677×	`fma-def_binary64`
339×	`sub-neg_binary64`
275×	`cancel-sign-sub-inv_binary64`
249×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	1979
1	271	1819
2	1005	1332
3	4537	1332

Stop Event

1×	node limit

Counts

84 → 60

prune65.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	52	8	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	9	61

Error

0.0b

Counts

61 → 9

Alt Table

Status	Error	Program
	30.9b	(/.f64 (.f64 (-.f64 (.f64 1/4 (.f64 x x)) (.f64 y y)) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) (fma.f64 x 1/2 y))
	0.5b	(-.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x)) (sqrt.f64 z))) (.f64 (.f64 y (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z)))
	16.1b	(.f64 (-.f64 (.f64 x 1/2) y) (cbrt.f64 (.f64 (pow.f64 (.f64 z 2) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) 3))))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
	0.6b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
	48.7b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
	29.8b	(pow.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))) 2)
	1.3b	(pow.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))) 3)
▶	0.5b	(.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)))

Compiler

Compiled 1855 to 1200 computations (35.3% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.3b	(.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))
✓	0.4b	(.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)))

series181.0ms (2.1%)

Counts

3 → 64

Calls

3 calls:

158.0ms

(*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

17.0ms

(*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))

6.0ms

(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

rewrite60.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
169×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
159×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	353	48
2	4338	48

Stop Event

1×	node limit

Counts

3 → 55

Calls

3 calls:

59.0ms

(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

59.0ms

(*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))

59.0ms

(*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
626×	`associate-r_binary64`
626×	`associate-l_binary64`
266×	`cancel-sign-sub-inv_binary64`
223×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1624
1	287	1600
2	1028	1416

Stop Event

1×	node limit

Counts

119 → 83

prune115.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	85	7	92

Error

0.0b

Counts

92 → 7

Alt Table

Status	Error	Program
▶	0.5b	(-.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x)) (sqrt.f64 z))) (.f64 (.f64 y (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z)))
	0.6b	(.f64 (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 t) t))))) 1) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)))
	0.6b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
	48.7b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
	29.8b	(pow.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))) 2)
	1.3b	(pow.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))) 3)
✓	0.5b	(.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)))

Compiler

Compiled 2235 to 1363 computations (39% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x)) (sqrt.f64 z))
✓	0.4b	(.f64 (.f64 y (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.4b	(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x))
✓	0.4b	(.f64 y (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

series980.0ms (11.2%)

Counts

4 → 16

Calls

4 calls:

294.0ms	(.f64 (.f64 y (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
243.0ms	(.f64 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x)) (sqrt.f64 z))
223.0ms	(.f64 y (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
219.0ms	(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x))

rewrite61.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

289×	`expm1-udef_binary64`
289×	`log1p-udef_binary64`
188×	`associate-r_binary64`
164×	`add-sqr-sqrt_binary64`
153×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	74
1	343	66
2	4169	66

Stop Event

1×	node limit

Counts

4 → 61

Calls

4 calls:

60.0ms	(.f64 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x)) (sqrt.f64 z))
60.0ms	(.f64 (.f64 y (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
60.0ms	(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x))
60.0ms	(.f64 y (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

simplify32.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

725×	`distribute-rgt-out_binary64`
691×	`fma-def_binary64`
603×	`associate-l_binary64`
548×	`distribute-lft-out_binary64`
439×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	556
1	202	504
2	685	418
3	3180	366

Stop Event

1×	node limit

Counts

77 → 91

prune80.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	91	7	98

Error

0.0b

Counts

98 → 7

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x)) (sqrt.f64 z))) (.f64 (.f64 y (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z)))
	0.6b	(.f64 (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 t) t))))) 1) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)))
▶	0.6b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
	48.7b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
	29.8b	(pow.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))) 2)
	1.3b	(pow.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))) 3)
✓	0.5b	(.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)))

Compiler

Compiled 3325 to 1835 computations (44.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))
✓	0.2b	(sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
✓	0.5b	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2)

series1.2s (13.8%)

Counts

4 → 88

Calls

4 calls:

530.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2)
514.0ms	(sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))
139.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
23.0ms	(sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))

rewrite63.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
161×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`
151×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	67
1	356	66
2	4088	66

Stop Event

1×	node limit

Counts

4 → 105

Calls

4 calls:

61.0ms	(sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))
61.0ms	(sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))
61.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
61.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2)

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
357×	`*-commutative_binary64`
343×	`sub-neg_binary64`
262×	`cancel-sign-sub-inv_binary64`
225×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	2881
1	357	2728
2	1250	2050
3	4347	2026

Stop Event

1×	node limit

Counts

193 → 116

prune105.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	116	7	123

Error

0.0b

Counts

123 → 7

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x)) (sqrt.f64 z))) (.f64 (.f64 y (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z)))
	0.6b	(.f64 (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 t) t))))) 1) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)))
✓	0.6b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
	48.7b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
	29.8b	(pow.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))) 2)
	1.3b	(pow.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))) 3)
✓	0.5b	(.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)))

Compiler

Compiled 2981 to 1867 computations (37.4% saved)

regimes1.4s (16.3%)

Accuracy

Total 0.3b remaining (91.1%)

Threshold costs 0.3b (91.1%)

Counts

104 → 1

Compiler

Compiled 32618 to 24791 computations (24% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	41
1	29	39
2	38	39
3	44	39
4	47	39
5	48	39

Stop Event

1×

saturated

end122.0ms (1.4%)

Compiler: Compiled 223 to 159 computations (28.7% saved)

Details

analyze923.0ms (10.5%)

sample2.9s (32.6%)

simplify27.0ms (0.3%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series180.0ms (2.1%)

rewrite56.0ms (0.6%)

simplify60.0ms (0.7%)

prune65.0ms (0.7%)

localize13.0ms (0.1%)

series181.0ms (2.1%)

rewrite60.0ms (0.7%)

simplify40.0ms (0.5%)

prune115.0ms (1.3%)

localize16.0ms (0.2%)

series980.0ms (11.2%)

rewrite61.0ms (0.7%)

simplify32.0ms (0.4%)

prune80.0ms (0.9%)

localize15.0ms (0.2%)

series1.2s (13.8%)

rewrite63.0ms (0.7%)

simplify68.0ms (0.8%)

prune105.0ms (1.2%)

regimes1.4s (16.3%)

simplify3.0ms (0%)

end122.0ms (1.4%)

Profiling