Details

analyze926.0ms (11.7%)

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)

sample2.7s (34.7%)

Results

1.5s	10999×	body	128	invalid
1.1s	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

prune5.0ms (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

0.3b

Counts

3 → 2

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)))
	0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))

Compiler

Compiled 119 to 89 computations (25.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.0b	(sqrt.f64 (exp.f64 t))
✓	0.0b	(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)))

series192.0ms (2.4%)

Counts

4 → 56

Calls

4 calls:

167.0ms	(.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))
2.0ms	(pow.f64 (sqrt.f64 (exp.f64 t)) t)
2.0ms	(sqrt.f64 (exp.f64 t))

rewrite60.0ms (0.8%)

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	54
1	333	50
2	4103	50

Stop Event

1×	node limit

Counts

4 → 77

Calls

4 calls:

58.0ms	(.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
58.0ms	(sqrt.f64 (exp.f64 t))
58.0ms	(pow.f64 (sqrt.f64 (exp.f64 t)) t)
58.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

779×	`fma-def_binary64`
340×	`sub-neg_binary64`
296×	`*-commutative_binary64`
275×	`cancel-sign-sub-inv_binary64`
256×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	1914
1	323	1788
2	1146	1581
3	4009	1581

Stop Event

1×	node limit

Counts

133 → 115

prune119.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	107	8	115
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Error

0.0b

Counts

117 → 8

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))
	1.4b	(.f64 (-.f64 (.f64 x 1/2) y) (*.f64 (sqrt.f64 2) (sqrt.f64 z)))
	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (*.f64 (pow.f64 (cbrt.f64 (exp.f64 t)) t) (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 t))) t))))
	0.5b	(.f64 (sqrt.f64 z) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) x)) (*.f64 y (pow.f64 (sqrt.f64 (exp.f64 t)) t)))))
	48.1b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
	17.7b	(.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))))
	0.5b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
	1.4b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

Compiler

Compiled 2908 to 1853 computations (36.3% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series367.0ms (4.7%)

Counts

3 → 72

Calls

3 calls:

190.0ms	(.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))
175.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))
2.0ms	(pow.f64 (exp.f64 t) t)

rewrite54.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
272×	`log1p-udef_binary64`
153×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`
145×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	314	41
2	3839	41

Stop Event

1×	node limit

Counts

3 → 54

Calls

3 calls:

53.0ms	(.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))
53.0ms	(pow.f64 (exp.f64 t) t)
53.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))

simplify39.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-def_binary64`
550×	`associate-r_binary64`
514×	`associate-l_binary64`
250×	`cancel-sign-sub-inv_binary64`
227×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	94	1984
1	289	1953
2	1027	1407

Stop Event

1×	node limit

Counts

126 → 87

prune98.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	87	8	95

Error

0.0b

Counts

95 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 (.f64 (pow.f64 (exp.f64 t) t) z)) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/2 x) y)))
	0.5b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
▶	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (*.f64 (pow.f64 (cbrt.f64 (exp.f64 t)) t) (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 t))) t))))
	48.1b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
	0.9b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))) 3)))
	17.7b	(.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))))
	1.4b	(.f64 (-.f64 (.f64 x 1/2) y) (*.f64 (sqrt.f64 2) (sqrt.f64 z)))
	1.4b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

Compiler

Compiled 2230 to 1456 computations (34.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series600.0ms (7.6%)

Counts

3 → 60

Calls

3 calls:

467.0ms

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

117.0ms

(cbrt.f64 (sqrt.f64 (exp.f64 t)))

16.0ms

(cbrt.f64 (exp.f64 t))

rewrite34.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

191×	`add-sqr-sqrt_binary64`
188×	`log1p-expm1-u_binary64`
188×	`expm1-log1p-u_binary64`
184×	`add-cbrt-cube_binary64`
181×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	46
1	414	34

Stop Event

1×	node limit

Counts

3 → 70

Calls

3 calls:

32.0ms

(cbrt.f64 (exp.f64 t))

32.0ms

(cbrt.f64 (sqrt.f64 (exp.f64 t)))

32.0ms

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

simplify61.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary64`
359×	`*-commutative_binary64`
340×	`sub-neg_binary64`
268×	`cancel-sign-sub-inv_binary64`
261×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	2265
1	326	2151
2	1196	1872
3	4155	1872

Stop Event

1×	node limit

Counts

130 → 102

prune175.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	130	8	138

Error

0.0b

Counts

138 → 8

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (sqrt.f64 (.f64 (pow.f64 (exp.f64 t) t) z)) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/2 x) y)))
	0.5b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (*.f64 (pow.f64 (cbrt.f64 (exp.f64 t)) t) (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 t))) t))))
	48.1b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
	0.9b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))) 3)))
	17.7b	(.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))))
	1.4b	(.f64 (-.f64 (.f64 x 1/2) y) (*.f64 (sqrt.f64 2) (sqrt.f64 z)))
	1.4b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

Compiler

Compiled 3877 to 2265 computations (41.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series338.0ms (4.3%)

Counts

3 → 84

Calls

3 calls:

179.0ms	(*.f64 (pow.f64 (exp.f64 t) t) z)
151.0ms	(.f64 (sqrt.f64 (.f64 (pow.f64 (exp.f64 t) t) z)) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/2 x) y)))
8.0ms	(.f64 (sqrt.f64 2) (-.f64 (.f64 1/2 x) y))

rewrite57.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
160×	`add-sqr-sqrt_binary64`
152×	`log1p-expm1-u_binary64`
152×	`expm1-log1p-u_binary64`
150×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	46
1	333	44
2	4045	44

Stop Event

1×	node limit

Counts

3 → 56

Calls

3 calls:

56.0ms	(*.f64 (pow.f64 (exp.f64 t) t) z)
56.0ms	(.f64 (sqrt.f64 (.f64 (pow.f64 (exp.f64 t) t) z)) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/2 x) y)))
56.0ms	(.f64 (sqrt.f64 2) (-.f64 (.f64 1/2 x) y))

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
534×	`associate-r_binary64`
518×	`associate-l_binary64`
340×	`sub-neg_binary64`
252×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	86	1711
1	270	1597
2	968	1519
3	4849	1519

Stop Event

1×	node limit

Counts

140 → 86

prune102.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	111	9	120

Error

Counts

120 → 9

Alt Table

Status	Error	Program
	32.9b	(.f64 (sqrt.f64 (.f64 (pow.f64 (exp.f64 t) t) z)) (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (-.f64 (.f64 1/2 x) y))) 2))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (*.f64 (pow.f64 (cbrt.f64 (exp.f64 t)) t) (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 t))) t))))
✓	0.5b	(.f64 (sqrt.f64 (.f64 (pow.f64 (exp.f64 t) t) z)) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/2 x) y)))
	0.5b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
	48.1b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
	0.9b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))) 3)))
	17.7b	(.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))))
	1.4b	(.f64 (-.f64 (.f64 x 1/2) y) (*.f64 (sqrt.f64 2) (sqrt.f64 z)))
	1.4b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

Compiler

Compiled 2617 to 1595 computations (39.1% saved)

regimes1.6s (19.9%)

Accuracy

Total 0.3b remaining (83.9%)

Threshold costs 0.3b (83.9%)

Counts

94 → 1

Compiler

Compiled 30979 to 23534 computations (24% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
2×	`+-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	17	23
1	25	23
2	29	23
3	31	23
4	32	23

Stop Event

1×

saturated

end152.0ms (1.9%)

Compiler: Compiled 227 to 173 computations (23.8% saved)

Details

analyze926.0ms (11.7%)

sample2.7s (34.7%)

simplify27.0ms (0.3%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

series192.0ms (2.4%)

rewrite60.0ms (0.8%)

simplify59.0ms (0.7%)

prune119.0ms (1.5%)

localize13.0ms (0.2%)

series367.0ms (4.7%)

rewrite54.0ms (0.7%)

simplify39.0ms (0.5%)

prune98.0ms (1.2%)

localize18.0ms (0.2%)

series600.0ms (7.6%)

rewrite34.0ms (0.4%)

simplify61.0ms (0.8%)

prune175.0ms (2.2%)

localize11.0ms (0.1%)

series338.0ms (4.3%)

rewrite57.0ms (0.7%)

simplify62.0ms (0.8%)

prune102.0ms (1.3%)

regimes1.6s (19.9%)

simplify3.0ms (0%)

end152.0ms (1.9%)

Profiling