Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

sample12.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 27.8b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

26.9b

(sqrt (* x (+ x x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 13

Calls

1 calls:

4.0ms

(sqrt (* x (+ x x)))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(sqrt (* x (+ x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4818	91
1	4818	91

prune38.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	10	6	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	7	17

Merged error: 0.1b

Counts

17 → 7

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* x (+ x x))))
0.5b	(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
26.9b	(sqrt (* x (+ x x)))
26.9b	(sqrt (* x (+ x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-pow1`
71×	`pow1`
33×	`sqrt-prod`
32×	`sqrt-div`
26×	`add-sqr-sqrt`
25×	`pow-prod-down`
22×	`pow1/2`
20×	`associate-*r/`
14×	`pow-prod-up`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3-+` `swap-sqr` `flip-+`
8×	`pow-sqr`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
4×	`frac-times` `add-log-exp` `unswap-sqr`
2×	`associate-*l/`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

5.0ms	(sqrt (sqrt (* x (+ x x))))
19.0ms	(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
4.0ms	(sqrt (* x (+ x x)))
5.0ms	(sqrt (* x (+ x x)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt (sqrt (* x (+ x x))))
4.0ms	(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
4.0ms	(sqrt (* x (+ x x)))
4.0ms	(sqrt (* x (+ x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4895	929
1	4895	929

prune115.0ms

Filtered

70 candidates to 136 candidates (-94.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	135	8	143

Merged error: 0.1b

Counts

143 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (sqrt (sqrt (sqrt (* x (+ x x))))) 3) (sqrt (sqrt (sqrt (* x (+ x x))))))
0.7b	(pow (sqrt (sqrt (sqrt (* x (+ x x))))) 3)
26.9b	(sqrt (* x (+ x x)))
26.9b	(sqrt (* x (+ x x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

104×	`sqrt-prod`
66×	`add-sqr-sqrt`
46×	`sqrt-div`
29×	`unpow-prod-down` `cube-prod`
26×	`associate-l`
24×	`unswap-sqr`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-*r/`
17×	`pow1`
16×	`sqrt-pow1`
10×	`add-exp-log` `associate-r`
9×	`flip3-+` `flip-+`
8×	`cube-div` `pow-pow`
7×	`add-cbrt-cube`
5×	`pow1/2` `sqr-pow`
4×	`frac-times` `add-log-exp`
3×	`pow-unpow` `pow-prod-down` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `associate-*l/` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 155

Calls

4 calls:

21.0ms	(* (pow (sqrt (sqrt (sqrt (* x (+ x x))))) 3) (sqrt (sqrt (sqrt (* x (+ x x))))))
8.0ms	(pow (sqrt (sqrt (sqrt (* x (+ x x))))) 3)
5.0ms	(sqrt (* x (+ x x)))
5.0ms	(sqrt (* x (+ x x)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (pow (sqrt (sqrt (sqrt (* x (+ x x))))) 3) (sqrt (sqrt (sqrt (* x (+ x x))))))
30.0ms	(pow (sqrt (sqrt (sqrt (* x (+ x x))))) 3)
4.0ms	(sqrt (* x (+ x x)))
4.0ms	(sqrt (* x (+ x x)))

simplify80.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4833	1797
1	4833	1797

prune158.0ms

Filtered

83 candidates to 167 candidates (-101.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	4	5
Picked	0	1	1
Done	1	1	2
Total	168	7	175

Merged error: 0.1b

Counts

175 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (sqrt (* x (+ x x)))))
0.3b	(* (pow (* x (+ x x)) 3/8) (sqrt (sqrt (sqrt (* x (+ x x))))))
26.9b	(sqrt (* x (+ x x)))
27.5b	(pow (* x (+ x x)) 3/8)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
22×	`add-sqr-sqrt` `sqrt-pow1`
18×	`pow1`
15×	`add-exp-log`
14×	`sqrt-div`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
8×	`associate-*r/`
6×	`prod-exp` `add-cbrt-cube` `unswap-sqr`
5×	`pow1/2` `associate-l` `sqr-pow`
4×	`pow-prod-down` `pow-exp` `add-log-exp`
3×	`pow-unpow` `flip3-+` `pow-prod-up` `flip-+`
2×	`pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `pow-pow`
1×	`*-commutative` `cbrt-unprod`

Counts

4 → 94

Calls

4 calls:

6.0ms	(sqrt (sqrt (sqrt (* x (+ x x)))))
13.0ms	(* (pow (* x (+ x x)) 3/8) (sqrt (sqrt (sqrt (* x (+ x x))))))
4.0ms	(sqrt (* x (+ x x)))
6.0ms	(pow (* x (+ x x)) 3/8)

series101.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (sqrt (sqrt (* x (+ x x)))))
50.0ms	(* (pow (* x (+ x x)) 3/8) (sqrt (sqrt (sqrt (* x (+ x x))))))
6.0ms	(sqrt (* x (+ x x)))
22.0ms	(pow (* x (+ x x)) 3/8)

simplify51.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5190	1189

prune131.0ms

Filtered

68 candidates to 106 candidates (-55.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	105	8	113

Merged error: 0.1b

Counts

113 → 8

regimes54.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.3b

bsearch11.0ms

Steps

Iters	Range		Point
8	-3.5992978060675945e-307	1.4098358971358471e-306	-5.01590506685105e-310

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample285.0ms

Algorithm

intervals

Results

190.0ms

8000×

body

valid

Details

analyze4.0ms

sample12.0ms

simplify3.0ms

prune9.0ms

localize5.0ms

rewrite5.0ms

series4.0ms

simplify51.0ms

prune38.0ms

localize7.0ms

rewrite38.0ms

series17.0ms

simplify79.0ms

prune115.0ms

localize10.0ms

rewrite45.0ms

series42.0ms

simplify80.0ms

prune158.0ms

localize14.0ms

rewrite32.0ms

series101.0ms

simplify51.0ms

prune131.0ms

regimes54.0ms

bsearch11.0ms

simplify1.0ms

end0.0ms

sample285.0ms

Profiling