Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	66×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Merged error: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 71

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
10.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series221.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(sqrt (+ x 1.0))
48.0ms	(+ 1.0 (sqrt (+ x 1.0)))
144.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	334	509
1	1210	457
2	5001	445

prune160.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Merged error: 0b

Counts

81 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ x 1.0)))
0.0b	(sqrt (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
64×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
30×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
16×	`distribute-lft-out`
15×	`times-frac`
14×	`associate-l`
10×	`associate-r`
9×	`flip3-+` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `associate-/r*` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 177

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ x 1.0)))
4.0ms	(sqrt (sqrt (+ x 1.0)))
21.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
18.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (sqrt (+ x 1.0)))
88.0ms	(sqrt (sqrt (+ x 1.0)))
145.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
31.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify79.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	530	1410
1	2396	1220
2	5001	1164

prune309.0ms

Filtered

189 candidates to 101 candidates (53.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	189	4	193

Merged error: 0b

Counts

193 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
3.3b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.8b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

810×	`add-sqr-sqrt`
770×	`*-un-lft-identity`
731×	`sqrt-prod`
578×	`prod-diff`
410×	`associate-r`
336×	`add-cube-cbrt`
239×	`associate-l`
221×	`swap-sqr`
179×	`distribute-lft-out`
178×	`unswap-sqr`
63×	`*-commutative`
62×	`sqrt-div`
36×	`times-frac`
34×	`fma-neg`
33×	`difference-of-squares`
32×	`flip3-+` `flip-+`
28×	`associate-*r/`
26×	`distribute-rgt-out--`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
19×	`pow-unpow`
16×	`sum-cubes` `frac-sub`
12×	`frac-times` `associate-/r*`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube`
8×	`associate-*l/`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `sub-div`
3×	`pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 880

Calls

4 calls:

10.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
6.0ms	(pow (sqrt (+ x 1.0)) 3)
59.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
20.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
69.0ms	(pow (sqrt (+ x 1.0)) 3)
60.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
202.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify173.0ms

Algorithm

egg-herbie

Counts

892 → 892

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1595	20021
1	5002	9611

prune584.0ms

Filtered

892 candidates to 140 candidates (15.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	892	0	892
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	892	4	896

Merged error: 0b

Counts

896 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
0.0b	(+ (sqrt (+ x 1.0)) 1.0)
0.2b	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

79×	`*-un-lft-identity`
63×	`add-sqr-sqrt`
52×	`times-frac`
46×	`sqrt-prod`
44×	`add-cube-cbrt`
30×	`associate-r`
17×	`distribute-lft-out`
13×	`associate-r/` `associate-/l`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
7×	`pow1` `fma-def`
6×	`associate-l` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`clear-num`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `prod-exp` `un-div-inv` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `sum-log` `*-commutative` `hypot-def`

Counts

4 → 162

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
9.0ms	(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) 1.0)
24.0ms	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
311.0ms	(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
41.0ms	(+ (sqrt (+ x 1.0)) 1.0)
142.0ms	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	570	1362
1	2436	1210
2	5002	1172

prune326.0ms

Filtered

174 candidates to 113 candidates (64.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	174	4	178

Merged error: 0b

Counts

178 → 4

regimes38.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample313.0ms

Algorithm

intervals

Results

156.0ms	7990×	body	80	valid
43.0ms	2595×	body	80	nan
1.0ms	10×	body	1280	valid