Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	79×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series183.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
141.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify34.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	290	412
1	1095	368
2	5001	361

prune118.0ms

Filtered

58 candidates to 45 candidates (77.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	4	59

Merged error: 0b

Counts

59 → 4

localize14.0ms

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)
2.6b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.0b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sum-cubes` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`pow-unpow` `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--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 194

Calls

4 calls:

11.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms	(pow (sqrt (+ x 1.0)) 3)
13.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
19.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
62.0ms	(pow (sqrt (+ x 1.0)) 3)
66.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
195.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify139.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (119.0ms)

Iter	Nodes	Cost
0	825	1791
1	4126	1518
2	5001	1510

prune448.0ms

Filtered

206 candidates to 109 candidates (52.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	206	4	210

Merged error: 0b

Counts

210 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ 1 (/ (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (/ x (+ 1.0 (sqrt (+ x 1.0))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))
2.6b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-exp-log`
60×	`sqrt-div`
44×	`*-un-lft-identity`
42×	`prod-exp`
37×	`add-cbrt-cube`
35×	`flip3-+` `div-exp` `flip-+`
34×	`add-sqr-sqrt`
33×	`associate-*r/`
26×	`sqrt-prod`
24×	`pow1`
22×	`add-cube-cbrt`
21×	`frac-times`
16×	`frac-sub`
14×	`associate-*l/` `cbrt-unprod`
12×	`times-frac` `1-exp`
11×	`swap-sqr`
10×	`cbrt-undiv` `associate-r` `distribute-lft-out`
8×	`sqrt-pow1` `pow1/2` `associate-l`
6×	`rec-exp` `pow-prod-down` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`pow-sqr` `associate-/l*`
2×	`associate-/r/` `*-commutative`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `distribute-lft-in` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff` `clear-num` `rem-square-sqrt` `flip--` `div-inv`

Counts

4 → 193

Calls

4 calls:

38.0ms	(* (* (/ 1 (/ (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (/ x (+ 1.0 (sqrt (+ x 1.0))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
11.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
8.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
13.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(* (* (/ 1 (/ (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (/ x (+ 1.0 (sqrt (+ x 1.0))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
141.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
70.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

simplify58.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1238	3349
1	5002	2591

prune454.0ms

Filtered

205 candidates to 116 candidates (56.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	205	4	209

Merged error: 0b

Counts

209 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
52×	`times-frac`
38×	`add-cube-cbrt`
35×	`sqrt-prod`
30×	`associate-r`
14×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `associate-/l*` `unswap-sqr`
5×	`pow1` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 125

Calls

3 calls:

9.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
18.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series482.0ms

Counts

3 → 9

Calls

3 calls:

301.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
140.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	511	1228
1	2196	1085
2	5001	1054

prune240.0ms

Filtered

134 candidates to 85 candidates (63.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	134	4	138

Merged error: 0b

Counts

138 → 4

regimes40.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	26
1	27	26

end0.0ms

sample315.0ms

Algorithm

intervals

Results

150.0ms	7997×	body	80	valid
50.0ms	2660×	body	80	nan
0.0ms	3×	body	1280	valid