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))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series190.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
148.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify36.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	278	393
1	1058	351
2	5002	347

prune100.0ms

Filtered

51 candidates to 38 candidates (74.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 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)))

rewrite58.0ms

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×	`sum-cubes` `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` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

10.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms	(pow (sqrt (+ x 1.0)) 3)
12.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
21.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
70.0ms	(pow (sqrt (+ x 1.0)) 3)
61.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
199.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify141.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	771	1703
1	3873	1474
2	5002	1459

prune398.0ms

Filtered

196 candidates to 98 candidates (50.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	196	4	200

Merged error: 0b

Counts

200 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 169

Calls

4 calls:

31.0ms	(* (* (/ 1 (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0))))) (/ 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)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
12.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(* (* (/ 1 (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0))))) (/ 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)))
144.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
62.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1022	2719
1	5001	2181

prune391.0ms

Filtered

181 candidates to 104 candidates (57.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	181	4	185

Merged error: 0b

Counts

185 → 4

localize7.0ms

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)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
53×	`add-sqr-sqrt`
52×	`times-frac`
37×	`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×	`flip3-+` `flip-+`
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 → 116

Calls

3 calls:

8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
20.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series485.0ms

Counts

3 → 9

Calls

3 calls:

300.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
48.0ms	(+ 1.0 (sqrt (+ x 1.0)))
136.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	491	1191
1	2142	1050
2	5002	1025

prune211.0ms

Filtered

125 candidates to 76 candidates (60.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	125	4	129

Merged error: 0b

Counts

129 → 4

regimes38.0ms

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	26	25
1	26	25

end0.0ms

sample321.0ms

Algorithm

intervals

Results

152.0ms	7997×	body	80	valid
47.0ms	2660×	body	80	nan
0.0ms	3×	body	1280	valid