Details

sample15.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
2.0ms	100×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite53.0ms

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:

16.0ms	(+ 1.0 (sqrt (+ x 1.0)))
35.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series170.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ 1.0 (sqrt (+ x 1.0)))
132.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify33.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (27.0ms)

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

prune101.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
3.7b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.1b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite180.0ms

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:

41.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
10.0ms	(pow (sqrt (+ x 1.0)) 3)
28.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
91.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
63.0ms	(pow (sqrt (+ x 1.0)) 3)
61.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
180.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify131.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	771	1703
1	3877	1474
2	5001	1459

prune413.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.1b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.7b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
127×	`*-un-lft-identity`
96×	`sqrt-div`
76×	`add-sqr-sqrt`
70×	`flip3-+` `flip-+`
66×	`associate-*r/`
65×	`associate-l`
63×	`associate-*l/`
59×	`add-cube-cbrt`
58×	`associate-/r/`
52×	`frac-sub`
36×	`add-exp-log`
33×	`distribute-lft-out`
29×	`add-cbrt-cube`
26×	`sqrt-prod`
21×	`pow1`
14×	`frac-times` `div-exp`
13×	`associate-/l*`
11×	`swap-sqr` `div-inv`
10×	`cbrt-undiv` `flip3--` `associate-r` `prod-exp` `flip--`
8×	`sqrt-pow1` `pow1/2`
7×	`cbrt-unprod`
6×	`add-log-exp` `unswap-sqr`
5×	`pow-prod-up`
4×	`pow-prod-down` `associate-/r*` `sub-div`
3×	`pow-sqr`
2×	`1-exp` `*-commutative`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-rgt-out--` `frac-2neg` `distribute-lft-in` `pow-plus` `sqrt-unprod` `diff-log` `clear-num` `rem-square-sqrt` `associate-/l/`

Counts

4 → 272

Calls

4 calls:

304.0ms	(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
753.0ms	(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
40.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
31.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

series739.0ms

Counts

4 → 12

Calls

4 calls:

403.0ms	(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
266.0ms	(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
14.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
55.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

simplify91.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1788	5707
1	5001	5172

prune772.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite140.0ms

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:

16.0ms	(+ 1.0 (sqrt (+ x 1.0)))
35.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
85.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series455.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ 1.0 (sqrt (+ x 1.0)))
283.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
133.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (51.0ms)

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

prune220.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	25
1	28	25
2	28	25

end0.0ms

sample359.0ms

Algorithm

intervals

Results

153.0ms	7996×	body	80	valid
47.0ms	2740×	body	80	nan
0.0ms	4×	body	1280	valid