Details

sample21.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
4.0ms	102×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`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×	`flip3-+` `flip-+` `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` `div-inv`

Counts

3 → 61

Calls

3 calls:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
17.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series217.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ 1.0 (sqrt (+ x 1.0)))
30.0ms	(sqrt (+ x 1.0))
141.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify34.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	317	483
1	1159	435
2	5001	427

prune131.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
8×	`pow1`
6×	`add-log-exp`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `flip-+`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 106

Calls

4 calls:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
17.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
42.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ 1.0 (sqrt (+ x 1.0)))
35.0ms	(sqrt (+ x 1.0))
103.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
144.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	452	821
1	1973	707
2	5002	668

prune188.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 86

Calls

4 calls:

13.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))

series494.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
219.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
89.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	681	1304
1	3037	1229
2	5002	1209

prune293.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (cbrt (+ x 1.0)))
0.2b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.2b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-prod`
38×	`cbrt-div`
33×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
14×	`flip3-+` `flip-+`
11×	`pow1`
9×	`pow1/3` `swap-sqr`
8×	`frac-times` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`associate-r/` `associate-l/` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

2.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (cbrt (+ x 1.0)))
8.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
20.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ x 1.0))
91.0ms	(cbrt (cbrt (+ x 1.0)))
111.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
104.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	506	966
1	1625	911
2	5002	859

prune396.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes43.0ms

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

sample525.0ms

Algorithm

intervals

Results

307.0ms	7999×	body	80	valid
94.0ms	2604×	body	80	nan
0.0ms	1×	body	1280	valid