Details

sample27.0ms

Algorithm

intervals

Results

5.0ms	63×	body	1280	valid
5.0ms	269×	body	80	nan
3.0ms	142×	body	80	valid
2.0ms	29×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	11×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

7.0ms	(sqrt (+ x 1.0))
45.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series94.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(sqrt (+ x 1.0))
66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify56.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	182	265
1	544	243
2	2020	233
3	5002	230

prune86.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
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 → 71

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
31.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
46.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series225.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt (+ x 1.0))
56.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
136.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	341	624
1	1239	566
2	5001	533

prune167.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

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:

27.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
28.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))

series440.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
95.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
85.0ms	(cbrt (+ x 1.0))
83.0ms	(cbrt (+ x 1.0))

simplify101.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	850	1475
1	3967	1385
2	5002	1364

prune349.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(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)))
0.3b	(cbrt (cbrt (+ x 1.0)))

rewrite67.0ms

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:

4.0ms	(cbrt (+ x 1.0))
14.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
40.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
5.0ms	(cbrt (cbrt (+ x 1.0)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (+ x 1.0))
252.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
100.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
82.0ms	(cbrt (cbrt (+ x 1.0)))

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	506	966
1	1627	918
2	5002	859

prune396.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

0% (0.1b 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	9	5
1	9	5

end0.0ms

sample735.0ms

Algorithm

intervals

Results

144.0ms	1715×	body	1280	valid
142.0ms	7894×	body	80	nan
80.0ms	1211×	body	640	valid
77.0ms	4125×	body	80	valid
30.0ms	614×	body	320	valid
11.0ms	335×	body	160	valid