Details

sample26.0ms

Algorithm

intervals

Results

5.0ms	63×	body	1280	valid
4.0ms	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

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def`

Counts

2 → 89

Calls

2 calls:

8.0ms	(sqrt (+ x 1.0))
56.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series115.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(sqrt (+ x 1.0))
82.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify53.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	299	1161
1	921	822
2	5001	744

prune168.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

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 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
33×	`distribute-lft-out`
32×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 94

Calls

3 calls:

10.0ms	(sqrt (+ x 1.0))
35.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
63.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series272.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(sqrt (+ x 1.0))
79.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
158.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	409	789
1	1675	716
2	5001	675

prune260.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 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))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
13×	`cbrt-prod`
12×	`times-frac`
10×	`associate-r`
9×	`sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
6×	`pow1` `cbrt-div`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-l` `associate-/r*` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 100

Calls

4 calls:

43.0ms	(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
26.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms	(cbrt (+ x 1.0))
9.0ms	(cbrt (+ x 1.0))

series536.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
111.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
100.0ms	(cbrt (+ x 1.0))
103.0ms	(cbrt (+ x 1.0))

simplify127.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	938	1649
1	4540	1538
2	5001	1534

prune763.0ms

Pruning

8 alts after pruning (6 fresh and 2 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)) (cbrt (+ x 1.0))))
0.2b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (cbrt (+ x 1.0)))

rewrite69.0ms

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×	`expm1-log1p-u` `associate-r/` `associate-l/` `add-cbrt-cube` `log1p-expm1-u` `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 → 109

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
14.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
41.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
5.0ms	(cbrt (cbrt (+ x 1.0)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (+ x 1.0))
121.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
118.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
102.0ms	(cbrt (cbrt (+ x 1.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	531	1002
1	1746	952
2	5002	887

prune496.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6

end0.0ms

sample735.0ms

Algorithm

intervals

Results

151.0ms	1715×	body	1280	valid
137.0ms	7894×	body	80	nan
87.0ms	4125×	body	80	valid
82.0ms	1211×	body	640	valid
31.0ms	614×	body	320	valid
11.0ms	335×	body	160	valid