Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	276×	body	80	nan
4.0ms	47×	body	1280	valid
3.0ms	155×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	21×	body	320	valid
0.0ms	11×	body	160	valid

simplify6.0ms

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: 23.8b

localize5.0ms

Local error

Found 1 expressions with local error:

3.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 70

Calls

1 calls:

28.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series72.0ms

Counts

1 → 3

Calls

1 calls:

72.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify135.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (127.0ms)

Iter	Nodes	Cost
0	252	1065
1	759	733
2	4363	623
3	5001	593

prune103.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 75

Calls

2 calls:

19.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
32.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series215.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
150.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	356	693
1	1446	627
2	5001	586

prune179.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.0b	(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

22.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0ms	(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.0ms	(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
30.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series1.5s

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
474.0ms	(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
856.0ms	(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
146.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	622	1165
1	2619	1024
2	5001	993

prune310.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

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

series394.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
95.0ms	(cbrt (+ x 1.0))
94.0ms	(cbrt (+ x 1.0))
95.0ms	(cbrt (+ x 1.0))

simplify167.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (151.0ms)

Iter	Nodes	Cost
0	321	818
1	1064	769
2	4750	694
3	5001	688

prune389.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes43.0ms

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	14	8
1	18	8
2	18	8

end0.0ms

sample681.0ms

Algorithm

intervals

Results

157.0ms	1749×	body	1280	valid
142.0ms	8072×	body	80	nan
79.0ms	1145×	body	640	valid
77.0ms	4152×	body	80	valid
33.0ms	655×	body	320	valid
12.0ms	299×	body	160	valid