Details

sample100.0ms

Algorithm

intervals

Results

56.0ms	123×	body	1280	valid
17.0ms	71×	body	640	valid
8.0ms	270×	body	80	nan
5.0ms	38×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	11×	body	80	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	6
1	25	6
2	40	6
3	65	6
4	98	6
5	122	6
6	135	6
7	137	6
8	137	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1.0 x) (- 1.0 x))
4.2b	(log (/ (+ 1.0 x) (- 1.0 x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
40×	`times-frac`
26×	`log-prod`
23×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
5×	`associate-/r*`
4×	`associate-/r/` `add-cbrt-cube` `associate-/l*`
3×	`pow1`
2×	`expm1-log1p-u` `flip3--` `div-exp` `rem-log-exp` `flip--` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 86

Calls

2 calls:

8.0ms	(/ (+ 1.0 x) (- 1.0 x))
7.0ms	(log (/ (+ 1.0 x) (- 1.0 x)))

series169.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (+ 1.0 x) (- 1.0 x))
130.0ms	(log (/ (+ 1.0 x) (- 1.0 x)))

simplify119.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	334	673
1	1078	636
2	4549	616
3	5001	613

prune217.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 2.0 (/ (pow x 2) (pow 1.0 2)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
69×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`add-exp-log` `unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 112

Calls

1 calls:

20.0ms

(* 2.0 (/ (pow x 2) (pow 1.0 2)))

series56.0ms

Counts

1 → 3

Calls

1 calls:

56.0ms

(* 2.0 (/ (pow x 2) (pow 1.0 2)))

simplify53.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	532	653
1	2211	536
2	5002	535

prune327.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (/ (+ 1.0 x) (- 1.0 x)))
0.0b	(expm1 (log1p (/ (+ 1.0 x) (- 1.0 x))))
0.0b	(/ (+ 1.0 x) (- 1.0 x))
58.9b	(log (expm1 (log1p (/ (+ 1.0 x) (- 1.0 x)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
20×	`times-frac`
16×	`add-cube-cbrt`
7×	`add-exp-log`
6×	`add-cbrt-cube` `distribute-lft-out`
5×	`pow1` `expm1-log1p-u` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`log-prod`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `flip3-+` `log1p-expm1` `div-exp` `rem-log-exp` `clear-num` `log-pow` `flip--` `flip-+` `div-inv` `expm1-udef`

Counts

4 → 83

Calls

4 calls:

1.0ms	(log1p (/ (+ 1.0 x) (- 1.0 x)))
1.0ms	(expm1 (log1p (/ (+ 1.0 x) (- 1.0 x))))
8.0ms	(/ (+ 1.0 x) (- 1.0 x))
1.0ms	(log (expm1 (log1p (/ (+ 1.0 x) (- 1.0 x)))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(log1p (/ (+ 1.0 x) (- 1.0 x)))
157.0ms	(expm1 (log1p (/ (+ 1.0 x) (- 1.0 x))))
37.0ms	(/ (+ 1.0 x) (- 1.0 x))
191.0ms	(log (expm1 (log1p (/ (+ 1.0 x) (- 1.0 x)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	518	790
1	1955	707
2	5003	694

prune260.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (log (sqrt (+ 1.0 x))) (log (/ (sqrt (+ 1.0 x)) (- 1.0 x))))
0.0b	(/ (sqrt (+ 1.0 x)) (- 1.0 x))
3.8b	(log (sqrt (+ 1.0 x)))
4.3b	(log (/ (sqrt (+ 1.0 x)) (- 1.0 x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

149×	`*-un-lft-identity`
109×	`add-sqr-sqrt`
105×	`times-frac`
96×	`log-prod`
72×	`sqrt-prod`
65×	`add-cube-cbrt`
41×	`associate-+r+`
22×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
13×	`pow1`
11×	`log-pow`
10×	`add-exp-log`
7×	`associate-+l+` `associate-/l*`
6×	`log-div` `fma-def` `sqrt-div` `associate-/r/` `add-cbrt-cube`
5×	`associate-/r*`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `rem-log-exp` `flip--` `div-inv`
2×	`associate-+l-` `sqrt-pow1` `pow1/2` `div-exp` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `clear-num` `sum-log`

Counts

4 → 215

Calls

4 calls:

17.0ms	(+ (log (sqrt (+ 1.0 x))) (log (/ (sqrt (+ 1.0 x)) (- 1.0 x))))
8.0ms	(/ (sqrt (+ 1.0 x)) (- 1.0 x))
4.0ms	(log (sqrt (+ 1.0 x)))
9.0ms	(log (/ (sqrt (+ 1.0 x)) (- 1.0 x)))

series916.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(+ (log (sqrt (+ 1.0 x))) (log (/ (sqrt (+ 1.0 x)) (- 1.0 x))))
97.0ms	(/ (sqrt (+ 1.0 x)) (- 1.0 x))
85.0ms	(log (sqrt (+ 1.0 x)))
413.0ms	(log (/ (sqrt (+ 1.0 x)) (- 1.0 x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	743	2210
1	2430	2080
2	5003	1989

prune502.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes67.0ms

Accuracy

0% (0.5b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	10
1	16	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	3387×	body	1280	valid
619.0ms	2474×	body	640	valid
228.0ms	8057×	body	80	nan
196.0ms	1293×	body	320	valid
56.0ms	619×	body	160	valid
10.0ms	227×	body	80	valid