Details

sample30.0ms

Algorithm

intervals

Results

10.0ms	118×	pre	10240	exit
7.0ms	256×	body	80	valid
2.0ms	138×	pre	80	true

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	12	3
2	12	3

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.0b

localize4.0ms

Local error

Found 2 expressions with local error:

0.8b	(/ x0 (- 1.0 x1))
7.4b	(- (/ x0 (- 1.0 x1)) x0)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`times-frac`
12×	`add-cube-cbrt`
6×	`difference-of-squares`
5×	`associate-/r*` `distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

10.0ms	(/ x0 (- 1.0 x1))
53.0ms	(- (/ x0 (- 1.0 x1)) x0)

series71.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ x0 (- 1.0 x1))
37.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify91.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	244	328
1	801	315
2	3123	310
3	5001	310

prune81.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 7.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ x0 (- 1.0 x1))
0.8b	(/ x0 (- 1.0 x1))
0.8b	(/ x0 (- 1.0 x1))
6.2b	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
34×	`add-cube-cbrt`
15×	`associate-/r*`
13×	`difference-of-squares`
12×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 124

Calls

4 calls:

10.0ms	(/ x0 (- 1.0 x1))
10.0ms	(/ x0 (- 1.0 x1))
13.0ms	(/ x0 (- 1.0 x1))
21.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

series162.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ x0 (- 1.0 x1))
34.0ms	(/ x0 (- 1.0 x1))
30.0ms	(/ x0 (- 1.0 x1))
67.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

simplify157.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	288	828
1	1116	773
2	4811	759
3	5001	759

prune226.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (/ x0 (- 1.0 x1)) x0)
0.8b	(/ x0 (- 1.0 x1))
0.8b	(/ x0 (- 1.0 x1))
6.2b	(- (* (/ x0 (- 1.0 x1)) (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
30×	`times-frac`
24×	`add-cube-cbrt`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

38.0ms	(+ (/ x0 (- 1.0 x1)) x0)
10.0ms	(/ x0 (- 1.0 x1))
12.0ms	(/ x0 (- 1.0 x1))
88.0ms	(- (* (/ x0 (- 1.0 x1)) (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

series182.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (/ x0 (- 1.0 x1)) x0)
29.0ms	(/ x0 (- 1.0 x1))
34.0ms	(/ x0 (- 1.0 x1))
85.0ms	(- (* (/ x0 (- 1.0 x1)) (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

simplify42.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	381	813
1	1522	765
2	5001	749

prune243.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ x0 (- 1.0 x1))
0.8b	(/ x0 (- 1.0 x1))
3.8b	(log (exp (- (* (/ x0 (- 1.0 x1)) (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))))
6.2b	(- (* (/ x0 (- 1.0 x1)) (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

rewrite421.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
26×	`add-cube-cbrt`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/l*` `add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/` `log-pow`
3×	`exp-prod` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `exp-sum` `clear-num` `div-inv`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp`

Counts

4 → 104

Calls

4 calls:

10.0ms	(/ x0 (- 1.0 x1))
10.0ms	(/ x0 (- 1.0 x1))
309.0ms	(log (exp (- (* (/ x0 (- 1.0 x1)) (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))))
88.0ms	(- (* (/ x0 (- 1.0 x1)) (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

series233.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ x0 (- 1.0 x1))
33.0ms	(/ x0 (- 1.0 x1))
85.0ms	(log (exp (- (* (/ x0 (- 1.0 x1)) (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))))
86.0ms	(- (* (/ x0 (- 1.0 x1)) (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1))))) (* x0 x0))

simplify42.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	351	1117
1	1364	1020
2	5001	999

prune304.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.3b

regimes49.0ms

Accuracy

77.3% (0.5b remaining)

Error of 4.6b against oracle of 4.2b and baseline of 6.3b

bsearch29.0ms

Steps

Iters	Range		Point
7	0.000209	0.0186	0.00021208908081054686

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	35
1	31	35

end0.0ms

sample679.0ms

Algorithm

intervals

Results

326.0ms	3991×	pre	10240	exit
119.0ms	8000×	body	80	valid
52.0ms	4009×	pre	80	true