Details

sample111.0ms

Algorithm

intervals

Results

40.0ms	832×	body	80	nan
10.0ms	196×	body	80	valid
7.0ms	24×	body	640	valid
4.0ms	20×	body	320	valid
3.0ms	4×	body	1280	valid
1.0ms	13×	body	160	valid

simplify135.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	9
1	49	9
2	118	9
3	256	9
4	533	9
5	1250	9
6	2637	9
7	4297	9
8	4573	9
9	4588	9
10	4588	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b	(* (- x 1.0) (log y))
7.0b	(log (- 1.0 y))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`log-prod`
13×	`add-cube-cbrt`
11×	`pow1`
10×	`associate-l`
9×	`add-exp-log` `add-log-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`flip3--` `associate-*l/` `flip--`
3×	`log-pow`
2×	`log-div` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-log-exp` `associate--l+` `sum-log`

Counts

4 → 94

Calls

4 calls:

30.0ms	(* (- z 1.0) (log (- 1.0 y)))
80.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
23.0ms	(* (- x 1.0) (log y))
5.0ms	(log (- 1.0 y))

series308.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- z 1.0) (log (- 1.0 y)))
162.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
57.0ms	(* (- x 1.0) (log y))
46.0ms	(log (- 1.0 y))

simplify49.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	498	803
1	1805	714
2	5001	701

prune297.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b	(* (- x 1.0) (log y))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
80×	`times-frac`
78×	`associate-r`
57×	`*-un-lft-identity`
56×	`unpow-prod-down`
50×	`add-cube-cbrt`
31×	`add-exp-log`
27×	`flip3--` `flip--`
24×	`log-prod` `associate-*l/` `unpow2` `sqr-pow`
19×	`unswap-sqr`
16×	`distribute-rgt-in` `distribute-lft-in` `frac-add`
13×	`associate-l` `add-cbrt-cube`
12×	`pow1` `frac-times` `prod-exp` `associate--l+`
10×	`associate-+r+`
9×	`div-exp`
7×	`associate-*r/`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`sub-neg` `cbrt-unprod` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
2×	`log-pow`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 223

Calls

4 calls:

36.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
78.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
29.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
25.0ms	(* (- x 1.0) (log y))

series343.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
69.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
157.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
61.0ms	(* (- x 1.0) (log y))

simplify54.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1332	2812
1	5001	2662

prune930.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (log (cbrt y)))
0.3b	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
20×	`add-sqr-sqrt`
18×	`cbrt-prod` `*-un-lft-identity`
16×	`add-cube-cbrt`
14×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-+r+`
7×	`pow1`
6×	`add-exp-log` `associate-*l/` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `associate-r` `associate-l` `flip--`
4×	`associate-+l+` `associate-*r/` `frac-add`
3×	`pow1/3`
2×	`sub-neg` `log-pow`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

24.0ms	(* (- x 1.0) (log (cbrt y)))
33.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series784.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (- x 1.0) (log (cbrt y)))
297.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
185.0ms	(cbrt y)
177.0ms	(cbrt y)

simplify62.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	450	835
1	2041	746
2	5002	703

prune531.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (log (cbrt y)))
0.3b	(+ (* (* 2 (log (pow y 1/3))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
0.6b	(cbrt y)
5.0b	(pow y 1/3)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
21×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`cbrt-prod`
14×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-+r+`
8×	`pow1`
7×	`add-exp-log`
6×	`associate-*l/` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `associate-r` `associate-l` `flip--`
4×	`associate-+l+` `associate-*r/` `frac-add`
3×	`unpow-prod-down` `pow-unpow`
2×	`sub-neg` `pow1/3` `log-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `flip3-+` `unpow1/3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

24.0ms	(* (- x 1.0) (log (cbrt y)))
30.0ms	(+ (* (* 2 (log (pow y 1/3))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
4.0ms	(cbrt y)
3.0ms	(pow y 1/3)

series909.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (- x 1.0) (log (cbrt y)))
425.0ms	(+ (* (* 2 (log (pow y 1/3))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
179.0ms	(cbrt y)
179.0ms	(pow y 1/3)

simplify74.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	536	854
1	2391	753
2	5001	720

prune541.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes262.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	22
1	38	22

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	23996×	body	80	nan
303.0ms	5831×	body	80	valid
226.0ms	776×	body	640	valid
164.0ms	274×	body	1280	valid
125.0ms	708×	body	320	valid
47.0ms	441×	body	160	valid