Details

sample117.0ms

Algorithm

intervals

Results

44.0ms	865×	body	80	nan
13.0ms	177×	body	80	valid
10.0ms	31×	body	640	valid
7.0ms	11×	body	1280	valid
6.0ms	28×	body	320	valid
1.0ms	11×	body	160	valid

simplify127.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 10.2b

localize15.0ms

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))
4.3b	(log (- 1.0 y))

rewrite33.0ms

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:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
11.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
7.0ms	(* (- x 1.0) (log y))
4.0ms	(log (- 1.0 y))

series296.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (- z 1.0) (log (- 1.0 y)))
149.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
58.0ms	(* (- x 1.0) (log y))
46.0ms	(log (- 1.0 y))

simplify47.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (39.0ms)

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

prune312.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 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))))))) t)
0.0b	(* (- 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))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 196

Calls

4 calls:

24.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
12.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
12.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
7.0ms	(* (- x 1.0) (log y))

series408.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
239.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
67.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
54.0ms	(* (- x 1.0) (log y))

simplify112.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	1020	1850
1	4567	1639
2	5002	1636

prune755.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (log (cbrt y)))
0.2b	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`cbrt-prod`
28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt` `associate-+l+`
12×	`associate-+r+`
10×	`associate-*l/`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `associate-r` `associate-l` `flip--`
4×	`frac-add`
3×	`pow1/3`
2×	`log-pow`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

8.0ms	(* (- x 1.0) (log (cbrt y)))
14.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series640.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (- x 1.0) (log (cbrt y)))
159.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
181.0ms	(cbrt y)
176.0ms	(cbrt y)

simplify75.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	522	1002
1	2415	876
2	5003	829

prune691.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (* 2 (log (cbrt y))))
0.2b	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (pow (* (log (pow y 1/3)) (- x 1.0)) 1))
0.6b	(cbrt y)
5.1b	(pow y 1/3)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

48×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
27×	`cbrt-prod`
26×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`add-cube-cbrt` `associate-+l+`
10×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`associate-l`
3×	`unpow-prod-down` `pow-unpow` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-*l/`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `flip3-+` `unpow1/3` `pow1/3` `associate-r` `pow-exp` `sum-log` `*-commutative` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

9.0ms	(* (- x 1.0) (* 2 (log (cbrt y))))
16.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (pow (* (log (pow y 1/3)) (- x 1.0)) 1))
1.0ms	(cbrt y)
2.0ms	(pow y 1/3)

series685.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (- x 1.0) (* 2 (log (cbrt y))))
219.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (pow (* (log (pow y 1/3)) (- x 1.0)) 1))
172.0ms	(cbrt y)
173.0ms	(pow y 1/3)

simplify66.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	512	1054
1	2073	855
2	5002	781

prune615.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes312.0ms

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	42	23
1	42	23

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	24606×	body	80	nan
343.0ms	5867×	body	80	valid
267.0ms	812×	body	640	valid
168.0ms	265×	body	1280	valid
138.0ms	699×	body	320	valid
49.0ms	401×	body	160	valid