Details

sample98.0ms

Algorithm

intervals

Results

36.0ms	735×	body	80	nan
10.0ms	189×	body	80	valid
8.0ms	26×	body	640	valid
4.0ms	6×	body	1280	valid
4.0ms	21×	body	320	valid
2.0ms	15×	body	160	valid

simplify130.0ms

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: 7.4b

localize16.0ms

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)
0.2b	(* (- x 1.0) (log y))
5.2b	(log (- 1.0 y))

rewrite68.0ms

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:

15.0ms	(* (- z 1.0) (log (- 1.0 y)))
36.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
12.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series313.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- z 1.0) (log (- 1.0 y)))
158.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
60.0ms	(* (- x 1.0) (log y))
47.0ms	(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

prune330.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 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))))))
0.2b	(* (- x 1.0) (log y))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `flip3--` `flip--`
25×	`*-un-lft-identity`
24×	`log-prod` `associate-*l/`
16×	`distribute-rgt-in` `add-cube-cbrt` `distribute-lft-in` `frac-add`
13×	`associate--l+`
12×	`frac-times`
11×	`add-log-exp`
10×	`pow1` `associate-+r+` `associate-r` `associate-l`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-*r/`
5×	`sub-neg` `distribute-lft-out--`
4×	`difference-of-squares`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `flip-+`

Counts

4 → 129

Calls

4 calls:

40.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
13.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
38.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
12.0ms	(* (- x 1.0) (log y))

series522.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
150.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
68.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
60.0ms	(* (- x 1.0) (log y))

simplify123.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	888	2535
1	4674	2460
2	5001	2448

prune664.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series747.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (cbrt y) (cbrt y))
177.0ms	(cbrt y)
181.0ms	(cbrt y)
181.0ms	(cbrt y)

simplify89.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune465.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (pow (/ 1 y) -1/3) (cbrt y))
0.6b	(cbrt y)
0.6b	(cbrt y)
5.0b	(pow (/ 1 y) -1/3)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
32×	`unpow-prod-down`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`times-frac`
21×	`add-exp-log`
17×	`associate-l`
14×	`cbrt-prod`
10×	`unswap-sqr`
8×	`pow-exp`
6×	`pow1` `associate-r` `prod-exp`
5×	`add-cbrt-cube`
4×	`div-exp` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `pow-pow`
2×	`pow-to-exp` `rec-exp` `pow1/3` `1-exp` `div-inv`
1×	`pow-flip` `*-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 102

Calls

4 calls:

18.0ms	(* (pow (/ 1 y) -1/3) (cbrt y))
0.0ms	(cbrt y)
1.0ms	(cbrt y)
4.0ms	(pow (/ 1 y) -1/3)

series745.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (pow (/ 1 y) -1/3) (cbrt y))
183.0ms	(cbrt y)
176.0ms	(cbrt y)
178.0ms	(pow (/ 1 y) -1/3)

simplify40.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	314	571
1	1283	531
2	5002	489

prune602.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

regimes573.0ms

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	24
1	42	24

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	23667×	body	80	nan
329.0ms	5917×	body	80	valid
241.0ms	768×	body	640	valid
152.0ms	250×	body	1280	valid
127.0ms	678×	body	320	valid
51.0ms	420×	body	160	valid