Details

sample100.0ms

Algorithm

intervals

Results

37.0ms	724×	body	80	nan
10.0ms	186×	body	80	valid
8.0ms	26×	body	640	valid
7.0ms	9×	body	1280	valid
5.0ms	26×	body	320	valid
1.0ms	9×	body	160	valid

simplify134.0ms

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: 5.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.2b	(* (- x 1.0) (log y))
6.1b	(log (- 1.0 y))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

37×	`log-prod`
35×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-*l/`
11×	`pow1`
10×	`associate-+r+` `associate-l`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
7×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
6×	`associate-+l+` `add-log-exp`
4×	`frac-add`
3×	`log-pow`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 109

Calls

4 calls:

14.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
14.0ms	(* (- z 1.0) (log (- 1.0 y)))
11.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series283.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
42.0ms	(* (- z 1.0) (log (- 1.0 y)))
58.0ms	(* (- x 1.0) (log y))
58.0ms	(log (- 1.0 y))

simplify65.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	621	970
1	2460	896
2	5003	883

prune388.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
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)))))))
0.2b	(* (- x 1.0) (log y))

rewrite103.0ms

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:

35.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
27.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
14.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
11.0ms	(* (- x 1.0) (log y))

series332.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
55.0ms	(* 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)))))))
56.0ms	(* (- x 1.0) (log y))

simplify59.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1332	2812
1	5001	2662

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.7b	(cbrt y)
0.7b	(cbrt y)
0.7b	(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))
0.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series781.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (cbrt y) (cbrt y))
204.0ms	(cbrt y)
181.0ms	(cbrt y)
187.0ms	(cbrt y)

simplify87.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (83.0ms)

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

prune471.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.7b	(cbrt y)
0.7b	(cbrt y)
4.9b	(pow (/ 1 y) -1/3)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `unpow-prod-down`
11×	`add-exp-log`
9×	`times-frac`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `pow-pow`
2×	`div-exp` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-to-exp` `rec-exp` `pow-flip` `pow-plus` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

6.0ms	(* (cbrt y) (cbrt y))
0.0ms	(cbrt y)
0.0ms	(cbrt y)
4.0ms	(pow (/ 1 y) -1/3)

series740.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (cbrt y) (cbrt y))
182.0ms	(cbrt y)
175.0ms	(cbrt y)
177.0ms	(pow (/ 1 y) -1/3)

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	276	402
1	1209	361
2	5002	320

prune479.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes242.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	35
1	41	35

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	24009×	body	80	nan
311.0ms	5885×	body	80	valid
245.0ms	803×	body	640	valid
145.0ms	238×	body	1280	valid
123.0ms	677×	body	320	valid
50.0ms	432×	body	160	valid