Details

sample140.0ms

Algorithm

intervals

Results

59.0ms	744×	body	80	nan
18.0ms	191×	body	80	valid
13.0ms	29×	body	640	valid
10.0ms	9×	body	1280	valid
5.0ms	15×	body	320	valid
2.0ms	13×	body	160	valid

simplify128.0ms

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: 6.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.1b	(* (- x 1.0) (log y))
4.3b	(log (- 1.0 y))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-+r+` `associate-*l/`
7×	`pow1`
6×	`add-exp-log` `associate-+l+` `flip3--` `flip--`
5×	`associate-l` `add-cbrt-cube` `add-log-exp`
4×	`associate-r` `frac-add` `distribute-lft-out--` `difference-of-squares`
2×	`log-div` `log-pow`
1×	`+-commutative` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 76

Calls

3 calls:

12.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
11.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series226.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
55.0ms	(* (- x 1.0) (log y))
45.0ms	(log (- 1.0 y))

simplify56.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	552	711
1	2111	664
2	5002	659

prune286.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 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	(+ (* (- 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))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 113

Calls

3 calls:

36.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
15.0ms	(+ (* (- 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))

series275.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
147.0ms	(+ (* (- x 1.0) (log y)) (* (- 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))

simplify116.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	833	2174
1	4457	2102
2	5001	2093

prune567.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

84×	`frac-add`
80×	`flip3--` `flip--`
62×	`associate-*r/`
50×	`associate-*l/`
30×	`log-prod`
26×	`add-sqr-sqrt`
24×	`frac-times`
22×	`*-un-lft-identity`
21×	`distribute-rgt-in` `distribute-lft-in`
18×	`add-cube-cbrt`
16×	`associate-+l+`
12×	`pow1` `sqrt-prod`
11×	`associate-+r+` `associate-r` `associate-l` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`sub-neg` `associate--l+` `log-pow`
4×	`flip3-+` `sum-log` `flip-+`
2×	`+-commutative` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 168

Calls

4 calls:

23.0ms	(+ (* (- x 1.0) (log (sqrt y))) (+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
11.0ms	(+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
11.0ms	(* (log (sqrt y)) (- x 1.0))
13.0ms	(* (- x 1.0) (log (sqrt y)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(+ (* (- x 1.0) (log (sqrt y))) (+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
197.0ms	(+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
70.0ms	(* (log (sqrt y)) (- x 1.0))
57.0ms	(* (- x 1.0) (log (sqrt y)))

simplify87.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1606	5903
1	5002	5838

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

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)

rewrite9.0ms

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)
0.0ms	(cbrt y)
1.0ms	(cbrt y)

series720.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (cbrt y) (cbrt y))
177.0ms	(cbrt y)
174.0ms	(cbrt y)
176.0ms	(cbrt y)

simplify85.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (80.0ms)

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

prune529.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes308.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	21
1	33	21
2	33	21

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.9s	24078×	body	80	nan
547.0ms	5863×	body	80	valid
355.0ms	779×	body	640	valid
219.0ms	277×	body	1280	valid
203.0ms	691×	body	320	valid
80.0ms	421×	body	160	valid