Details

sample150.0ms

Algorithm

intervals

Results

67.0ms	818×	body	80	nan
16.0ms	181×	body	80	valid
11.0ms	25×	body	640	valid
9.0ms	11×	body	1280	valid
8.0ms	28×	body	320	valid
3.0ms	14×	body	160	valid

simplify129.0ms

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: 8.8b

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)))
0.1b	(* (- x 1.0) (log y))
7.8b	(log (- 1.0 y))

rewrite45.0ms

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:

12.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
16.0ms	(* (- z 1.0) (log (- 1.0 y)))
11.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series262.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
44.0ms	(* (- z 1.0) (log (- 1.0 y)))
57.0ms	(* (- x 1.0) (log y))
42.0ms	(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

prune378.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))

rewrite99.0ms

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:

29.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
34.0ms	(* (- 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)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
14.0ms	(* (- x 1.0) (log y))

series319.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
66.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
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)))))))
54.0ms	(* (- x 1.0) (log y))

simplify61.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1332	2881
1	5002	2658

prune938.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 197

Calls

4 calls:

27.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
37.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
10.0ms	(+ (* (- x 1.0) (log y)) (pow (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 1))
11.0ms	(* (- x 1.0) (log y))

series328.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
62.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
152.0ms	(+ (* (- x 1.0) (log y)) (pow (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 1))
60.0ms	(* (- x 1.0) (log y))

simplify44.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1025	1878
1	5001	1619

prune802.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
0.5b	(cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.5b	(cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.5b	(cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

838×	`associate-*l/`
820×	`flip3--` `flip--`
738×	`cbrt-div`
656×	`frac-add`
652×	`frac-times`
182×	`associate-*r/`
41×	`flip3-+` `flip-+`
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 → 487

Calls

4 calls:

67.0ms	(* (cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
7.0ms	(cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
7.0ms	(cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
7.0ms	(cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

series8.3s

Counts

4 → 12

Calls

4 calls:

2.5s	(* (cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
1.9s	(cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
2.0s	(cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.9s	(cbrt (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

simplify448.0ms

Algorithm

egg-herbie

Counts

499 → 499

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1815	49618
1	5001	49409

prune3.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes268.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	32	16

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.0s	23888×	body	80	nan
542.0ms	5906×	body	80	valid
342.0ms	745×	body	640	valid
219.0ms	272×	body	1280	valid
201.0ms	662×	body	320	valid
85.0ms	451×	body	160	valid