Details

sample153.0ms

Algorithm

intervals

Results

76.0ms	1620×	body	80	nan
14.0ms	256×	body	80	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	9
1	59	9
2	153	9
3	360	9
4	813	9
5	1639	9
6	3143	9
7	5001	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.2b	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.2b	(* (- a 0.5) (log t))
0.6b	(+ (log (+ x y)) (log z))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
19×	`log-prod`
18×	`add-sqr-sqrt`
15×	`pow1`
14×	`add-log-exp`
12×	`add-cube-cbrt`
9×	`associate-+r+` `log-pow` `distribute-lft-out`
7×	`associate-+l+`
6×	`add-exp-log` `distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*l/` `sum-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`
5×	`associate-+l-` `associate-l`
4×	`log-div` `flip3-+` `diff-log` `associate-r` `frac-add` `flip-+`
2×	`+-commutative` `associate--l-` `sub-neg` `associate--l+` `difference-of-squares`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

28.0ms	(- (+ (log (+ x y)) (log z)) t)
99.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
11.0ms	(* (- a 0.5) (log t))
6.0ms	(+ (log (+ x y)) (log z))

series508.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(- (+ (log (+ x y)) (log z)) t)
203.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
61.0ms	(* (- a 0.5) (log t))
73.0ms	(+ (log (+ x y)) (log z))

simplify61.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	618	1003
1	2230	940
2	5001	924

prune393.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
0.2b	(* (- a 0.5) (log t))
0.4b	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
0.5b	(+ (log (+ x y)) (log (sqrt z)))

rewrite616.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
28×	`log-prod`
24×	`pow1`
23×	`distribute-lft-out`
19×	`add-sqr-sqrt`
18×	`associate-+r+` `log-pow`
15×	`add-cube-cbrt` `add-log-exp`
11×	`sum-log`
8×	`associate-+l+`
7×	`associate-+l-`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sqrt-prod` `add-cbrt-cube`
5×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
4×	`log-div` `associate-r` `frac-add`
3×	`+-commutative` `diff-log`
1×	`sub-neg` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

564.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
10.0ms	(* (- a 0.5) (log t))
28.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
9.0ms	(+ (log (+ x y)) (log (sqrt z)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
61.0ms	(* (- a 0.5) (log t))
174.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
153.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify76.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	759	1405
1	2762	1276
2	5002	1251

prune483.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (+ (log (+ x y)) (* 2 (log (sqrt z)))) (- t (* (log (sqrt t)) (- a 0.5)))) (* (log (sqrt t)) (- a 0.5)))
0.2b	(* (log (sqrt t)) (- a 0.5))
0.2b	(* (log (sqrt t)) (- a 0.5))
0.6b	(+ (log (+ x y)) (* 2 (log (sqrt z))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `add-log-exp`
19×	`*-un-lft-identity`
16×	`associate-+r+` `log-prod` `associate-*r/`
14×	`flip3--` `flip--`
13×	`add-cube-cbrt`
12×	`pow1` `distribute-rgt-in` `distribute-lft-in` `associate-l` `frac-add`
10×	`associate-r`
8×	`add-exp-log` `associate-+l+` `sum-log` `frac-sub` `add-cbrt-cube`
7×	`sub-neg` `flip3-+` `flip-+`
6×	`diff-log` `sqrt-prod` `log-pow`
3×	`associate-+l-`
2×	`+-commutative` `log-div` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`associate--l+` `distribute-lft-out` `associate--r-`

Counts

4 → 123

Calls

4 calls:

77.0ms	(+ (- (+ (log (+ x y)) (* 2 (log (sqrt z)))) (- t (* (log (sqrt t)) (- a 0.5)))) (* (log (sqrt t)) (- a 0.5)))
11.0ms	(* (log (sqrt t)) (- a 0.5))
10.0ms	(* (log (sqrt t)) (- a 0.5))
7.0ms	(+ (log (+ x y)) (* 2 (log (sqrt z))))

series701.0ms

Counts

4 → 12

Calls

4 calls:

379.0ms	(+ (- (+ (log (+ x y)) (* 2 (log (sqrt z)))) (- t (* (log (sqrt t)) (- a 0.5)))) (* (log (sqrt t)) (- a 0.5)))
72.0ms	(* (log (sqrt t)) (- a 0.5))
74.0ms	(* (log (sqrt t)) (- a 0.5))
176.0ms	(+ (log (+ x y)) (* 2 (log (sqrt z))))

simplify110.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	996	2363
1	4434	2264
2	5001	2252

prune621.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
19.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt (+ x y))
140.0ms	(cbrt (+ x y))
132.0ms	(cbrt (+ x y))
173.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))

simplify142.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	246	671
1	888	634
2	4196	584
3	5001	580

prune533.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes662.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	25
1	30	25

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	54937×	body	80	nan
437.0ms	8032×	body	80	valid