Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	261×	body	80	valid
1.0ms	7×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	13×	body	160	valid
1.0ms	9×	body	320	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1498	6
6	3410	6
7	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.8b	(+ x (/ (* (- y z) (- t x)) (- a z)))
18.9b	(/ (* (- y z) (- t x)) (- a z))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

17.0ms	(* (- y z) (- t x))
13.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
13.0ms	(/ (* (- y z) (- t x)) (- a z))

series311.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* (- y z) (- t x))
149.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
128.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	466	583
1	2158	534
2	5001	534

prune238.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
3.3b	(+ x (/ (- y z) (/ (- a z) (- t x))))
6.8b	(/ (- y z) (/ (- a z) (- t x)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

10.0ms	(/ (- a z) (- t x))
64.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
20.0ms	(/ (- y z) (/ (- a z) (- t x)))

series497.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- a z) (- t x))
150.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
296.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify97.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	1021	3042
1	4255	2973
2	5001	2973

prune584.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.5b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.3b	(* (- y z) (/ (- t x) (- a z)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

10.0ms	(/ (- t x) (- a z))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
31.0ms	(* (- y z) (/ (- t x) (- a z)))

series322.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- t x) (- a z))
148.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
125.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	473	869
1	2012	820
2	5001	820

prune288.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.3b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
6.7b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-r`
10×	`cbrt-prod` `flip3--` `flip--`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-/r/`
6×	`pow1` `frac-times` `add-log-exp`
5×	`associate-l`
4×	`cbrt-undiv` `div-exp` `associate-*l/`
3×	`associate-*r/` `distribute-lft-out--` `difference-of-squares`
2×	`times-frac` `pow1/3` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 85

Calls

4 calls:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
56.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series716.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- a z))
146.0ms	(cbrt (- a z))
272.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
152.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	668	1363
1	2615	1151
2	5001	1129

prune337.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 2.1b

regimes272.0ms

Accuracy

41.4% (4.7b remaining)

Error of 8.9b against oracle of 4.1b and baseline of 12.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	38
1	43	38

end0.0ms

sample690.0ms

Algorithm

intervals

Results

257.0ms	7822×	body	80	valid
60.0ms	477×	body	640	valid
41.0ms	450×	body	320	valid
36.0ms	223×	body	1280	valid
18.0ms	289×	body	160	valid
4.0ms	20×	body	2560	valid