Details

sample39.0ms

Algorithm

intervals

Results

15.0ms	249×	body	80	valid
4.0ms	12×	body	1280	valid
3.0ms	19×	body	320	valid
3.0ms	13×	body	640	valid
1.0ms	8×	body	160	valid
1.0ms	2×	body	2560	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	44	6
2	122	6
3	327	6
4	868	6
5	1727	6
6	3544	6
7	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.4b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.0b	(* (- y z) (/ (- t x) (- a z)))

rewrite50.0ms

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))))
32.0ms	(* (- y z) (/ (- t x) (- a z)))

series325.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- t x) (- a z))
145.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
129.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify53.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

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

prune317.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.7b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
10.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
79.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series735.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- a z))
141.0ms	(cbrt (- a z))
295.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
154.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	744	1831
1	3287	1663
2	5001	1576

prune460.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
3.9b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

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

series603.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (- a z))
146.0ms	(cbrt (- a z))
151.0ms	(cbrt (- a z))
153.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify134.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	262	689
1	810	633
2	4502	622
3	5003	616

prune314.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 3.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (cbrt (- a z)))
1.7b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
10.7b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

114×	`cbrt-div`
40×	`add-exp-log`
35×	`flip3--` `associate-r` `flip--`
34×	`associate-/r/`
33×	`frac-times`
28×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`cbrt-prod`
17×	`associate-l` `associate-*l/`
15×	`prod-exp` `cbrt-unprod`
12×	`cbrt-undiv` `div-exp`
11×	`add-cube-cbrt` `times-frac` `associate-*r/`
6×	`pow1` `add-log-exp`
4×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `div-inv` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 128

Calls

4 calls:

2.0ms	(cbrt (- a z))
3.0ms	(cbrt (cbrt (- a z)))
103.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

series758.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (- a z))
151.0ms	(cbrt (cbrt (- a z)))
301.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
155.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

simplify99.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1025	2702
1	4063	2355
2	5001	2335

prune546.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.8b

regimes417.0ms

Accuracy

57.9% (3.7b remaining)

Error of 7.0b against oracle of 3.4b and baseline of 12.1b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	37
1	41	37

end0.0ms

sample1.0s

Algorithm

intervals

Results

470.0ms	7842×	body	80	valid
111.0ms	469×	body	640	valid
74.0ms	411×	body	320	valid
73.0ms	262×	body	1280	valid
30.0ms	267×	body	160	valid
6.0ms	18×	body	2560	valid