Details

sample41.0ms

Algorithm

intervals

Results

18.0ms	248×	body	80	valid
4.0ms	15×	body	640	valid
3.0ms	16×	body	320	valid
2.0ms	8×	body	1280	valid
1.0ms	8×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 25.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.9b	(+ x (/ (* (- y z) (- t x)) (- a z)))
20.4b	(/ (* (- y z) (- t x)) (- a z))

rewrite46.0ms

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:

18.0ms	(* (- y z) (- t x))
11.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
13.0ms	(/ (* (- y z) (- t x)) (- a z))

series311.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (- y z) (- t x))
146.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
128.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify53.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

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

prune230.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.4b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.3b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite97.0ms

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))
81.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
5.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series737.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (- a z))
145.0ms	(cbrt (- a z))
300.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
151.0ms	(+ 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 (69.0ms)

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

prune451.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.2b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.7b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
98×	`times-frac`
84×	`cbrt-prod`
74×	`*-un-lft-identity`
69×	`add-exp-log`
61×	`associate-r`
44×	`cbrt-div`
42×	`add-cbrt-cube`
36×	`add-cube-cbrt`
29×	`associate-l`
27×	`cbrt-undiv` `div-exp`
24×	`prod-exp` `cbrt-unprod`
19×	`distribute-lft-out--` `difference-of-squares`
18×	`associate-/r/`
15×	`flip3--` `flip--`
12×	`unswap-sqr`
9×	`frac-times`
6×	`pow1` `add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`div-inv`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 183

Calls

4 calls:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
144.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
3.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series985.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (- a z))
337.0ms	(cbrt (- a z))
337.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
157.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1131	4150
1	5001	3682

prune770.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
0.8b	(* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (/ (- t x) (cbrt (cbrt (- a z))))))
8.8b	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (/ (- t x) (cbrt (cbrt (- a z)))))))

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

247×	`cbrt-prod`
242×	`times-frac`
162×	`add-exp-log`
160×	`associate-l`
136×	`add-sqr-sqrt` `*-un-lft-identity`
82×	`add-cube-cbrt`
71×	`cbrt-undiv` `div-exp`
69×	`add-cbrt-cube`
59×	`prod-exp` `cbrt-unprod`
30×	`cbrt-div`
27×	`distribute-lft-out--` `difference-of-squares`
24×	`associate-/r/`
14×	`flip3--` `flip--`
12×	`div-inv`
9×	`pow1`
6×	`add-log-exp`
5×	`frac-times` `associate-*r/`
3×	`pow-prod-down` `associate-*l/`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

4 → 275

Calls

4 calls:

2.0ms	(cbrt (- y z))
2.0ms	(cbrt (- y z))
309.0ms	(* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (/ (- t x) (cbrt (cbrt (- a z))))))
3.0ms	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (/ (- t x) (cbrt (cbrt (- a z)))))))

series779.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (- y z))
156.0ms	(cbrt (- y z))
309.0ms	(* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (/ (- t x) (cbrt (cbrt (- a z))))))
165.0ms	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (/ (- t x) (cbrt (cbrt (- a z)))))))

simplify84.0ms

Algorithm

egg-herbie

Counts

287 → 287

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1312	7936
1	5001	6950

prune1.2s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 4.6b

regimes487.0ms

Accuracy

14.4% (6.9b remaining)

Error of 11.1b against oracle of 4.2b and baseline of 12.3b

bsearch122.0ms

Steps

Iters	Range		Point
8	6.173255014219474e-128	2.3127944077603705e-125	8.738039030242588e-128
8	-1.6482409485603015e-77	-7.839661694105776e-81	-1.3251830678825456e-80

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	57
1	49	57

end0.0ms

sample1.1s

Algorithm

intervals

Results

499.0ms	7827×	body	80	valid
108.0ms	462×	body	640	valid
87.0ms	292×	body	1280	valid
78.0ms	427×	body	320	valid
34.0ms	266×	body	160	valid
7.0ms	20×	body	2560	valid