Details

sample31.0ms

Algorithm

intervals

Results

10.0ms	262×	body	80	valid
2.0ms	12×	body	1280	valid
1.0ms	11×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	1×	body	2560	valid

simplify69.0ms

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: 26.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.4b	(+ x (/ (* (- y z) (- t x)) (- a z)))
19.5b	(/ (* (- y z) (- t x)) (- a z))

rewrite96.0ms

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:

37.0ms	(* (- y z) (- t x))
24.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
32.0ms	(/ (* (- y z) (- t x)) (- a z))

series352.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* (- y z) (- t x))
168.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
145.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify55.0ms

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

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
2.2b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.8b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`cbrt-prod`
54×	`associate-r`
52×	`times-frac`
34×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
18×	`add-cbrt-cube`
14×	`flip3--` `flip--`
13×	`pow1`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `pow1/3` `div-exp`
6×	`add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

4.0ms	(cbrt (- a z))
38.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
134.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series760.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (- a z))
129.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
310.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
176.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify124.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	844	2163
1	4193	1974
2	5002	1855

prune546.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
9.5b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite22.0ms

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:

4.0ms	(cbrt (- t x))
4.0ms	(cbrt (- t x))
4.0ms	(cbrt (- t x))
8.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series620.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (- t x))
151.0ms	(cbrt (- t x))
151.0ms	(cbrt (- t x))
174.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify34.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	262	842
1	832	735
2	5001	722

prune342.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.5b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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:

4.0ms	(cbrt (- t x))
4.0ms	(cbrt (- t x))
4.0ms	(cbrt (- t x))
12.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (* (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x)))) (cbrt (cbrt (- t x)))) (cbrt (cbrt (- a z))))))

series632.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- t x))
154.0ms	(cbrt (- t x))
152.0ms	(cbrt (- t x))
180.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (* (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x)))) (cbrt (cbrt (- t x)))) (cbrt (cbrt (- a z))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	268	995
1	877	903
2	5001	892

prune393.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.5b

regimes372.0ms

Accuracy

22.4% (6.8b remaining)

Error of 10.2b against oracle of 3.4b and baseline of 12.2b

bsearch200.0ms

Steps

Iters	Range		Point
9	3.906933855206174e-64	1.6847351699293705e-56	3.982205837801959e-64
10	1.2849880842943817e-112	4.093128636353914e-99	3.054054256923968e-110
6	2.54027261473107e-123	2.3383613813366375e-122	3.054635075798594e-123
8	-1.4355383054732265e-147	-3.954270623759517e-151	-2.539948061879686e-148

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	97
1	62	97

end0.0ms

sample752.0ms

Algorithm

intervals

Results

242.0ms	7703×	body	80	valid
51.0ms	478×	body	640	valid
38.0ms	282×	body	1280	valid
32.0ms	387×	body	320	valid
18.0ms	267×	body	160	valid
2.0ms	14×	body	2560	valid