Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	252×	body	80	valid
2.0ms	12×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	10×	body	160	valid

simplify79.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.4b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.2b	(/ (* (- y z) (- t x)) (- a z))

rewrite43.0ms

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))
10.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
13.0ms	(/ (* (- y z) (- t x)) (- a z))

series337.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (- y z) (- t x))
173.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
128.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify60.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

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

prune262.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.5b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite95.0ms

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))
77.0ms	(* (/ (- 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)))))

series743.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a z))
146.0ms	(cbrt (- a z))
298.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
150.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (77.0ms)

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

prune498.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.5b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.0b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite155.0ms

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))
136.0ms	(* (/ (/ (- 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))))))

series780.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (- a z))
150.0ms	(cbrt (- a z))
312.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
161.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1131	4150
1	5001	3682

prune839.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.5b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.0b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

530×	`cbrt-div`
141×	`frac-times`
117×	`flip3--` `flip--`
101×	`associate-l`
90×	`associate-/r/`
85×	`add-sqr-sqrt`
80×	`times-frac`
78×	`cbrt-prod`
74×	`*-un-lft-identity`
69×	`add-exp-log`
61×	`associate-r`
53×	`associate-*r/`
47×	`associate-*l/`
42×	`add-cbrt-cube`
36×	`add-cube-cbrt`
27×	`cbrt-undiv` `div-exp`
24×	`prod-exp` `cbrt-unprod`
19×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-log-exp`
4×	`unswap-sqr`
3×	`div-inv`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 247

Calls

4 calls:

2.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
297.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (* (* (cbrt (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 (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (- a z))
152.0ms	(cbrt (- a z))
304.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z)))))
161.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify77.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1367	7008
1	5001	6370

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.7b

regimes462.0ms

Accuracy

16.8% (6.9b remaining)

Error of 11.2b against oracle of 4.3b and baseline of 12.6b

bsearch201.0ms

Steps

Iters	Range		Point
9	3.0183211553061986e-130	3.317763405440665e-124	1.3082408098972084e-125
10	-2.211777368186794e-257	-1.8300679438425768e-268	-2.1818450075179132e-257
6	-1.1326466945507658e-187	-1.0523864653523711e-188	-1.6519652265531684e-188
8	-7.189517843117326e-85	-8.522686855083726e-88	-8.617935768654497e-88

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	84
1	57	84
2	60	84
3	60	84

end0.0ms

sample684.0ms

Algorithm

intervals

Results

250.0ms	7760×	body	80	valid
67.0ms	491×	body	640	valid
38.0ms	262×	body	1280	valid
37.0ms	416×	body	320	valid
18.0ms	256×	body	160	valid
4.0ms	24×	body	2560	valid