Details

sample46.0ms

Algorithm

intervals

Results

15.0ms	244×	body	80	valid
5.0ms	15×	body	1280	valid
2.0ms	13×	body	320	valid
2.0ms	9×	body	640	valid
1.0ms	2×	body	2560	valid
0.0ms	3×	body	160	valid

simplify66.0ms

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: 22.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.3b	(+ x (/ (* (- y z) (- t x)) (- a z)))
15.4b	(/ (* (- y z) (- t x)) (- a z))

rewrite31.0ms

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:

9.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series314.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (- y z) (- t x))
152.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
127.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify61.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

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

prune243.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

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))))
6.4b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite56.0ms

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:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
40.0ms	(* (/ (- 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)))))

series755.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (- a z))
150.0ms	(cbrt (- a z))
307.0ms	(* (/ (- 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)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (70.0ms)

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

prune487.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.7b	(* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
2.2b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

172×	`add-sqr-sqrt`
132×	`cbrt-prod`
126×	`times-frac`
120×	`*-un-lft-identity`
70×	`associate-l`
58×	`add-cube-cbrt`
46×	`associate-r`
31×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
15×	`unswap-sqr`
10×	`add-cbrt-cube`
8×	`cbrt-div`
6×	`pow1` `add-log-exp`
4×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative` `flip-+`

Counts

4 → 192

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
66.0ms	(* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (- a z))
150.0ms	(cbrt (- a z))
2.0s	(* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
156.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify95.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	914	2613
1	3514	2493
2	5001	2479

prune808.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
5.2b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

rewrite14.0ms

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:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
4.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

series608.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (- a z))
152.0ms	(cbrt (- a z))
152.0ms	(cbrt (- a z))
152.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	265	825
1	828	753
2	5002	744

prune335.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.7b

regimes358.0ms

Accuracy

8.5% (7.0b remaining)

Error of 11.5b against oracle of 4.5b and baseline of 12.2b

bsearch127.0ms

Steps

Iters	Range		Point
9	6.16613922102604e-280	2.5049479274625752e-272	2.4684183222348114e-272
8	-1.0308405028667604e-278	-7.876890058089722e-283	-7.454512941735669e-281

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	34
1	42	34

end0.0ms

sample715.0ms

Algorithm

intervals

Results

269.0ms	7742×	body	80	valid
69.0ms	524×	body	640	valid
41.0ms	259×	body	1280	valid
40.0ms	415×	body	320	valid
18.0ms	220×	body	160	valid
6.0ms	17×	body	2560	valid