Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	244×	body	80	valid
2.0ms	15×	body	1280	valid
1.0ms	13×	body	320	valid
1.0ms	9×	body	640	valid
0.0ms	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

localize10.0ms

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))

series317.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* (- y z) (- t x))
150.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
128.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify58.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

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

prune254.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize18.0ms

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)))))

rewrite52.0ms

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))
36.0ms	(* (/ (- 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)))))

series767.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (- a z))
153.0ms	(cbrt (- a z))
306.0ms	(* (/ (- 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)))))

simplify94.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (79.0ms)

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

prune495.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.7b

localize17.0ms

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)) (pow (cbrt (- a z)) 1))) (/ (- t x) (cbrt (- a z))))
6.4b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (pow (cbrt (- a z)) 1))) (/ (- t x) (cbrt (- a z)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
47×	`times-frac`
46×	`associate-r`
41×	`add-exp-log`
36×	`cbrt-prod`
27×	`add-cube-cbrt`
20×	`add-cbrt-cube`
16×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
13×	`div-exp`
11×	`associate-l`
8×	`cbrt-div` `cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`associate-*l/` `unswap-sqr`
2×	`pow-to-exp` `pow1/3` `pow-exp` `div-inv`
1×	`+-commutative` `frac-times` `flip3-+` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip-+`

Counts

4 → 129

Calls

4 calls:

7.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
34.0ms	(* (/ (- y z) (* (cbrt (- a z)) (pow (cbrt (- a z)) 1))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (pow (cbrt (- a z)) 1))) (/ (- t x) (cbrt (- a z)))))

series768.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a z))
154.0ms	(cbrt (- a z))
312.0ms	(* (/ (- y z) (* (cbrt (- a z)) (pow (cbrt (- a z)) 1))) (/ (- t x) (cbrt (- a z))))
154.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (pow (cbrt (- a z)) 1))) (/ (- t x) (cbrt (- a z)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	743	1808
1	3523	1496
2	5001	1396

prune492.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.7b

localize20.0ms

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 (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
7.6b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

124×	`cbrt-div`
58×	`add-exp-log`
38×	`add-cbrt-cube`
35×	`flip3--` `associate-r` `flip--`
34×	`associate-/r/`
33×	`frac-times`
25×	`prod-exp` `cbrt-unprod`
22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp` `associate-l` `associate-*l/`
11×	`times-frac` `associate-*r/`
10×	`cbrt-prod` `add-cube-cbrt`
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 → 131

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
55.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (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 (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

series775.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (- a z))
152.0ms	(cbrt (- a z))
304.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
163.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

simplify100.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1002	2984
1	3954	2272
2	5002	2175

prune680.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.7b

regimes495.0ms

Accuracy

44.9% (4.6b remaining)

Error of 9.1b against oracle of 4.5b and baseline of 12.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	70
1	50	70

end0.0ms

sample715.0ms

Algorithm

intervals

Results

267.0ms	7742×	body	80	valid
68.0ms	524×	body	640	valid
43.0ms	259×	body	1280	valid
39.0ms	415×	body	320	valid
17.0ms	220×	body	160	valid
3.0ms	17×	body	2560	valid