Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	242×	body	80	valid
2.0ms	18×	body	320	valid
2.0ms	12×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	11×	body	160	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	44	6
2	122	6
3	327	6
4	868	6
5	1727	6
6	3544	6
7	5001	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.8b	(+ x (* (- y z) (/ (- t x) (- a z))))
3.9b	(* (- y z) (/ (- t x) (- a z)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

8.0ms	(/ (- t x) (- a z))
4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
16.0ms	(* (- y z) (/ (- t x) (- a z)))

series325.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (- t x) (- a z))
147.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
131.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify52.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	473	869
1	2012	820
2	5001	820

prune309.0ms

Filtered

128 candidates to 88 candidates (68.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.6b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite53.0ms

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))
37.0ms	(* (/ (- 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)))))

series747.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a z))
150.0ms	(cbrt (- a z))
295.0ms	(* (/ (- 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)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (73.0ms)

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

prune465.0ms

Filtered

146 candidates to 103 candidates (70.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
10.1b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
36×	`cbrt-div`
26×	`add-sqr-sqrt`
22×	`add-cbrt-cube`
17×	`associate-l`
16×	`-un-lft-identity` `times-frac` `associate-r*` `associate-/r/`
15×	`prod-exp` `cbrt-unprod`
14×	`flip3--` `flip--`
13×	`cbrt-prod`
12×	`cbrt-undiv` `div-exp`
10×	`add-cube-cbrt`
9×	`frac-times`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`associate-r/` `associate-l/`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 110

Calls

4 calls:

3.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
32.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
3.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series932.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- t x))
342.0ms	(cbrt (- t x))
291.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
152.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify92.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	838	2470
1	3318	2130
2	5001	2090

prune529.0ms

Filtered

122 candidates to 90 candidates (73.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
9.6b	(+ x (* (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (cbrt (- t x)) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- 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 (- t x))
3.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
4.0ms	(+ x (* (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (cbrt (- t x)) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series585.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- t x))
142.0ms	(cbrt (- t x))
146.0ms	(cbrt (- t x))
151.0ms	(+ x (* (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (cbrt (- t x)) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify35.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	265	978
1	835	888
2	5001	877

prune360.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.6b

regimes444.0ms

Accuracy

62% (3.4b remaining)

Error of 6.6b against oracle of 3.2b and baseline of 12.2b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	45
1	44	45

end0.0ms

sample727.0ms

Algorithm

intervals

Results

265.0ms	7828×	body	80	valid
58.0ms	466×	body	640	valid
43.0ms	269×	body	1280	valid
38.0ms	416×	body	320	valid
18.0ms	286×	body	160	valid
1.0ms	8×	body	2560	valid