Details

sample23.0ms

Algorithm

intervals

Results

7.0ms	242×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	3×	body	1280	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 23.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
3.8b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.9b	(/ (* (- y z) (- t x)) (- a z))

rewrite48.0ms

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:

20.0ms	(* (- y z) (- t x))
11.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
14.0ms	(/ (* (- y z) (- t x)) (- a z))

series326.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* (- y z) (- t x))
147.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
145.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

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

prune253.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.2b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
10.6b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite96.0ms

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))
82.0ms	(* (/ (- 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)))))

series758.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a z))
147.0ms	(cbrt (- a z))
310.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
152.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (70.0ms)

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

prune427.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.6b	(cbrt (cbrt (- a z)))
1.3b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.6b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
167×	`add-sqr-sqrt`
123×	`cbrt-prod`
104×	`*-un-lft-identity`
80×	`associate-l`
78×	`cbrt-div`
61×	`associate-r`
60×	`add-cube-cbrt`
42×	`associate-/r/`
36×	`add-exp-log`
33×	`flip3--` `flip--`
22×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
21×	`frac-times`
20×	`unswap-sqr`
14×	`cbrt-undiv` `div-exp`
11×	`associate-r/` `associate-l/`
10×	`prod-exp` `cbrt-unprod`
6×	`pow1` `div-inv` `add-log-exp`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 233

Calls

4 calls:

2.0ms	(cbrt (- a z))
3.0ms	(cbrt (cbrt (- a z)))
160.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (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 (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series763.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (- a z))
148.0ms	(cbrt (cbrt (- a z)))
305.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
158.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1407	5010
1	5001	4769

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
9.4b	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (/ (- t x) (cbrt (cbrt (- a z)))))))

rewrite11.0ms

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:

2.0ms	(cbrt (- y z))
2.0ms	(cbrt (- y z))
2.0ms	(cbrt (- y z))
3.0ms	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (/ (- t x) (cbrt (cbrt (- a z)))))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (- y z))
145.0ms	(cbrt (- y z))
150.0ms	(cbrt (- y z))
156.0ms	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (cbrt (- a z)))) (/ (- t x) (cbrt (cbrt (- a z)))))))

simplify35.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	267	842
1	838	768
2	5001	759

prune317.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 3.7b

regimes393.0ms

Accuracy

17.1% (6.7b remaining)

Error of 10.8b against oracle of 4.1b and baseline of 12.2b

bsearch102.0ms

Steps

Iters	Range		Point
8	9.406377240637868e-157	1.2444488060589802e-152	5.165813913438712e-154
7	-1.9725596831333072e-112	-1.701482398250145e-114	-8.241137967832466e-114

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	35
1	41	35

end0.0ms

sample674.0ms

Algorithm

intervals

Results

246.0ms	7803×	body	80	valid
62.0ms	497×	body	640	valid
38.0ms	416×	body	320	valid
34.0ms	238×	body	1280	valid
20.0ms	289×	body	160	valid
2.0ms	12×	body	2560	valid