Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	255×	body	80	valid
2.0ms	17×	body	640	valid
2.0ms	18×	body	320	valid
2.0ms	10×	body	1280	valid
0.0ms	5×	body	160	valid

simplify74.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.2b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite50.0ms

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:

10.0ms	(/ (- t x) (- a z))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
30.0ms	(* (- y z) (/ (- t x) (- a z)))

series317.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- t x) (- a z))
147.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
123.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify53.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

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

prune315.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
10.3b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite10.0ms

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

series572.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (- t x))
139.0ms	(cbrt (- t x))
143.0ms	(cbrt (- t x))
145.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify33.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	252	689
1	775	601
2	5002	588

prune304.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.1b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.8b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite85.0ms

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))
72.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
2.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series718.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (- a z))
143.0ms	(cbrt (- a z))
285.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
146.0ms	(+ 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 (72.0ms)

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

prune450.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.1b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
7.9b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

112×	`cbrt-div`
40×	`add-exp-log`
35×	`flip3--` `associate-r` `flip--`
34×	`associate-/r/`
33×	`frac-times`
28×	`add-cbrt-cube`
22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
17×	`associate-l` `associate-*l/`
15×	`prod-exp` `cbrt-unprod`
12×	`cbrt-undiv` `div-exp`
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 → 125

Calls

4 calls:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
97.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
2.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (- a z))
142.0ms	(cbrt (- a z))
297.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
151.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

simplify96.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	950	2654
1	3901	2309
2	5003	2292

prune527.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.2b

regimes330.0ms

Accuracy

14.7% (7.4b remaining)

Error of 10.8b against oracle of 3.3b and baseline of 12.1b

bsearch63.0ms

Steps

Iters	Range		Point
3	1.829737677608388e-73	2.20669767931691e-73	1.9946576783558662e-73
7	-1.0411090379625735e-32	-7.240415757318844e-35	-7.37556037696158e-35

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	46
1	43	46

end0.0ms

sample712.0ms

Algorithm

intervals

Results

263.0ms	7854×	body	80	valid
61.0ms	463×	body	640	valid
42.0ms	238×	body	1280	valid
40.0ms	439×	body	320	valid
18.0ms	293×	body	160	valid
4.0ms	19×	body	2560	valid