Details

sample33.0ms

Algorithm

intervals

Results

13.0ms	244×	body	80	valid
2.0ms	13×	body	1280	valid
2.0ms	15×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	6×	body	160	valid

simplify71.0ms

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: 14.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.5b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.6b	(* (- y z) (/ (- t x) (- a z)))

rewrite51.0ms

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

series326.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- t x) (- a z))
148.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
127.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify55.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

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

prune312.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
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 (- a z))
2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
3.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- a z))
147.0ms	(cbrt (- a z))
141.0ms	(cbrt (- a z))
149.0ms	(+ 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	258	689
1	784	601
2	5002	590

prune298.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
5.2b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
5.6b	(* (- y z) (* (- t x) (/ 1 (- a z))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-r/` `associate-l` `associate-l/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 146

Calls

4 calls:

6.0ms	(/ 1 (- a z))
25.0ms	(* (- t x) (/ 1 (- a z)))
3.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
32.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (- a z))
52.0ms	(* (- t x) (/ 1 (- a z)))
151.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
126.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

simplify72.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	585	1027
1	2810	910
2	5003	865

prune366.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
2.9b	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
3.0b	(* (cbrt (- y z)) (/ (- t x) (- a z)))
9.1b	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

114×	`cbrt-div`
84×	`frac-times`
58×	`flip3--` `flip--`
52×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`associate-*l/`
32×	`associate-r`
30×	`add-exp-log`
27×	`times-frac` `associate-*r/`
18×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
15×	`prod-exp` `cbrt-unprod`
12×	`cbrt-prod` `distribute-lft-out--` `difference-of-squares`
9×	`associate-l` `pow-prod-down`
6×	`add-log-exp`
4×	`unswap-sqr`
3×	`cbrt-undiv` `div-exp`
2×	`associate-/r/` `*-commutative`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `flip-+` `div-inv`

Counts

4 → 166

Calls

4 calls:

2.0ms	(cbrt (- y z))
58.0ms	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
33.0ms	(* (cbrt (- y z)) (/ (- t x) (- a z)))
3.0ms	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- y z))
127.0ms	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
614.0ms	(* (cbrt (- y z)) (/ (- t x) (- a z)))
154.0ms	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	895	2524
1	3311	2274
2	5001	2231

prune437.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.8b

regimes349.0ms

Accuracy

16.9% (7.9b remaining)

Error of 11.9b against oracle of 4.0b and baseline of 13.5b

bsearch64.0ms

Steps

Iters	Range		Point
2	4.963635864246088e-197	5.656435322295428e-197	5.521402742635328e-197
7	-6.0413703284063e-57	-4.145532328501884e-59	-4.256678409304163e-59

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

end0.0ms

sample922.0ms

Algorithm

intervals

Results

438.0ms	7771×	body	80	valid
80.0ms	484×	body	640	valid
52.0ms	280×	body	1280	valid
45.0ms	385×	body	320	valid
24.0ms	272×	body	160	valid
3.0ms	13×	body	2560	valid