Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	253×	body	80	valid
2.0ms	15×	body	1280	valid
1.0ms	14×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid

simplify70.0ms

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: 29.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.1b	(+ x (/ (* (- y z) (- t x)) (- a z)))
23.1b	(/ (* (- y z) (- t x)) (- a z))

rewrite88.0ms

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:

35.0ms	(* (- y z) (- t x))
19.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
31.0ms	(/ (* (- y z) (- t x)) (- a z))

series275.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(* (- y z) (- t x))
132.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
113.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify57.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

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

prune231.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite146.0ms

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:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
123.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series680.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(cbrt (- a z))
134.0ms	(cbrt (- a z))
268.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
140.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (76.0ms)

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

prune426.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* 1 (cbrt (- a z)))))
8.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* 1 (cbrt (- a z))))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
120.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* 1 (cbrt (- a z)))))
10.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* 1 (cbrt (- a z))))))

series676.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt (- a z))
133.0ms	(cbrt (- a z))
271.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* 1 (cbrt (- a z)))))
138.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* 1 (cbrt (- a z))))))

simplify79.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	660	1455
1	3127	1227
2	5002	1095

prune325.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.9b	(* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (* 1 (cbrt (- a z)))))
8.5b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (* 1 (cbrt (- a z))))))

rewrite894.0ms

Algorithm

rewrite-expression-head

Rules

384×	`cbrt-div`
137×	`frac-times`
111×	`flip3--` `flip--`
104×	`add-exp-log`
89×	`associate-l`
82×	`associate-/r/`
54×	`prod-exp`
53×	`associate-*r/` `add-cbrt-cube`
45×	`associate-*l/`
38×	`cbrt-unprod`
31×	`div-exp`
22×	`cbrt-undiv`
20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
11×	`associate-r`
10×	`cbrt-prod` `add-cube-cbrt` `times-frac`
6×	`pow1` `add-log-exp`
5×	`1-exp`
4×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 189

Calls

4 calls:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
859.0ms	(* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (* 1 (cbrt (- a z)))))
7.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (* 1 (cbrt (- a z))))))

series695.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (- a z))
138.0ms	(cbrt (- a z))
272.0ms	(* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (* 1 (cbrt (- a z)))))
150.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (* 1 (cbrt (- a z))))))

simplify155.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	1094	4137
1	4986	3228
2	5003	3165

prune992.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.3b

regimes422.0ms

Accuracy

22.4% (7.0b remaining)

Error of 11.0b against oracle of 4.1b and baseline of 13.1b

bsearch86.0ms

Steps

Iters	Range		Point
9	1.709955451654599e-144	3.5303979959117466e-138	6.559704169034857e-143
6	-8.689192513681542e-190	-1.0915813278155385e-190	-7.955121187742058e-190

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	60
1	59	60
2	59	60

end0.0ms

sample763.0ms

Algorithm

intervals

Results

234.0ms	7687×	body	80	valid
61.0ms	495×	body	640	valid
38.0ms	290×	body	1280	valid
33.0ms	422×	body	320	valid
14.0ms	260×	body	160	valid
1.0ms	9×	body	2560	valid