Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	261×	body	80	valid
1.0ms	7×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	13×	body	160	valid

simplify75.0ms

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: 12.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.5b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.3b	(* (- y z) (/ (- t x) (- a z)))

rewrite49.0ms

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

series333.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- t x) (- a z))
149.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
131.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

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

prune338.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.3b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
6.7b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
56.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (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)))))

series757.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (- a z))
151.0ms	(cbrt (- a z))
289.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
158.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	668	1363
1	2615	1151
2	5001	1129

prune382.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (- a z)))
0.6b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
1.3b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
6.7b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

2.0ms	(cbrt (cbrt (- a z)))
7.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
53.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

series718.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (cbrt (- a z)))
132.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
286.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
151.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

simplify81.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	770	1666
1	2955	1451
2	5001	1429

prune465.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
4.7b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
6.3b	(* (- y z) (* (- t x) (/ 1 (- a z))))

rewrite73.0ms

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:

5.0ms	(/ 1 (- a z))
26.0ms	(* (- t x) (/ 1 (- a z)))
3.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
32.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (- a z))
53.0ms	(* (- t x) (/ 1 (- a z)))
157.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
133.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

simplify73.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (61.0ms)

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

prune342.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.1b

regimes247.0ms

Accuracy

19.8% (6.5b remaining)

Error of 10.6b against oracle of 4.1b and baseline of 12.2b

bsearch105.0ms

Steps

Iters	Range		Point
9	1.0559418289661973e-179	1.2881465185077925e-174	1.2047109982673527e-174
6	-1.1928496952383683e-230	-7.816205266974664e-232	-5.877654282997229e-231

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	54
1	44	54

end0.0ms

sample686.0ms

Algorithm

intervals

Results

259.0ms	7822×	body	80	valid
57.0ms	477×	body	640	valid
44.0ms	449×	body	320	valid
34.0ms	223×	body	1280	valid
18.0ms	290×	body	160	valid
4.0ms	20×	body	2560	valid