Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	250×	body	80	valid
2.0ms	15×	body	640	valid
2.0ms	12×	body	1280	valid
1.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.4b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.3b	(* (- y z) (/ (- t x) (- a z)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`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/`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
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 → 128

Calls

3 calls:

24.0ms	(/ (- t x) (- a z))
7.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
56.0ms	(* (- y z) (/ (- t x) (- a z)))

series295.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (- t x) (- a z))
134.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
114.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	488	901
1	2066	849
2	5001	847

prune552.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.8b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
6.8b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
18×	`add-sqr-sqrt`
16×	`cbrt-div`
15×	`*-un-lft-identity`
14×	`add-cbrt-cube`
13×	`associate-r`
10×	`cbrt-prod` `flip3--` `flip--`
9×	`add-cube-cbrt` `prod-exp` `cbrt-unprod`
8×	`associate-/r/`
6×	`pow1` `frac-times` `add-log-exp`
5×	`associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u`
3×	`fma-def` `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 → 96

Calls

4 calls:

4.0ms	(cbrt (- t x))
4.0ms	(cbrt (- t x))
103.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
8.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series677.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (- t x))
137.0ms	(cbrt (- t x))
262.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
142.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	704	1444
1	2744	1230
2	5001	1149

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.8b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
9.6b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`add-sqr-sqrt` `associate-r`
12×	`cbrt-div`
10×	`*-un-lft-identity`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `flip3--` `associate-/r/` `flip--`
6×	`pow1` `cbrt-prod` `frac-times`
5×	`associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/`
2×	`times-frac` `pow1/3` `unswap-sqr`
1×	`pow-prod-down` `*-commutative` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 82

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
101.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series936.0ms

Counts

4 → 12

Calls

4 calls:

350.0ms	(cbrt x)
171.0ms	(cbrt x)
269.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
145.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	556	1207
1	2210	1020
2	5002	980

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
0.8b	(* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
9.5b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
21×	`add-sqr-sqrt`
20×	`cbrt-div`
17×	`cbrt-prod`
15×	`*-un-lft-identity`
13×	`associate-r`
10×	`flip3--` `flip--`
9×	`add-cube-cbrt` `prod-exp` `add-cbrt-cube` `cbrt-unprod`
8×	`associate-l` `associate-/r/`
6×	`pow1` `frac-times`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`times-frac` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`pow-prod-down` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 95

Calls

4 calls:

4.0ms	(cbrt (- y z))
4.0ms	(cbrt (- y z))
103.0ms	(* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series11.2s

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (- y z))
137.0ms	(cbrt (- y z))
10.7s	(* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
154.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	585	1540
1	2116	1362
2	5001	1307

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.8b

regimes1.1s

Accuracy

13.9% (7.7b remaining)

Error of 11.2b against oracle of 3.5b and baseline of 12.4b

bsearch131.0ms

Steps

Iters	Range		Point
8	2.4909543539839805e-126	1.8908109543398897e-123	1.731734774815035e-124
8	-3.647411327571071e-249	-2.031783625471612e-252	-1.7259749993791018e-250

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	18
1	31	18

end0.0ms

sample745.0ms

Algorithm

intervals

Results

289.0ms	7829×	body	80	valid
67.0ms	459×	body	640	valid
46.0ms	436×	body	320	valid
42.0ms	258×	body	1280	valid
18.0ms	262×	body	160	valid
2.0ms	11×	body	2560	valid