Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

269×

body

valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	5
1	35	5
2	56	5
3	94	5
4	150	5
5	185	5
6	203	5
7	230	5
8	280	5
9	368	5
10	457	5
11	723	5
12	922	5
13	1038	5
14	1060	5
15	1060	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.3b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `div-exp` `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 → 113

Calls

3 calls:

2.0ms	(+ x (* y (/ (- z t) (- z a))))
10.0ms	(/ (- z t) (- z a))
23.0ms	(* y (/ (- z t) (- z a)))

series171.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(+ x (* y (/ (- z t) (- z a))))
41.0ms	(/ (- z t) (- z a))
60.0ms	(* y (/ (- z t) (- z a)))

simplify44.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	423	747
1	1655	704
2	5001	704

prune266.0ms

Filtered

122 candidates to 83 candidates (68.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

3.2b	(* y (* (* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a)))) (cbrt (/ (- z t) (- z a)))))
6.2b	(cbrt (/ (- z t) (- z a)))
6.2b	(cbrt (/ (- z t) (- z a)))
6.2b	(cbrt (/ (- z t) (- z a)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
38×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
15×	`cbrt-div`
13×	`pow1` `add-exp-log`
10×	`associate-*r/`
9×	`add-cbrt-cube`
6×	`pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod`
5×	`frac-times` `associate-*l/`
4×	`add-log-exp`
3×	`flip3--` `pow1/3` `associate-l` `flip--` `div-inv`
1×	`associate-r` `*-commutative`

Counts

4 → 148

Calls

4 calls:

200.0ms	(* y (* (* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a)))) (cbrt (/ (- z t) (- z a)))))
5.0ms	(cbrt (/ (- z t) (- z a)))
5.0ms	(cbrt (/ (- z t) (- z a)))
5.0ms	(cbrt (/ (- z t) (- z a)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* y (* (* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a)))) (cbrt (/ (- z t) (- z a)))))
130.0ms	(cbrt (/ (- z t) (- z a)))
122.0ms	(cbrt (/ (- z t) (- z a)))
121.0ms	(cbrt (/ (- z t) (- z a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	349	1680
1	864	1550
2	2809	1469
3	5001	1410

prune451.0ms

Filtered

160 candidates to 107 candidates (66.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

2.0b	(* y (* (* (cbrt (/ (- z t) (- z a))) (cbrt (- z t))) (cbrt (/ (- z t) (- z a)))))
3.0b	(/ (* y (* (* (cbrt (/ (- z t) (- z a))) (cbrt (- z t))) (cbrt (/ (- z t) (- z a))))) (cbrt (- z a)))
6.2b	(cbrt (/ (- z t) (- z a)))
6.2b	(cbrt (/ (- z t) (- z a)))

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt` `*-un-lft-identity`
72×	`cbrt-prod`
58×	`times-frac`
44×	`cbrt-div`
32×	`associate-*r/`
31×	`add-cube-cbrt`
27×	`add-exp-log`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`frac-times`
15×	`add-cbrt-cube`
14×	`associate-*l/`
13×	`pow1`
12×	`prod-exp` `cbrt-unprod`
11×	`flip3--` `flip--` `associate-/l/`
8×	`associate-/r*`
6×	`pow-prod-down` `associate-/r/`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-l` `div-inv`
2×	`pow1/3`
1×	`frac-2neg` `associate-r` `clear-num` `-commutative` `associate-/l`

Counts

4 → 160

Calls

4 calls:

145.0ms	(* y (* (* (cbrt (/ (- z t) (- z a))) (cbrt (- z t))) (cbrt (/ (- z t) (- z a)))))
148.0ms	(/ (* y (* (* (cbrt (/ (- z t) (- z a))) (cbrt (- z t))) (cbrt (/ (- z t) (- z a))))) (cbrt (- z a)))
5.0ms	(cbrt (/ (- z t) (- z a)))
9.0ms	(cbrt (/ (- z t) (- z a)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* y (* (* (cbrt (/ (- z t) (- z a))) (cbrt (- z t))) (cbrt (/ (- z t) (- z a)))))
65.0ms	(/ (* y (* (* (cbrt (/ (- z t) (- z a))) (cbrt (- z t))) (cbrt (/ (- z t) (- z a))))) (cbrt (- z a)))
129.0ms	(cbrt (/ (- z t) (- z a)))
124.0ms	(cbrt (/ (- z t) (- z a)))

simplify62.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	592	2148
1	1906	1936
2	5002	1908

prune596.0ms

Filtered

172 candidates to 123 candidates (71.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- z t) (- z a))
0.3b	(pow (/ (- z t) (- z a)) 3)
3.2b	(* y (cbrt (pow (/ (- z t) (- z a)) 3)))
13.3b	(cbrt (pow (/ (- z t) (- z a)) 3))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

246×	`add-sqr-sqrt`
231×	`*-un-lft-identity`
177×	`times-frac`
142×	`cbrt-prod`
95×	`unpow-prod-down` `cube-prod`
87×	`add-cube-cbrt`
72×	`distribute-lft-out--` `difference-of-squares`
71×	`associate-r`
14×	`associate-/r/`
11×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`flip3--` `flip--`
7×	`pow1` `div-inv` `unswap-sqr`
5×	`associate-/r` `associate-/l`
4×	`add-log-exp` `sqr-pow`
3×	`cube-div` `cube-mult` `pow-unpow` `unpow3` `associate-l`
2×	`cbrt-undiv` `cbrt-div` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 305

Calls

4 calls:

10.0ms	(/ (- z t) (- z a))
12.0ms	(pow (/ (- z t) (- z a)) 3)
71.0ms	(* y (cbrt (pow (/ (- z t) (- z a)) 3)))
14.0ms	(cbrt (pow (/ (- z t) (- z a)) 3))

series312.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (- z t) (- z a))
165.0ms	(pow (/ (- z t) (- z a)) 3)
64.0ms	(* y (cbrt (pow (/ (- z t) (- z a)) 3)))
42.0ms	(cbrt (pow (/ (- z t) (- z a)) 3))

simplify93.0ms

Algorithm

egg-herbie

Counts

317 → 317

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	721	2293
1	3237	2165
2	5001	2138

prune537.0ms

Filtered

317 candidates to 139 candidates (43.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes304.0ms

Accuracy

42.7% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 1.5b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	14
1	25	14

end0.0ms

sample516.0ms

Algorithm

intervals

Results

266.0ms	8699×	body	80	valid
0.0ms	2×	body	1280	valid