Details

sample41.0ms

Algorithm

intervals

Results

16.0ms

281×

body

valid

simplify948.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	21	11
2	35	11
3	56	11
4	94	11
5	140	11
6	167	11
7	183	11
8	206	11
9	239	11
10	296	11
11	328	11
12	370	11
13	405	11
14	417	11
done	417	11

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite89.0ms

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:

7.0ms	(+ x (* y (/ (- z t) (- z a))))
24.0ms	(/ (- z t) (- z a))
52.0ms	(* y (/ (- z t) (- z a)))

series251.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(+ x (* y (/ (- z t) (- z a))))
64.0ms	(/ (- z t) (- z a))
75.0ms	(* y (/ (- z t) (- z a)))

simplify2.4s

Counts

122 → 122

Iterations

Useful iterations: 2 (284.0ms)

Iter	Nodes	Cost
0	162	1555
1	419	1454
2	1176	1368
3	3710	1368
done	5001	1368

prune334.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- z a))
0.5b	(cbrt (- z a))
0.5b	(cbrt (- z a))
5.2b	(* (/ y (* (cbrt (- z a)) (cbrt (- z a)))) (/ (- z t) (cbrt (- z a))))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
50×	`times-frac`
46×	`associate-r`
42×	`cbrt-prod`
28×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`cbrt-div`
18×	`add-cbrt-cube`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 136

Calls

4 calls:

4.0ms	(cbrt (- z a))
4.0ms	(cbrt (- z a))
5.0ms	(cbrt (- z a))
183.0ms	(* (/ y (* (cbrt (- z a)) (cbrt (- z a)))) (/ (- z t) (cbrt (- z a))))

series640.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt (- z a))
153.0ms	(cbrt (- z a))
178.0ms	(cbrt (- z a))
124.0ms	(* (/ y (* (cbrt (- z a)) (cbrt (- z a)))) (/ (- z t) (cbrt (- z a))))

simplify1.7s

Counts

148 → 148

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	223	2832
1	624	2712
2	2390	2339
done	5000	2207

prune577.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- z a))
0.0b	(+ x (pow (* (- z t) (/ y (- z a))) 1))
9.0b	(* (- z t) (/ y (- z a)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-l` `associate-/r*` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`associate-/l*`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `distribute-lft-out`

Counts

3 → 95

Calls

3 calls:

24.0ms	(/ y (- z a))
14.0ms	(+ x (pow (* (- z t) (/ y (- z a))) 1))
78.0ms	(* (- z t) (/ y (- z a)))

series242.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ y (- z a))
118.0ms	(+ x (pow (* (- z t) (/ y (- z a))) 1))
86.0ms	(* (- z t) (/ y (- z a)))

simplify1.3s

Counts

104 → 104

Iterations

Useful iterations: 2 (231.0ms)

Iter	Nodes	Cost
0	157	1262
1	370	1141
2	1370	1063
done	5000	1063

prune334.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (sqrt (/ (- z t) (- z a))))
0.1b	(* (* y (sqrt (/ (- z t) (- z a)))) (sqrt (/ (- z t) (- z a))))
3.2b	(sqrt (/ (- z t) (- z a)))
3.2b	(sqrt (/ (- z t) (- z a)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

144×	`add-sqr-sqrt`
131×	`*-un-lft-identity`
126×	`sqrt-prod`
103×	`times-frac`
68×	`associate-r`
51×	`add-cube-cbrt`
40×	`distribute-lft-out--` `difference-of-squares`
13×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
7×	`sqrt-div`
4×	`rem-sqrt-square` `flip3--` `associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`sqrt-pow1` `pow1/2` `*-commutative`
1×	`frac-times` `associate-*l/`

Counts

4 → 190

Calls

4 calls:

68.0ms	(* y (sqrt (/ (- z t) (- z a))))
142.0ms	(* (* y (sqrt (/ (- z t) (- z a)))) (sqrt (/ (- z t) (- z a))))
22.0ms	(sqrt (/ (- z t) (- z a)))
19.0ms	(sqrt (/ (- z t) (- z a)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* y (sqrt (/ (- z t) (- z a))))
77.0ms	(* (* y (sqrt (/ (- z t) (- z a)))) (sqrt (/ (- z t) (- z a))))
147.0ms	(sqrt (/ (- z t) (- z a)))
139.0ms	(sqrt (/ (- z t) (- z a)))

simplify1.8s

Counts

202 → 202

Iterations

Useful iterations: 2 (224.0ms)

Iter	Nodes	Cost
0	208	3304
1	450	2896
2	1044	2704
3	2395	2704
done	5001	2704

prune699.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes540.0ms

Accuracy

15.9% (1.2b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 1.5b

bsearch124.0ms

Steps

Iters	Range		Point
9	1.244754775604451e-168	1.1967843400343603e-160	9.403031276241487e-164
7	-5.825291196675339e-101	-4.3305558754680174e-103	-6.9640366385812096e-102

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	52
1	29	42
done	29	42

end0.0ms

sample963.0ms

Algorithm

intervals

Results

404.0ms	8726×	body	80	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	640	valid