Details

sample34.0ms

Algorithm

intervals

Results

11.0ms	263×	body	80	valid
1.0ms	9×	body	640	valid
1.0ms	6×	body	1280	valid
1.0ms	11×	body	320	valid
0.0ms	2×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
7	2087
6	873
5	342
4	176
3	101
2	50
1	22
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
0.8b	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.4b	(/ (* (- z t) y) (- a t))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

26.0ms	(* (- z t) y)
61.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
22.0ms	(/ (* (- z t) y) (- a t))

series305.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* (- z t) y)
162.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
101.0ms	(/ (* (- z t) y) (- a t))

simplify1.2s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
2	1366
1	392
0	150

prune475.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.5b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
4.9b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
9×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
7×	`frac-times` `cbrt-undiv` `div-exp`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
5×	`associate-l/` `associate-r/`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sum-log` `sub-neg` `pow-prod-down` `associate--l+` `*-commutative`

Counts

4 → 127

Calls

4 calls:

5.0ms	(cbrt (- a t))
5.0ms	(cbrt (- a t))
136.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
38.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series703.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(cbrt (- a t))
173.0ms	(cbrt (- a t))
148.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
171.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify2.4s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
2	3099
1	795
0	274

prune818.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.7b

localize104.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
5.6b	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

14×	`frac-sub`
10×	`frac-times` `associate-*l/`
9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity` `flip3-+` `add-cube-cbrt` `flip-+`
6×	`associate-*r/`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`pow1/3`
2×	`diff-log`
1×	`sum-log` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)
60.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

288.0ms	(cbrt y)
264.0ms	(cbrt y)
231.0ms	(cbrt y)
278.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

simplify1.8s

Counts

73 → 73

Iterations

Iter	Nodes
done	5005
2	1697
1	430
0	151

prune670.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.8b	(* (/ (- z t) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
5.1b	(- (+ x y) (* (/ (- z t) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

296×	`cbrt-div`
139×	`frac-times`
112×	`flip3--` `flip--`
89×	`associate-l`
82×	`associate-/r/`
52×	`cbrt-prod` `add-sqr-sqrt`
47×	`associate-l/` `associate-r/`
41×	`*-un-lft-identity` `times-frac`
39×	`associate-r`
36×	`add-exp-log`
29×	`add-cube-cbrt`
24×	`add-cbrt-cube`
14×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares`
4×	`unswap-sqr`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sum-log` `sub-neg` `pow-prod-down` `associate--l+` `*-commutative`

Counts

4 → 210

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
317.0ms	(* (/ (- z t) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
29.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(cbrt (- a t))
194.0ms	(cbrt (- a t))
156.0ms	(* (/ (- z t) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
163.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

simplify2.3s

Counts

222 → 222

Iterations

Iter	Nodes
done	5001
1	1218
0	402

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.7b

regimes971.0ms

Accuracy

30.1% (5.1b remaining)

Error of 9.4b against oracle of 4.3b and baseline of 11.6b

bsearch133.0ms

Steps

Iters	Range		Point
8	8.391520337805593e-109	2.206490995737268e-106	2.0634699544571633e-108
6	-4.151288806614406e-87	-6.816939173909149e-88	-7.762846694516816e-88

simplify14.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample1.5s

Algorithm

intervals

Results

654.0ms	7354×	body	80	valid
164.0ms	434×	body	320	valid
141.0ms	450×	body	640	valid
78.0ms	257×	body	1280	valid
31.0ms	249×	body	160	valid
7.0ms	17×	body	2560	valid