Details

sample50.0ms

Algorithm

intervals

Results

18.0ms	283×	body	80	valid
5.0ms	81×	body	80	nan

simplify104.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	285
1	22	285
2	46	285
3	72	285
4	97	285
5	118	285
done	118	285

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
6.0b	(* (* x y) z)
7.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
6×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `-commutative` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

15.0ms	(- (* z z) (* t a))
26.0ms	(* (* x y) z)
23.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms	(sqrt (- (* z z) (* t a)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* z z) (* t a))
31.0ms	(* (* x y) z)
118.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
93.0ms	(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts

98 → 98

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	146	26392
1	385	23608
2	2299	23488
done	5000	23383

prune792.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
2.8b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
24×	`associate-r` `sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
6×	`associate-/r*` `sqrt-div` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `associate-r/` `-commutative`

Counts

4 → 122

Calls

4 calls:

12.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
66.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
17.0ms	(sqrt (- (* z z) (* t a)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ z (sqrt (- (* z z) (* t a))))
53.0ms	(- (* z z) (* t a))
148.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
76.0ms	(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts

134 → 134

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	178	42931
1	496	38597
2	3169	38114
done	5000	38089

prune932.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

localize53.0ms

Local error

Found 4 expressions with local error:

6.1b	(* (/ (* x y) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
23.2b	(sqrt (- (* z z) (* t a)))
23.2b	(sqrt (- (* z z) (* t a)))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
41×	`add-sqr-sqrt`
33×	`associate-r`
32×	`add-cbrt-cube`
31×	`times-frac`
27×	`*-un-lft-identity` `add-cube-cbrt`
20×	`cbrt-prod` `sqrt-div`
19×	`sqrt-prod`
18×	`prod-exp` `cbrt-unprod`
14×	`cbrt-div`
13×	`cbrt-undiv` `div-exp` `associate-l`
10×	`flip3--` `associate-/r/` `flip--`
9×	`pow1`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 135

Calls

4 calls:

169.0ms	(* (/ (* x y) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
15.0ms	(sqrt (- (* z z) (* t a)))
16.0ms	(sqrt (- (* z z) (* t a)))
16.0ms	(sqrt (- (* z z) (* t a)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (/ (* x y) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
86.0ms	(sqrt (- (* z z) (* t a)))
83.0ms	(sqrt (- (* z z) (* t a)))
88.0ms	(sqrt (- (* z z) (* t a)))

simplify3.3s

Counts

147 → 147

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	222	67774
1	697	61572
2	4153	60771
done	5000	56656

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.3b

localize84.0ms

Local error

Found 4 expressions with local error:

4.9b	(* (/ x (cbrt (sqrt (- (* z z) (* t a))))) (* (/ y (cbrt (sqrt (- (* z z) (* t a))))) (/ z (cbrt (sqrt (- (* z z) (* t a)))))))
23.2b	(sqrt (- (* z z) (* t a)))
23.2b	(sqrt (- (* z z) (* t a)))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
33×	`associate-l`
32×	`add-cbrt-cube`
29×	`add-sqr-sqrt`
27×	`times-frac`
26×	`*-un-lft-identity` `add-cube-cbrt`
18×	`cbrt-prod` `prod-exp` `sqrt-prod` `cbrt-unprod`
13×	`cbrt-undiv` `div-exp`
12×	`pow1`
8×	`sqrt-div`
5×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-*l/`
2×	`cbrt-div` `associate-/r/`
1×	`associate-r` `*-commutative` `div-inv`

Counts

4 → 124

Calls

4 calls:

127.0ms	(* (/ x (cbrt (sqrt (- (* z z) (* t a))))) (* (/ y (cbrt (sqrt (- (* z z) (* t a))))) (/ z (cbrt (sqrt (- (* z z) (* t a)))))))
13.0ms	(sqrt (- (* z z) (* t a)))
17.0ms	(sqrt (- (* z z) (* t a)))
17.0ms	(sqrt (- (* z z) (* t a)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (/ x (cbrt (sqrt (- (* z z) (* t a))))) (* (/ y (cbrt (sqrt (- (* z z) (* t a))))) (/ z (cbrt (sqrt (- (* z z) (* t a)))))))
93.0ms	(sqrt (- (* z z) (* t a)))
380.0ms	(sqrt (- (* z z) (* t a)))
103.0ms	(sqrt (- (* z z) (* t a)))

simplify2.6s

Counts

136 → 136

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	183	57154
1	543	53219
2	2442	52578
done	5001	51663

prune999.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.3b

regimes1.2s

Accuracy

82.5% (3.6b remaining)

Error of 7.0b against oracle of 3.4b and baseline of 23.8b

bsearch165.0ms

Steps

Iters	Range		Point
7	4.962524782877993e+148	5.8027159941114316e+150	5.492884630545356e+148
10	-5.3387252649757745e+174	-1.6115166414884948e+164	-1.6311711944705693e+164

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	587
1	26	587
2	28	587
done	28	587

end0.0ms

sample1.4s

Algorithm

intervals

Results

756.0ms	8857×	body	80	valid
205.0ms	2816×	body	80	nan