Details

sample88.0ms

Algorithm

intervals

Results

37.0ms	286×	body	80	valid
8.0ms	102×	body	80	nan

simplify95.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
5.0b	(* (* x y) z)
10.2b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.7b	(sqrt (- (* z z) (* t a)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

9.0ms	(- (* z z) (* t a))
27.0ms	(* (* x y) z)
72.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms	(sqrt (- (* z z) (* t a)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* z z) (* t a))
33.0ms	(* (* x y) z)
115.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
83.0ms	(sqrt (- (* z z) (* t a)))

simplify861.0ms

Counts: 88 → 88

prune403.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
3.4b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.7b	(sqrt (- (* z z) (* t a)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

21.0ms	(/ z (sqrt (- (* z z) (* t a))))
9.0ms	(- (* z z) (* t a))
66.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ z (sqrt (- (* z z) (* t a))))
48.0ms	(- (* z z) (* t a))
130.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
96.0ms	(sqrt (- (* z z) (* t a)))

simplify976.0ms

Counts: 124 → 124

prune428.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.7b	(* y (/ z (sqrt (- (* z z) (* t a)))))
25.7b	(sqrt (- (* z z) (* t a)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

12.0ms	(- (* z z) (* t a))
69.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
60.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
14.0ms	(sqrt (- (* z z) (* t a)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* z z) (* t a))
137.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
94.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
67.0ms	(sqrt (- (* z z) (* t a)))

simplify809.0ms

Counts: 104 → 104

prune429.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

localize43.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
1.6b	(* x (* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
25.7b	(sqrt (- (* z z) (* t a)))
25.7b	(sqrt (- (* z z) (* t a)))

rewrite867.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
62×	`add-cbrt-cube`
61×	`associate-r`
60×	`sqrt-prod`
54×	`times-frac`
46×	`add-sqr-sqrt`
44×	`add-cube-cbrt` `*-un-lft-identity`
41×	`prod-exp` `cbrt-unprod`
27×	`cbrt-prod`
20×	`pow1`
16×	`cbrt-undiv` `div-exp`
9×	`associate-*r/` `pow-prod-down`
8×	`sqrt-div`
4×	`associate-l` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `associate-/r/` `-commutative`
1×	`div-inv`

Counts

4 → 156

Calls

4 calls:

273.0ms	(* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
532.0ms	(* x (* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
14.0ms	(sqrt (- (* z z) (* t a)))
32.0ms	(sqrt (- (* z z) (* t a)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
171.0ms	(* x (* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
77.0ms	(sqrt (- (* z z) (* t a)))
90.0ms	(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts: 168 → 168

prune734.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.8b

regimes473.0ms

Accuracy

82.7% (3.4b remaining)

Error of 6.7b against oracle of 3.2b and baseline of 23.2b

bsearch101.0ms

Steps

Iters	Range		Point
8	2.2645749879393821e+105	9.796547886431805e+107	4.946971173738666e+105
8	-2.1912854531733245e+76	-2.3726545645478223e+73	-4.7965124393733665e+73

simplify4.4s

end0.0ms

sample1.6s

Algorithm

intervals

Results

700.0ms	8847×	body	80	valid
172.0ms	2947×	body	80	nan