Details

sample127.0ms

Algorithm

intervals

Results

47.0ms	283×	body	80	valid
7.0ms	83×	body	80	nan

simplify903.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	107
6	107
5	98
4	78
3	59
2	37
1	22
0	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
10.5b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.4b	(sqrt (- (* z z) (* t a)))

rewrite146.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-l` `prod-diff` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

18.0ms	(- (* z z) (* t a))
33.0ms	(* (* x y) z)
65.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.0ms	(sqrt (- (* z z) (* t a)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* z z) (* t a))
44.0ms	(* (* x y) z)
228.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
311.0ms	(sqrt (- (* z z) (* t a)))

simplify10.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1480
1	377
0	146

prune3.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
2.3b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.4b	(sqrt (- (* z z) (* t a)))

rewrite562.0ms

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×	`expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-r/` `associate-l` `prod-diff` `clear-num` `-commutative`

Counts

4 → 122

Calls

4 calls:

66.0ms	(/ z (sqrt (- (* z z) (* t a))))
60.0ms	(- (* z z) (* t a))
330.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.0ms	(sqrt (- (* z z) (* t a)))

series943.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ z (sqrt (- (* z z) (* t a))))
95.0ms	(- (* z z) (* t a))
260.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
341.0ms	(sqrt (- (* z z) (* t a)))

simplify10.9s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	1822
1	494
0	178

prune2.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.1b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.9b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
26.4b	(sqrt (- (* z z) (* t a)))

rewrite687.0ms

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×	`expm1-log1p-u` `sqrt-div` `pow-prod-down` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `div-inv`

Counts

4 → 102

Calls

4 calls:

61.0ms	(- (* z z) (* t a))
254.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
329.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.0ms	(sqrt (- (* z z) (* t a)))

series915.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(- (* z z) (* t a))
136.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
345.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
162.0ms	(sqrt (- (* z z) (* t a)))

simplify6.0s

Counts

114 → 114

Iterations

Iter	Nodes
done	5014
2	1409
1	438
0	173

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

localize366.0ms

Local error

Found 4 expressions with local error:

10.4b	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
26.4b	(sqrt (- (* z z) (* t a)))
26.4b	(sqrt (- (* z z) (* t a)))
26.4b	(sqrt (- (* z z) (* t a)))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`associate-*r/`
1×	`cbrt-prod` `cbrt-div` `pow1/3`

Counts

4 → 63

Calls

4 calls:

213.0ms	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
25.0ms	(sqrt (- (* z z) (* t a)))
21.0ms	(sqrt (- (* z z) (* t a)))
26.0ms	(sqrt (- (* z z) (* t a)))

series2.7s

Counts

4 → 12

Calls

4 calls:

1.4s	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
324.0ms	(sqrt (- (* z z) (* t a)))
449.0ms	(sqrt (- (* z z) (* t a)))
545.0ms	(sqrt (- (* z z) (* t a)))

simplify11.9s

Counts

75 → 75

Iterations

Iter	Nodes
done	5002
3	2304
2	742
1	277
0	117

prune3.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.7b

regimes4.9s

Accuracy

82.8% (3.4b remaining)

Error of 6.7b against oracle of 3.2b and baseline of 23.3b

bsearch1.4s

Steps

Iters	Range		Point
9	1.6100917271418707e+137	6.896997489231346e+142	5.4360171926206224e+141
6	2.624847451243116e-110	2.3808260139075385e-109	5.269881922884741e-110
7	-1.26166263512079e-276	-9.495748746157915e-279	-5.724817248923862e-277
10	-2.473174617620054e+121	-1.6898447500521535e+111	-2.1064933800072495e+111

simplify394.0ms

Iterations

Iter	Nodes
done	46
2	46
1	43
0	33

end10.0ms

sample10.8s

Algorithm

intervals

Results

4.4s	8840×	body	80	valid
462.0ms	2973×	body	80	nan