Details

sample153.0ms

Algorithm

intervals

Results

64.0ms	363×	body	80	valid
34.0ms	407×	body	80	nan

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4006
4	855
3	244
2	84
1	37
0	20

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

22.0ms	(* (- x 0.5) (log x))
56.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
18.0ms	(- (* (- x 0.5) (log x)) x)
49.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

383.0ms	(* (- x 0.5) (log x))
658.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
653.0ms	(- (* (- x 0.5) (log x)) x)
144.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify806.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	1981
1	527
0	216

prune800.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log (sqrt x)))
0.2b	(+ (- (* (- x 0.5) (log (sqrt x))) x) 0.91893853320467)
0.3b	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (- x 0.5) (log (sqrt x))) x) 0.91893853320467))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

42.0ms	(* (- x 0.5) (log (sqrt x)))
72.0ms	(+ (- (* (- x 0.5) (log (sqrt x))) x) 0.91893853320467)
133.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (- x 0.5) (log (sqrt x))) x) 0.91893853320467))
63.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series672.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (- x 0.5) (log (sqrt x)))
190.0ms	(+ (- (* (- x 0.5) (log (sqrt x))) x) 0.91893853320467)
238.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (- x 0.5) (log (sqrt x))) x) 0.91893853320467))
127.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.5s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	3615
1	774
0	284

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.7b

localize128.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467)
0.2b	(+ (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467) (* (log (sqrt (sqrt x))) (- x 0.5)))
0.2b	(+ (* (log (sqrt (sqrt x))) (- x 0.5)) (+ (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467) (* (log (sqrt (sqrt x))) (- x 0.5))))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite748.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-log-exp`
24×	`frac-add` `associate-*r/`
16×	`sum-log`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `flip3-+` `flip3--` `add-cube-cbrt` `flip-+` `flip--`
11×	`associate-+l+`
9×	`times-frac`
7×	`sub-neg`
6×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube` `add-exp-log`
5×	`associate-+r+` `associate-+l-`
4×	`pow1` `associate--l+`
3×	`+-commutative` `associate-/r` `diff-log` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `associate-+r-` `frac-2neg` `div-exp` `div-inv` `distribute-lft-out`

Counts

4 → 104

Calls

4 calls:

45.0ms	(+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467)
198.0ms	(+ (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467) (* (log (sqrt (sqrt x))) (- x 0.5)))
458.0ms	(+ (* (log (sqrt (sqrt x))) (- x 0.5)) (+ (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467) (* (log (sqrt (sqrt x))) (- x 0.5))))
42.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

227.0ms	(+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467)
541.0ms	(+ (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467) (* (log (sqrt (sqrt x))) (- x 0.5)))
487.0ms	(+ (* (log (sqrt (sqrt x))) (- x 0.5)) (+ (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467) (* (log (sqrt (sqrt x))) (- x 0.5))))
90.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify534.0ms

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
1	1096
0	342

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.5b	(cbrt x)
0.5b	(cbrt x)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
24×	`cbrt-prod` `associate-+l+`
12×	`associate-+r+`
9×	`times-frac`
8×	`associate-*l/`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `flip3--` `frac-add` `flip--`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

42.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
61.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
234.0ms	(cbrt x)
303.0ms	(cbrt x)
136.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.2s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	2798
1	648
0	238

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.7b

regimes996.0ms

Accuracy

66.7% (1.8b remaining)

Error of 2.4b against oracle of 0.7b and baseline of 6.0b

bsearch753.0ms

Steps

Iters	Range		Point
11	2.1402104874322472e+127	6.029479529397184e+147	2.7248093103244077e+127
8	-7.119538902109541e+65	-4.7944425865334455e+62	-1.1244228903454717e+64

simplify15.0ms

Iterations

Iter	Nodes
done	67
3	67
2	65
1	63
0	45

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.9s	11622×	body	80	valid
1.5s	11597×	body	80	nan