Details

sample204.0ms

Algorithm

intervals

Results

92.0ms	368×	body	80	valid
72.0ms	401×	body	80	nan

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3225
5	1468
4	651
3	234
2	83
1	37
0	20

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(* (- x 0.5) (log x))
0.1b	(- (* (- x 0.5) (log x)) x)
3.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite172.0ms

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` `insert-posit16`
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 → 102

Calls

4 calls:

69.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
17.0ms	(* (- x 0.5) (log x))
22.0ms	(- (* (- x 0.5) (log x)) x)
61.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

686.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
344.0ms	(* (- x 0.5) (log x))
666.0ms	(- (* (- x 0.5) (log x)) x)
135.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1470
1	530
0	220

prune736.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (log (sqrt x)) (- x 0.5))
0.2b	(+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467)
0.3b	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
3.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
14×	`add-cube-cbrt`
10×	`associate-+l+`
9×	`times-frac`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`sum-log` `sub-neg`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `associate-*r/`
5×	`flip3-+` `associate-r` `flip-+`
4×	`frac-add` `associate--l+` `insert-posit16`
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-` `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 → 105

Calls

4 calls:

22.0ms	(* (log (sqrt x)) (- x 0.5))
41.0ms	(+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467)
157.0ms	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
41.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series748.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (log (sqrt x)) (- x 0.5))
267.0ms	(+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467)
236.0ms	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
109.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.0s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	2512
1	696
0	247

prune841.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize99.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5))) x) 0.91893853320467))
0.4b	(* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5)))
0.5b	(* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
3.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite694.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
15×	`add-cube-cbrt`
14×	`associate-r` `associate-*r/`
13×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
9×	`times-frac`
8×	`flip3-+` `sqrt-prod` `flip-+`
7×	`associate-l`
5×	`distribute-rgt-in` `sum-log` `distribute-lft-in` `flip3--` `flip--`
4×	`frac-times` `associate-+l+` `sub-neg` `pow-prod-down` `frac-add` `prod-exp` `cbrt-unprod` `insert-posit16` `difference-of-squares`
3×	`associate-/r` `log-pow` `associate-/l`
2×	`associate-l/` `-commutative` `distribute-lft-out` `distribute-lft-out--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `associate-+l-` `div-inv` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

561.0ms	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5))) x) 0.91893853320467))
39.0ms	(* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5)))
50.0ms	(* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
42.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

497.0ms	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5))) x) 0.91893853320467))
230.0ms	(* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5)))
988.0ms	(* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
93.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.9s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
1	1302
0	414

prune906.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
0.5b	(* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
0.5b	(* (sqrt (* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))) (sqrt (* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))))
3.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite428.0ms

Algorithm

rewrite-expression-head

Rules

168×	`associate-*r/`
144×	`frac-times` `sqrt-div`
141×	`pow1`
77×	`pow-prod-down`
61×	`flip3-+` `flip-+`
60×	`sqrt-pow1` `flip3--` `flip--`
48×	`associate-*l/`
36×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`associate-r`
18×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
17×	`pow-prod-up`
16×	`sqrt-prod`
12×	`pow1/2`
11×	`pow-sqr`
9×	`times-frac`
8×	`difference-of-squares`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `swap-sqr` `insert-posit16` `distribute-lft-out--` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*`
2×	`associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `div-inv` `unswap-sqr`

Counts

4 → 251

Calls

4 calls:

46.0ms	(* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
46.0ms	(* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
283.0ms	(* (sqrt (* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))) (sqrt (* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))))
45.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.4s

Counts

4 → 12

Calls

4 calls:

758.0ms	(* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
765.0ms	(* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
799.0ms	(* (sqrt (* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))) (sqrt (* (* (log (sqrt x)) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))))
100.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.0s

Counts

263 → 263

Iterations

Iter	Nodes
done	5000
2	3553
1	1011
0	444

prune1.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.0b

regimes628.0ms

Accuracy

0% (2.2b remaining)

Error of 6.0b against oracle of 3.8b and baseline of 6.0b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	38
1	38
0	27

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.9s	11823×	body	80	valid
2.1s	11750×	body	80	nan