Details

sample89.0ms

Algorithm

intervals

Results

31.0ms	372×	body	80	valid
27.0ms	370×	body	80	nan

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 4 (84.0ms)

Iter	Nodes	Cost
0	20	24
1	40	23
2	91	23
3	213	23
4	493	22
5	1037	22
6	1788	22
7	4317	22
done	5000	22

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`associate-+l+` `add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*l/` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `fma-neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

31.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
10.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(* (- x 0.5) (log x))
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

449.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
438.0ms	(- (* (- x 0.5) (log x)) x)
255.0ms	(* (- x 0.5) (log x))
88.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify742.0ms

Counts

128 → 128

Iterations

Useful iterations: done (738.0ms)

Iter	Nodes	Cost
0	238	1852
1	564	1682
2	1569	1549
done	5000	1505

prune528.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 0.5) (log x) (- (* x 1)))
0.1b	(+ (fma (- x 0.5) (log x) (- (* x 1))) (+ (- 0.91893853320467 x) x))
3.6b	(+ (- 0.91893853320467 x) x)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`add-log-exp`
12×	`associate-+l+`
9×	`times-frac` `prod-diff`
8×	`fma-def`
7×	`sum-log` `distribute-lft-out`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l` `distribute-lft-out--`
2×	`+-commutative` `associate-+l-` `diff-log` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `associate-+r-` `sub-neg` `associate-+r+` `frac-2neg` `div-exp` `clear-num` `div-inv` `difference-of-squares`

Counts

4 → 98

Calls

4 calls:

0.0ms	(fma (- x 0.5) (log x) (- (* x 1)))
33.0ms	(+ (fma (- x 0.5) (log x) (- (* x 1))) (+ (- 0.91893853320467 x) x))
16.0ms	(+ (- 0.91893853320467 x) x)
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series866.0ms

Counts

4 → 12

Calls

4 calls:

485.0ms	(fma (- x 0.5) (log x) (- (* x 1)))
293.0ms	(+ (fma (- x 0.5) (log x) (- (* x 1))) (+ (- 0.91893853320467 x) x))
1.0ms	(+ (- 0.91893853320467 x) x)
87.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify678.0ms

Counts

110 → 110

Iterations

Useful iterations: done (674.0ms)

Iter	Nodes	Cost
0	187	1712
1	475	1387
2	1327	1176
done	5001	1149

prune504.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series643.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt x)
185.0ms	(cbrt x)
181.0ms	(cbrt x)
90.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify992.0ms

Counts

82 → 82

Iterations

Useful iterations: 3 (332.0ms)

Iter	Nodes	Cost
0	101	939
1	225	870
2	611	794
3	1847	767
done	5001	767

prune434.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (fma (- x 0.5) (log x) (- (* x 1))) (+ (- 0.91893853320467 x) x))
0.3b	(/ 1 (/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)))
3.6b	(+ (- 0.91893853320467 x) x)
5.0b	(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
78×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
18×	`add-log-exp`
17×	`add-exp-log`
16×	`associate-/r*`
12×	`associate-+l+`
11×	`add-cbrt-cube`
9×	`prod-diff`
8×	`fma-def` `div-exp`
7×	`sum-log` `distribute-lft-out`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`+-commutative` `associate-+l-` `rec-exp` `frac-2neg` `flip3-+` `diff-log` `1-exp` `clear-num` `flip-+`
1×	`associate-+r-` `sub-neg` `associate-+r+` `pow-flip` `associate-/r/` `fma-udef` `inv-pow` `difference-of-squares`

Counts

4 → 164

Calls

4 calls:

33.0ms	(+ (fma (- x 0.5) (log x) (- (* x 1))) (+ (- 0.91893853320467 x) x))
5.0ms	(/ 1 (/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)))
19.0ms	(+ (- 0.91893853320467 x) x)
2.0ms	(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

series489.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(+ (fma (- x 0.5) (log x) (- (* x 1))) (+ (- 0.91893853320467 x) x))
88.0ms	(/ 1 (/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)))
1.0ms	(+ (- 0.91893853320467 x) x)
111.0ms	(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

simplify912.0ms

Counts

176 → 176

Iterations

Useful iterations: done (905.0ms)

Iter	Nodes	Cost
0	288	3475
1	688	3030
2	1734	2645
done	5000	2615

prune633.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.2b

regimes361.0ms

Accuracy

67.8% (0.9b remaining)

Error of 4.0b against oracle of 3.1b and baseline of 6.0b

bsearch1.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	60	119
1	87	117
2	89	117
done	89	117

end0.0ms

sample1.8s

Algorithm

intervals

Results

683.0ms	11786×	body	80	valid
559.0ms	11664×	body	80	nan