Details

sample96.0ms

Algorithm

intervals

Results

31.0ms	364×	body	80	valid
26.0ms	352×	body	80	nan

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 4 (274.0ms)

Iter	Nodes	Cost
0	20	24
1	40	23
2	92	23
3	263	23
4	576	22
5	1144	22
6	2010	22
7	4222	22
done	5000	22

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.5b

localize46.0ms

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)
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite283.0ms

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:

132.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
24.0ms	(* (- x 0.5) (log x))
32.0ms	(- (* (- x 0.5) (log x)) x)
90.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.0s

Counts

4 → 12

Calls

4 calls:

752.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
441.0ms	(* (- x 0.5) (log x))
696.0ms	(- (* (- x 0.5) (log x)) x)
120.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.6s

Counts

128 → 128

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	238	1852
1	574	1682
2	1609	1549
done	5000	1485

prune739.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x))))
0.5b	(* (sqrt x) (sqrt x))
3.5b	(+ (- 0.91893853320467 x) x)
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`pow1`
18×	`sqrt-prod`
11×	`associate-+l+`
9×	`times-frac` `prod-diff` `add-log-exp`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `swap-sqr` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`fma-def` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `pow-sqr` `associate-/l`
2×	`flip3-+` `sum-log` `flip-+` `associate-/l/` `distribute-lft-out` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `pow2` `associate-+l-` `sub-neg` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `difference-of-squares`

Counts

4 → 125

Calls

4 calls:

1.0ms	(fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x))))
16.0ms	(* (sqrt x) (sqrt x))
32.0ms	(+ (- 0.91893853320467 x) x)
70.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series463.0ms

Counts

4 → 12

Calls

4 calls:

308.0ms	(fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x))))
22.0ms	(* (sqrt x) (sqrt x))
1.0ms	(+ (- 0.91893853320467 x) x)
132.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.3s

Counts

137 → 137

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	211	1634
1	471	1200
2	1380	1017
3	4846	983
done	5000	983

prune822.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 0.5) (log x) (- (exp (log x))))
3.5b	(+ (- 0.91893853320467 x) x)
5.4b	(exp (log x))
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`times-frac` `prod-diff` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `fma-def`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u`
3×	`log-prod` `exp-sum` `associate-/r` `associate-/l`
2×	`flip3-+` `sum-log` `flip-+` `associate-/l/` `distribute-lft-out` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `log-pow` `fma-udef` `div-inv` `rem-exp-log` `difference-of-squares`

Counts

4 → 91

Calls

4 calls:

1.0ms	(fma (- x 0.5) (log x) (- (exp (log x))))
65.0ms	(+ (- 0.91893853320467 x) x)
7.0ms	(exp (log x))
113.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series636.0ms

Counts

4 → 12

Calls

4 calls:

500.0ms	(fma (- x 0.5) (log x) (- (exp (log x))))
2.0ms	(+ (- 0.91893853320467 x) x)
16.0ms	(exp (log x))
118.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.3s

Counts

103 → 103

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	181	1283
1	396	1077
2	1010	909
3	3159	861
done	5001	853

prune786.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.5b	(+ (- 0.91893853320467 x) x)
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
67.0ms	(+ (- 0.91893853320467 x) x)
87.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series806.0ms

Counts

4 → 12

Calls

4 calls:

334.0ms	(cbrt x)
325.0ms	(cbrt x)
2.0ms	(+ (- 0.91893853320467 x) x)
144.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.5s

Counts

102 → 102

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	142	1144
1	322	991
2	878	823
3	2863	785
done	5000	782

prune921.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

regimes562.0ms

Accuracy

91.7% (0.2b remaining)

Error of 4.3b against oracle of 4.1b and baseline of 6.2b

bsearch110.0ms

Steps

Iters	Range		Point
5	4.687878925179287e+24	1.6644311860639604e+25	4.755205523904898e+24

simplify36.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	70
1	57	70
2	59	70
done	59	70

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.0s	11688×	body	80	valid
1.5s	11626×	body	80	nan