Details

sample156.0ms

Algorithm

intervals

Results

46.0ms	407×	body	80	nan
46.0ms	363×	body	80	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4181
4	921
3	265
2	92
1	40
0	20

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize53.0ms

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)

rewrite150.0ms

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-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `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` `fma-neg` `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 → 116

Calls

4 calls:

18.0ms	(* (- x 0.5) (log x))
57.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
21.0ms	(- (* (- x 0.5) (log x)) x)
51.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.2s

Counts

4 → 12

Calls

4 calls:

812.0ms	(* (- x 0.5) (log x))
675.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
635.0ms	(- (* (- x 0.5) (log x)) x)
97.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.9s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	2700
1	636
0	241

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.7b

localize81.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x))))
0.2b	(+ (fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x)))) (+ 0.91893853320467 (fma x -1 x)))
0.5b	(* (sqrt x) (sqrt x))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

0.0ms	(fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x))))
24.0ms	(+ (fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x)))) (+ 0.91893853320467 (fma x -1 x)))
22.0ms	(* (sqrt x) (sqrt x))
82.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series763.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x))))
346.0ms	(+ (fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x)))) (+ 0.91893853320467 (fma x -1 x)))
16.0ms	(* (sqrt x) (sqrt x))
116.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.8s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
2	2356
1	528
0	205

prune963.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize83.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 0.5) (log x) (- (exp (log x))))
0.2b	(+ (fma (- x 0.5) (log x) (- (exp (log x)))) (+ 0.91893853320467 (fma x -1 x)))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.5b	(exp (log x))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

0.0ms	(fma (- x 0.5) (log x) (- (exp (log x))))
23.0ms	(+ (fma (- x 0.5) (log x) (- (exp (log x)))) (+ 0.91893853320467 (fma x -1 x)))
48.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
16.0ms	(exp (log x))

series1.2s

Counts

4 → 12

Calls

4 calls:

460.0ms	(fma (- x 0.5) (log x) (- (exp (log x))))
569.0ms	(+ (fma (- x 0.5) (log x) (- (exp (log x)))) (+ 0.91893853320467 (fma x -1 x)))
110.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
24.0ms	(exp (log x))

simplify1.7s

Counts

91 → 91

Iterations

Iter	Nodes
done	5002
2	1648
1	441
0	180

prune947.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize92.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 0.5) (log x) (- (exp (log x))))
0.2b	(+ (fma (- x 0.5) (log x) (- (exp (log x)))) (+ 0.91893853320467 (fma x -1 x)))
5.2b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))
5.5b	(exp (log x))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube` `add-log-exp`
7×	`pow1`
4×	`expm1-log1p-u` `exp-prod` `prod-exp` `log1p-expm1-u`
3×	`log-prod` `sum-log` `fma-def` `flip3-+` `associate-l` `exp-sum` `flip-+` `distribute-lft-out` `unswap-sqr`
2×	`frac-times` `div-exp` `associate-*l/` `cbrt-unprod` `fma-udef`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `associate-+l+` `associate-+r+` `1-exp` `pow-prod-down` `associate-r/` `log-pow` `un-div-inv` `-commutative` `div-inv` `rem-exp-log`

Counts

4 → 90

Calls

4 calls:

0.0ms	(fma (- x 0.5) (log x) (- (exp (log x))))
12.0ms	(+ (fma (- x 0.5) (log x) (- (exp (log x)))) (+ 0.91893853320467 (fma x -1 x)))
105.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))
5.0ms	(exp (log x))

series1.1s

Counts

4 → 12

Calls

4 calls:

455.0ms	(fma (- x 0.5) (log x) (- (exp (log x))))
536.0ms	(+ (fma (- x 0.5) (log x) (- (exp (log x)))) (+ 0.91893853320467 (fma x -1 x)))
132.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))
14.0ms	(exp (log x))

simplify2.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5002
2	2830
1	555
0	209

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

regimes660.0ms

Accuracy

67.6% (1.7b remaining)

Error of 2.4b against oracle of 0.7b and baseline of 5.9b

bsearch503.0ms

Steps

Iters	Range		Point
11	2.1402104874322472e+127	6.029479529397184e+147	2.7248093103244077e+127
8	-7.119538902109541e+65	-4.7944425865334455e+62	-1.1514827941302142e+64

simplify17.0ms

Iterations

Iter	Nodes
done	60
1	60
0	43

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.8s	11597×	body	80	nan
1.7s	11622×	body	80	valid