Details

sample130.0ms

Algorithm

intervals

Results

66.0ms	367×	body	80	valid
29.0ms	320×	body	80	nan

simplify6.2s

Counts

1 → 1

Iterations

Useful iterations: 4 (158.0ms)

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.5b

localize25.0ms

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)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite225.0ms

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:

26.0ms	(* (- x 0.5) (log x))
98.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
19.0ms	(- (* (- x 0.5) (log x)) x)
78.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.9s

Counts

4 → 12

Calls

4 calls:

466.0ms	(* (- x 0.5) (log x))
659.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
679.0ms	(- (* (- x 0.5) (log x)) x)
141.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.7s

Counts

128 → 128

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	238	1852
1	574	1682
2	1606	1549
done	5001	1485

prune673.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.6b	(* (cbrt x) (cbrt x))
1.8b	(+ (- 0.91893853320467 x) x)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

1.0ms	(cbrt x)
12.0ms	(* (cbrt x) (cbrt x))
45.0ms	(+ (- 0.91893853320467 x) x)
76.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series738.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(cbrt x)
315.0ms	(* (cbrt x) (cbrt x))
1.0ms	(+ (- 0.91893853320467 x) x)
135.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.2s

Counts

131 → 131

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	179	1414
1	395	1164
2	1151	1003
3	4118	957
done	5000	957

prune963.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize88.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- 0.91893853320467 x) x)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
6.1b	(pow x 2/3)
6.1b	(pow x 2/3)

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

44.0ms	(+ (- 0.91893853320467 x) x)
93.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.0ms	(pow x 2/3)
5.0ms	(pow x 2/3)

series773.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ (- 0.91893853320467 x) x)
151.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
318.0ms	(pow x 2/3)
302.0ms	(pow x 2/3)

simplify3.4s

Counts

114 → 114

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	156	1254
1	364	1089
2	932	903
3	3052	859
done	5001	848

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.6b	(* (cbrt x) (cbrt x))
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`add-exp-log` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 99

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
24.0ms	(* (cbrt x) (cbrt x))
80.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

666.0ms	(cbrt x)
281.0ms	(cbrt x)
344.0ms	(* (cbrt x) (cbrt x))
115.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.5s

Counts

111 → 111

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	138	1209
1	298	1041
2	884	973
3	3105	940
done	5002	937

prune802.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

regimes482.0ms

Accuracy

89.3% (0.2b remaining)

Error of 4.1b against oracle of 3.8b and baseline of 6.0b

bsearch111.0ms

Steps

Iters	Range		Point
6	380432113365.94904	4289611374333.411	839179103462.1295

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	79
1	64	79
2	68	79
done	68	79

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	11637×	body	80	valid
1.6s	11710×	body	80	nan