Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	27×	body	1280	valid
6.0ms	183×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	23×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	12×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	4691
8	1531
7	665
6	318
5	164
4	74
3	53
2	34
1	20
0	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
2.2b	(+ 1.0 (/ (- beta alpha) (+ (+ alpha 2.0) beta)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 72

Calls

2 calls:

71.0ms	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
87.0ms	(+ 1.0 (/ (- beta alpha) (+ (+ alpha 2.0) beta)))

series192.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
116.0ms	(+ 1.0 (/ (- beta alpha) (+ (+ alpha 2.0) beta)))

simplify909.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
2	1406
1	341
0	127

prune387.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ beta alpha) 2.0))
0.2b	(exp (log (+ 1.0 (/ (- beta alpha) (+ (+ beta alpha) 2.0)))))
2.2b	(+ 1.0 (/ (- beta alpha) (+ (+ beta alpha) 2.0)))
4.3b	(log (+ 1.0 (/ (- beta alpha) (+ (+ beta alpha) 2.0))))

rewrite425.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

50.0ms	(/ (- beta alpha) (+ (+ beta alpha) 2.0))
125.0ms	(exp (log (+ 1.0 (/ (- beta alpha) (+ (+ beta alpha) 2.0)))))
120.0ms	(+ 1.0 (/ (- beta alpha) (+ (+ beta alpha) 2.0)))
123.0ms	(log (+ 1.0 (/ (- beta alpha) (+ (+ beta alpha) 2.0))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (- beta alpha) (+ (+ beta alpha) 2.0))
88.0ms	(exp (log (+ 1.0 (/ (- beta alpha) (+ (+ beta alpha) 2.0)))))
81.0ms	(+ 1.0 (/ (- beta alpha) (+ (+ beta alpha) 2.0)))
187.0ms	(log (+ 1.0 (/ (- beta alpha) (+ (+ beta alpha) 2.0))))

simplify1.1s

Counts

121 → 121

Iterations

Iter	Nodes
done	5002
2	1636
1	414
0	173

prune808.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ (+ beta alpha) 2.0))
0.1b	(* (- beta alpha) (/ 1 (+ (+ beta alpha) 2.0)))
5.6b	(+ 1.0 (* (- beta alpha) (/ 1 (+ (+ beta alpha) 2.0))))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
16×	`add-exp-log`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-/r` `associate-l*` `add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `flip3--` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `flip--`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

3 → 111

Calls

3 calls:

65.0ms	(/ 1 (+ (+ beta alpha) 2.0))
144.0ms	(* (- beta alpha) (/ 1 (+ (+ beta alpha) 2.0)))
12.0ms	(+ 1.0 (* (- beta alpha) (/ 1 (+ (+ beta alpha) 2.0))))

series225.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ 1 (+ (+ beta alpha) 2.0))
63.0ms	(* (- beta alpha) (/ 1 (+ (+ beta alpha) 2.0)))
89.0ms	(+ 1.0 (* (- beta alpha) (/ 1 (+ (+ beta alpha) 2.0))))

simplify3.3s

Counts

120 → 120

Iterations

Iter	Nodes
done	5002
2	3368
1	465
0	168

prune527.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.3b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (/ (+ (pow 1.0 3) (pow (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 3)) (fma (- (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 1.0) (/ (- beta alpha) (+ 2.0 (+ alpha beta))) (* 1.0 1.0)))))
1.9b	(- (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 1.0)
2.2b	(+ (pow 1.0 3) (pow (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 3))
4.3b	(log (/ (+ (pow 1.0 3) (pow (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 3)) (fma (- (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 1.0) (/ (- beta alpha) (+ 2.0 (+ alpha beta))) (* 1.0 1.0))))

rewrite898.0ms

Algorithm

rewrite-expression-head

Rules

321×	`*-un-lft-identity`
155×	`times-frac`
154×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
95×	`distribute-lft-out`
93×	`prod-diff`
62×	`log-prod`
31×	`unpow-prod-down` `fma-neg` `cube-prod` `exp-sum`
22×	`difference-of-squares`
21×	`distribute-lft-out--`
12×	`fma-def`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `sum-cubes`
6×	`pow1` `div-inv`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `rem-log-exp` `log-pow`
1×	`associate--l-` `cube-mult` `+-commutative` `sum-log` `sub-neg` `flip3--` `exp-diff` `diff-log` `unpow3` `div-sub` `div-exp` `flip--` `sqr-pow` `rem-exp-log`

Counts

4 → 263

Calls

4 calls:

186.0ms	(exp (log (/ (+ (pow 1.0 3) (pow (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 3)) (fma (- (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 1.0) (/ (- beta alpha) (+ 2.0 (+ alpha beta))) (* 1.0 1.0)))))
285.0ms	(- (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 1.0)
205.0ms	(+ (pow 1.0 3) (pow (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 3))
191.0ms	(log (/ (+ (pow 1.0 3) (pow (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 3)) (fma (- (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 1.0) (/ (- beta alpha) (+ 2.0 (+ alpha beta))) (* 1.0 1.0))))

series1.6s

Counts

4 → 12

Calls

4 calls:

365.0ms	(exp (log (/ (+ (pow 1.0 3) (pow (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 3)) (fma (- (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 1.0) (/ (- beta alpha) (+ 2.0 (+ alpha beta))) (* 1.0 1.0)))))
141.0ms	(- (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 1.0)
376.0ms	(+ (pow 1.0 3) (pow (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 3))
694.0ms	(log (/ (+ (pow 1.0 3) (pow (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 3)) (fma (- (/ (- beta alpha) (+ 2.0 (+ alpha beta))) 1.0) (/ (- beta alpha) (+ 2.0 (+ alpha beta))) (* 1.0 1.0))))

simplify1.3s

Counts

275 → 275

Iterations

Iter	Nodes
done	5004
2	2512
1	777
0	345

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.3b

regimes308.0ms

Accuracy

0% (0.3b remaining)

Error of 16.4b against oracle of 16.1b and baseline of 16.4b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	32
2	32
1	31
0	29

end0.0ms

sample1.8s

Algorithm

intervals

Results

750.0ms	733×	body	640	valid
352.0ms	5808×	body	80	valid
211.0ms	849×	body	1280	valid
153.0ms	8000×	pre	80	true
55.0ms	379×	body	320	valid
23.0ms	231×	body	160	valid