Details

sample80.0ms

Algorithm

intervals

Results

25.0ms	256×	pre	80	true
13.0ms	187×	body	80	valid
7.0ms	20×	body	1280	valid
6.0ms	23×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	106	27
3	478	26
4	2726	26
done	5000	26

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.4b

localize30.0ms

Local error

Found 3 expressions with local error:

0.3b

(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))

0.3b

(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))

2.5b

(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
7×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-/l/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

3 → 93

Calls

3 calls:

34.0ms

(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))

37.0ms

(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))

1.0ms

(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series407.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms

(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))

153.0ms

(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))

164.0ms

(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.1s

Counts

102 → 102

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	172	1935
1	401	1877
2	1674	1748
done	5000	1746

prune400.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
0.2b	(/ 1 (fma 2.0 i (+ alpha beta)))
0.3b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
4.0b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
40×	`times-frac`
31×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`associate-r` `add-cbrt-cube`
8×	`associate-/l*`
7×	`pow1` `associate-/r*` `distribute-lft-out`
5×	`div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `associate-/r/` `cbrt-unprod` `associate-/l/`
1×	`flip3--` `pow-flip` `div-sub` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip--` `fma-udef` `inv-pow`

Counts

4 → 134

Calls

4 calls:

45.0ms	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
6.0ms	(/ 1 (fma 2.0 i (+ alpha beta)))
30.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
1.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

series485.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
94.0ms	(/ 1 (fma 2.0 i (+ alpha beta)))
101.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
195.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

simplify3.1s

Counts

146 → 146

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	216	2503
1	534	2341
2	3352	2089
done	5000	2081

prune600.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (fma 2.0 i (+ alpha beta)))
0.3b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
2.5b	(log1p (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)))
4.0b	(fma (expm1 (log1p (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
29×	`times-frac`
23×	`add-cube-cbrt`
10×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
7×	`associate-/r*`
6×	`distribute-lft-out`
5×	`pow1` `expm1-log1p-u` `distribute-lft-out--` `difference-of-squares`
4×	`log1p-expm1-u` `add-log-exp`
3×	`div-exp`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/r/` `div-inv` `associate-/l/`
1×	`rec-exp` `log1p-udef` `flip3--` `pow-flip` `flip3-+` `1-exp` `div-sub` `log1p-expm1` `flip--` `flip-+` `fma-udef` `inv-pow`

Counts

4 → 102

Calls

4 calls:

6.0ms	(/ 1 (fma 2.0 i (+ alpha beta)))
31.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0ms	(log1p (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms	(fma (expm1 (log1p (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

series679.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ 1 (fma 2.0 i (+ alpha beta)))
114.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
192.0ms	(log1p (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)))
280.0ms	(fma (expm1 (log1p (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

simplify980.0ms

Counts

114 → 114

Iterations

Useful iterations: 2 (289.0ms)

Iter	Nodes	Cost
0	185	2050
1	405	1926
2	1535	1748
done	5002	1748

prune524.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 16.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ beta alpha) (fma 2.0 i (+ beta alpha))) 1.0) 3)
0.3b	(/ (+ beta alpha) (fma 2.0 i (+ beta alpha)))
0.3b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
2.5b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ beta alpha) (fma 2.0 i (+ beta alpha))) 1.0)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
32×	`times-frac`
27×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
7×	`associate-/r*`
5×	`pow1` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`cube-mult` `pow-to-exp` `flip3--` `pow-pow` `unpow3` `div-sub` `pow-exp` `flip--` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

3.0ms	(pow (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ beta alpha) (fma 2.0 i (+ beta alpha))) 1.0) 3)
26.0ms	(/ (+ beta alpha) (fma 2.0 i (+ beta alpha)))
49.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ beta alpha) (fma 2.0 i (+ beta alpha))) 1.0)

series660.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(pow (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ beta alpha) (fma 2.0 i (+ beta alpha))) 1.0) 3)
85.0ms	(/ (+ beta alpha) (fma 2.0 i (+ beta alpha)))
132.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
180.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ beta alpha) (fma 2.0 i (+ beta alpha))) 1.0)

simplify1.6s

Counts

130 → 130

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	201	2894
1	518	2725
2	2317	2504
done	5001	2502

prune706.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.0b

regimes303.0ms

Accuracy

0% (0.3b remaining)

Error of 12.1b against oracle of 11.8b and baseline of 12.1b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	31
1	24	31
done	24	31

end0.0ms

sample2.2s

Algorithm

intervals

Results

990.0ms	6398×	body	80	valid
262.0ms	504×	body	1280	valid
239.0ms	556×	body	640	valid
235.0ms	8000×	pre	80	true
77.0ms	354×	body	320	valid
31.0ms	188×	body	160	valid