Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	193×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	20×	body	1280	valid
3.0ms	22×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	106	27
3	477	26
4	2270	26
done	5001	26

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

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

2.1b

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

rewrite45.0ms

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:

19.0ms

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

22.0ms

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

0.0ms

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

series317.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms

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

94.0ms

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

149.0ms

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

simplify1.8s

Counts

102 → 102

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	172	1935
1	391	1877
2	1095	1746
3	3539	1744
done	5000	1741

prune283.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
0.0b	(/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.2b	(* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
4.1b	(fma (* (- beta alpha) (/ 1 (+ (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

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

Counts

4 → 133

Calls

4 calls:

17.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
13.0ms	(/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))
41.0ms	(* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series381.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
73.0ms	(/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))
91.0ms	(* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
145.0ms	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.1s

Counts

145 → 145

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	213	2499
1	496	2253
2	1491	2040
done	5000	2039

prune380.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.2b

localize18.0ms

Local error

Found 4 expressions with local error:

2.4b	(cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
2.4b	(cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
2.4b	(cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
4.1b	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (* (* (cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) (cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) (cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-prod`
46×	`*-un-lft-identity`
36×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`fma-udef`

Counts

4 → 91

Calls

4 calls:

5.0ms	(cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
5.0ms	(cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
5.0ms	(cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
0.0ms	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (* (* (cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) (cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) (cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

328.0ms	(cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
333.0ms	(cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
336.0ms	(cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
173.0ms	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (* (* (cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) (cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) (cbrt (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)

simplify2.2s

Counts

103 → 103

Iterations

Useful iterations: 4 (951.0ms)

Iter	Nodes	Cost
0	106	2415
1	176	2376
2	380	1932
3	958	1886
4	3538	1871
done	5000	1871

prune439.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.1b	(exp (log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))
2.1b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
3.7b	(log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

25.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
3.0ms	(exp (log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))
0.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
1.0ms	(log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0))

series657.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
152.0ms	(exp (log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))
155.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
257.0ms	(log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	159	2494
1	345	2417
2	878	2112
3	2726	2109
done	5002	2094

prune308.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.2b

regimes182.0ms

Accuracy

0% (0.3b remaining)

Error of 12.7b against oracle of 12.3b and baseline of 12.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	57
1	21	57
done	21	57

end0.0ms

sample811.0ms

Algorithm

intervals

Results

226.0ms	6316×	body	80	valid
108.0ms	8000×	pre	80	true
95.0ms	538×	body	1280	valid
89.0ms	590×	body	640	valid
43.0ms	365×	body	320	valid
13.0ms	191×	body	160	valid