Details

sample49.0ms

Algorithm

intervals

Results

21.0ms	247×	body	80	valid
3.0ms	16×	body	1280	valid
2.0ms	10×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	7×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 3 (17.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	326	12
5	1002	12
6	3984	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
13.0b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

33.0ms	(/ (- y x) (- a t))
0.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series521.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(/ (- y x) (- a t))
434.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify2.5s

Counts

70 → 70

Iterations

Useful iterations: 3 (770.0ms)

Iter	Nodes	Cost
0	118	918
1	275	890
2	851	838
3	4610	836
done	5000	836

prune311.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.3b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
5.9b	(* (/ (- y x) (- a t)) (- z t))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`add-cube-cbrt` `times-frac`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-r` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

48.0ms	(/ (- y x) (- a t))
30.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
127.0ms	(* (/ (- y x) (- a t)) (- z t))

series630.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ (- y x) (- a t))
214.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
333.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify1.8s

Counts

179 → 179

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	256	3107
1	719	2752
2	3321	2516
done	5001	2490

prune644.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.9b	(+ (* (- y x) (/ (- z t) (- a t))) x)
3.4b	(* (- y x) (/ (- z t) (- a t)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

52.0ms	(/ (- z t) (- a t))
45.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)
82.0ms	(* (- y x) (/ (- z t) (- a t)))

series555.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ (- z t) (- a t))
278.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)
183.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify2.1s

Counts

135 → 135

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	189	1881
1	518	1777
2	2627	1669
done	5002	1667

prune489.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
3.4b	(* (- y x) (* (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (/ (- z t) (cbrt (- a t)))))
8.2b	(+ (* (- y x) (* (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (/ (- z t) (cbrt (- a t))))) x)

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
24×	`add-cbrt-cube`
21×	`prod-exp`
17×	`div-exp`
13×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
10×	`cbrt-prod`
9×	`pow1` `cbrt-undiv` `frac-times`
7×	`add-cube-cbrt`
6×	`flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`associate-l` `associate-*l/`
4×	`expm1-log1p-u` `cbrt-div` `log1p-expm1-u`
3×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`rec-exp` `pow1/3` `1-exp`
1×	`+-commutative` `fma-def` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

4 → 95

Calls

4 calls:

9.0ms	(cbrt (- a t))
7.0ms	(cbrt (- a t))
200.0ms	(* (- y x) (* (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (/ (- z t) (cbrt (- a t)))))
224.0ms	(+ (* (- y x) (* (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (/ (- z t) (cbrt (- a t))))) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

223.0ms	(cbrt (- a t))
241.0ms	(cbrt (- a t))
332.0ms	(* (- y x) (* (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (/ (- z t) (cbrt (- a t)))))
256.0ms	(+ (* (- y x) (* (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (/ (- z t) (cbrt (- a t))))) x)

simplify1.8s

Counts

107 → 107

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	222	2518
1	617	2389
2	2646	1972
done	5001	1887

prune567.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.9b

regimes374.0ms

Accuracy

24.5% (6.2b remaining)

Error of 9.8b against oracle of 3.7b and baseline of 11.8b

bsearch163.0ms

Steps

Iters	Range		Point
8	2.868692110509727e-161	8.553278728760235e-158	9.616031131563335e-161
11	-2.1564359723426472e-113	-3.179459174436537e-139	-5.320969638428747e-139

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	46
1	28	34
done	28	34

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	7836×	body	80	valid
122.0ms	450×	body	320	valid
119.0ms	468×	body	640	valid
86.0ms	274×	body	1280	valid
35.0ms	273×	body	160	valid
5.0ms	14×	body	2560	valid