Details

sample29.0ms

Algorithm

intervals

Results

8.0ms	257×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	11×	body	640	valid
1.0ms	8×	body	1280	valid
0.0ms	8×	body	160	valid
0.0ms	2×	body	2560	valid

simplify5.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (15.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	322	12
5	770	12
6	1556	12
7	2865	12
8	4698	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
15.7b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite26.0ms

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:

23.0ms	(/ (- y x) (- a t))
0.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series163.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (- y x) (- a t))
102.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.0s

Counts

70 → 70

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	118	918
1	270	890
2	658	838
3	1740	836
done	5000	830

prune207.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* (- y x) (/ 1 (- a t)))
15.7b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 105

Calls

3 calls:

12.0ms	(/ 1 (- a t))
46.0ms	(* (- y x) (/ 1 (- a t)))
0.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series205.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ 1 (- a t))
62.0ms	(* (- y x) (/ 1 (- a t)))
105.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify1.7s

Counts

114 → 114

Iterations

Useful iterations: 3 (859.0ms)

Iter	Nodes	Cost
0	155	1285
1	345	1052
2	954	948
3	3237	946
done	5001	946

prune265.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.4b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
7.0b	(* (/ (- y x) (- a t)) (- z t))

rewrite123.0ms

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:

23.0ms	(/ (- y x) (- a t))
28.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
64.0ms	(* (/ (- y x) (- a t)) (- z t))

series473.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/ (- y x) (- a t))
171.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
239.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify1.1s

Counts

179 → 179

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	256	3107
1	667	2740
2	1939	2516
done	5001	2490

prune466.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.8b	(* (- y x) (/ (- z t) (- a t)))
2.5b	(+ (* (- y x) (/ (- z t) (- a t))) x)

rewrite111.0ms

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:

23.0ms	(/ (- z t) (- a t))
56.0ms	(* (- y x) (/ (- z t) (- a t)))
26.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

series374.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (- z t) (- a t))
134.0ms	(* (- y x) (/ (- z t) (- a t)))
185.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify917.0ms

Counts

135 → 135

Iterations

Useful iterations: done (913.0ms)

Iter	Nodes	Cost
0	189	1881
1	487	1765
2	1769	1669
done	5000	1667

prune346.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.5b

regimes257.0ms

Accuracy

12.4% (7.1b remaining)

Error of 10.8b against oracle of 3.7b and baseline of 11.8b

bsearch94.0ms

Steps

Iters	Range		Point
8	1.0742526209927486e-222	5.910843807315664e-220	1.5302023893518548e-220
9	-3.14580386158863e-55	-1.6550014685892204e-61	-2.4158579409769696e-58

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	21	44
1	25	33
done	25	33

end0.0ms

sample791.0ms

Algorithm

intervals

Results

247.0ms	7783×	body	80	valid
59.0ms	500×	body	640	valid
45.0ms	273×	body	1280	valid
33.0ms	391×	body	320	valid
16.0ms	273×	body	160	valid
4.0ms	21×	body	2560	valid