Details

sample56.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
3.0ms	16×	body	640	valid
3.0ms	10×	body	1280	valid
2.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid

simplify9.3s

Counts

1 → 1

Iterations

Useful iterations: 3 (24.0ms)

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
16.1b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite30.0ms

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:

26.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series254.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(/ (- y x) (- a t))
162.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.5s

Counts

70 → 70

Iterations

Useful iterations: done (1.5s)

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

prune302.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.6b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.7b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
7.1b	(* (/ (- y x) (- a t)) (- z t))

rewrite194.0ms

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:

37.0ms	(/ (- y x) (- a t))
37.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
107.0ms	(* (/ (- y x) (- a t)) (- z t))

series614.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (- y x) (- a t))
223.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
306.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify1.6s

Counts

179 → 179

Iterations

Useful iterations: done (1.6s)

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

prune741.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.9b	(* (- y x) (/ (- z t) (- a t)))
2.8b	(+ (* (- y x) (/ (- z t) (- a t))) x)

rewrite211.0ms

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:

30.0ms	(/ (- z t) (- a t))
119.0ms	(* (- y x) (/ (- z t) (- a t)))
49.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

series587.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ (- z t) (- a t))
190.0ms	(* (- y x) (/ (- z t) (- a t)))
311.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify1.4s

Counts

135 → 135

Iterations

Useful iterations: done (1.4s)

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

prune610.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.8b	(+ (* (* (- y x) (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- z t)) (cbrt (- a t)))) x)

rewrite567.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

4 → 65

Calls

4 calls:

7.0ms	(cbrt (- a t))
7.0ms	(cbrt (- a t))
7.0ms	(cbrt (- a t))
542.0ms	(+ (* (* (- y x) (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- z t)) (cbrt (- a t)))) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

242.0ms	(cbrt (- a t))
285.0ms	(cbrt (- a t))
233.0ms	(cbrt (- a t))
279.0ms	(+ (* (* (- y x) (/ (* (cbrt (- z t)) (cbrt (- z t))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- z t)) (cbrt (- a t)))) x)

simplify3.2s

Counts

77 → 77

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	112	1336
1	273	1300
2	788	884
3	4164	761
done	5000	761

prune481.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.0b

regimes362.0ms

Accuracy

11.6% (7.1b remaining)

Error of 10.9b against oracle of 3.8b and baseline of 11.8b

bsearch99.0ms

Steps

Iters	Range		Point
4	1.5818187033891164e-118	2.9004484112062707e-118	1.608687110652099e-118
8	-2.557633363288514e-148	-2.53740932421929e-152	-2.1997307668862962e-150

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	90
1	35	56
done	35	56

end0.0ms

sample1.1s

Algorithm

intervals

Results

350.0ms	7809×	body	80	valid
70.0ms	469×	body	640	valid
54.0ms	425×	body	320	valid
54.0ms	276×	body	1280	valid
24.0ms	305×	body	160	valid
3.0ms	14×	body	2560	valid