Details

sample37.0ms

Algorithm

intervals

Results

12.0ms	269×	body	80	valid
2.0ms	14×	body	640	valid
2.0ms	9×	body	1280	valid
1.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify9.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (18.0ms)

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
14.1b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite43.0ms

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:

29.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series244.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(/ (- y x) (- a t))
133.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.7s

Counts

70 → 70

Iterations

Useful iterations: done (1.7s)

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

prune333.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.1b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
6.5b	(* (/ (- y x) (- a t)) (- z t))

rewrite159.0ms

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:

29.0ms	(/ (- y x) (- a t))
30.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
83.0ms	(* (/ (- y x) (- a t)) (- z t))

series847.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(/ (- y x) (- a t))
321.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
412.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify1.8s

Counts

179 → 179

Iterations

Useful iterations: done (1.7s)

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

prune730.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.9b	(* (- y x) (/ (- z t) (- a t)))
2.1b	(+ (* (- y x) (/ (- z t) (- a t))) x)

rewrite175.0ms

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:

29.0ms	(/ (- z t) (- a t))
106.0ms	(* (- y x) (/ (- z t) (- a t)))
34.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

series617.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ (- z t) (- a t))
225.0ms	(* (- y x) (/ (- z t) (- a t)))
293.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify1.7s

Counts

135 → 135

Iterations

Useful iterations: done (1.6s)

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

prune607.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- y x))
0.6b	(/ 1 (/ (- a t) (- y x)))
4.6b	(+ (* (/ 1 (/ (- a t) (- y x))) (- z t)) x)
6.5b	(* (/ 1 (/ (- a t) (- y x))) (- z t))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
362×	`add-sqr-sqrt`
350×	`*-un-lft-identity`
182×	`add-cube-cbrt`
98×	`associate-l`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log` `prod-diff` `associate-/r*`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-r` `unswap-sqr`
4×	`expm1-log1p-u` `sub-neg` `rec-exp` `1-exp` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*r/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `fma-def` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `inv-pow`

Counts

4 → 396

Calls

4 calls:

28.0ms	(/ (- a t) (- y x))
33.0ms	(/ 1 (/ (- a t) (- y x)))
61.0ms	(+ (* (/ 1 (/ (- a t) (- y x))) (- z t)) x)
140.0ms	(* (/ 1 (/ (- a t) (- y x))) (- z t))

series1.3s

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- a t) (- y x))
378.0ms	(/ 1 (/ (- a t) (- y x)))
322.0ms	(+ (* (/ 1 (/ (- a t) (- y x))) (- z t)) x)
549.0ms	(* (/ 1 (/ (- a t) (- y x))) (- z t))

simplify2.8s

Counts

408 → 408

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	462	7464
1	1153	6238
2	3068	5575
done	5001	5473

prune1.2s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 3.6b

regimes513.0ms

Accuracy

20.5% (6.5b remaining)

Error of 10.3b against oracle of 3.8b and baseline of 12.0b

bsearch70.0ms

Steps

Iters	Range		Point
2	9.352176213475081e-141	1.0417804927957906e-140	9.75178698140614e-141
5	-2.1349897266323535e-158	-5.771560909560032e-159	-7.261774436029236e-159

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample2.1s

Algorithm

intervals

Results

674.0ms	7772×	body	80	valid
486.0ms	294×	body	160	valid
182.0ms	473×	body	640	valid
77.0ms	282×	body	1280	valid
71.0ms	425×	body	320	valid
4.0ms	11×	body	2560	valid