Details

sample221.0ms

Algorithm

intervals

Results

93.0ms	256×	body	80	valid
73.0ms	270×	body	80	nan

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
5	5020
4	1334
3	350
2	100
1	50
0	28

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.5b	(/ 2.0 (* t 3.0))
3.1b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
4.5b	(/ (* z (sqrt (+ t a))) t)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub`
16×	`add-cbrt-cube` `add-exp-log`
15×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`associate-r`
6×	`pow1` `times-frac` `associate--r+` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `associate-/r` `sqrt-div` `div-exp` `insert-posit16` `associate-/l`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `associate-*l/` `associate--l+` `div-inv` `unswap-sqr` `associate-/l/`
1×	`diff-log` `pow-prod-down` `*-commutative` `distribute-lft-out`

Counts

4 → 105

Calls

4 calls:

29.0ms	(* z (sqrt (+ t a)))
12.0ms	(/ 2.0 (* t 3.0))
36.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
18.0ms	(/ (* z (sqrt (+ t a))) t)

series500.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* z (sqrt (+ t a)))
36.0ms	(/ 2.0 (* t 3.0))
289.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
98.0ms	(/ (* z (sqrt (+ t a))) t)

simplify1.8s

Counts

117 → 117

Iterations

Iter	Nodes
2	4466
1	1031
0	350

prune3.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize94.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (* t 3.0))
3.1b	(- (/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
4.5b	(/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t)
54.4b	(posit16->real (real->posit16 (* z (sqrt (+ t a)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
11×	`add-cbrt-cube` `add-exp-log`
9×	`flip3--` `flip--`
8×	`frac-times`
6×	`associate-/l*` `associate--r+` `add-log-exp`
4×	`pow1` `associate-/r` `associate-r/` `insert-posit16`
3×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `flip3-+` `div-exp` `flip-+`
2×	`clear-num` `frac-2neg` `associate-*l/` `associate--l+` `div-inv`
1×	`diff-log` `prod-exp` `cbrt-unprod` `remove-posit16`

Counts

4 → 92

Calls

4 calls:

12.0ms	(/ 2.0 (* t 3.0))
40.0ms	(- (/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
8.0ms	(/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t)
1.0ms	(posit16->real (real->posit16 (* z (sqrt (+ t a)))))

series553.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 2.0 (* t 3.0))
310.0ms	(- (/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
90.0ms	(/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t)
118.0ms	(posit16->real (real->posit16 (* z (sqrt (+ t a)))))

simplify1.4s

Counts

104 → 104

Iterations

Iter	Nodes
2	3951
1	921
0	321

prune3.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize108.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (* t 3.0))
3.1b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
4.5b	(/ (* z (sqrt (+ t a))) t)
48.8b	(posit16->real (real->posit16 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub`
14×	`add-cbrt-cube` `add-exp-log`
9×	`flip3--` `flip--`
8×	`add-sqr-sqrt` `frac-times` `*-un-lft-identity` `add-cube-cbrt`
6×	`times-frac` `associate-*r/` `associate--r+` `add-log-exp`
4×	`pow1` `cbrt-undiv` `associate-/r` `flip3-+` `div-exp` `flip-+` `insert-posit16` `associate-/l`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-*l/` `prod-exp` `associate--l+` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`diff-log` `remove-posit16`

Counts

4 → 88

Calls

4 calls:

13.0ms	(/ 2.0 (* t 3.0))
52.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
23.0ms	(/ (* z (sqrt (+ t a))) t)
1.0ms	(posit16->real (real->posit16 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))

series762.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 2.0 (* t 3.0))
288.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
144.0ms	(/ (* z (sqrt (+ t a))) t)
294.0ms	(posit16->real (real->posit16 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))

simplify1.8s

Counts

100 → 100

Iterations

Iter	Nodes
2	4157
1	946
0	314

prune3.5s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.5b

localize111.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t))
1.8b	(* z (* (- a (/ 5.0 6.0)) (* t 3.0)))
8.2b	(- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)))
26.5b	(/ (- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

2980×	`associate-*l/`
2580×	`associate-*r/`
1808×	`frac-sub`
1606×	`flip3--` `flip--`
1584×	`frac-times`
744×	`sqrt-div`
678×	`flip3-+` `flip-+`
500×	`associate-/l/`
110×	`sub-div`
32×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
15×	`prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`pow-prod-down`
8×	`associate-l` `add-cube-cbrt`
6×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
3×	`times-frac` `associate-/l*`
2×	`associate-r` `associate-/r/` `*-commutative`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 1147

Calls

4 calls:

726.0ms	(* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t))
69.0ms	(* z (* (- a (/ 5.0 6.0)) (* t 3.0)))
980.0ms	(- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)))
1.3s	(/ (- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series2.1s

Counts

4 → 12

Calls

4 calls:

283.0ms	(* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t))
93.0ms	(* z (* (- a (/ 5.0 6.0)) (* t 3.0)))
819.0ms	(- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)))
871.0ms	(/ (- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify12.1s

Counts

1159 → 1159

Iterations

Iter	Nodes
1	11410
0	2945

prune50.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes978.0ms

Accuracy

28.6% (5.2b remaining)

Error of 6.2b against oracle of 1.1b and baseline of 8.3b

bsearch662.0ms

Steps

Iters	Range		Point
8	3.0862283108810165e-88	1.9757690640208618e-84	2.4912890196465165e-86
10	-2.392276742047856e-93	-2.9486524712877733e-109	-1.734220830051257e-93

simplify69.0ms

Iterations

Iter	Nodes
2	76
1	76
0	55

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.4s	7940×	body	80	nan
2.4s	8000×	body	80	valid