Details

sample61.0ms

Algorithm

intervals

Results

14.0ms	228×	body	80	valid
4.0ms	18×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	8×	body	1280	valid
1.0ms	10×	body	160	valid

simplify5.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1890
5	788
4	299
3	108
2	43
1	20
0	11

prune78.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize94.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.1b	(fma (/ (- z t) (- a t)) (- y x) x)

rewrite77.0ms

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-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 66

Calls

2 calls:

70.0ms	(/ (- z t) (- a t))
2.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

series368.0ms

Counts

2 → 6

Calls

2 calls:

106.0ms	(/ (- z t) (- a t))
261.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

simplify5.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5008
3	2144
2	678
1	274
0	118

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize140.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.0b	(* (/ (- z t) (- a t)) (- y x))
2.0b	(+ (* (/ (- z t) (- a t)) (- y x)) x)

rewrite425.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`times-frac` `add-cube-cbrt`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`frac-times` `cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `-commutative` `flip-+`

Counts

3 → 173

Calls

3 calls:

109.0ms	(/ (- z t) (- a t))
198.0ms	(* (/ (- z t) (- a t)) (- y x))
94.0ms	(+ (* (/ (- z t) (- a t)) (- y x)) x)

series1.3s

Counts

3 → 9

Calls

3 calls:

90.0ms	(/ (- z t) (- a t))
744.0ms	(* (/ (- z t) (- a t)) (- y x))
501.0ms	(+ (* (/ (- z t) (- a t)) (- y x)) x)

simplify5.1s

Counts

182 → 182

Iterations

Iter	Nodes
done	5000
2	2201
1	716
0	258

prune2.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.1b

localize169.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- z t))
0.5b	(cbrt (- z t))
2.0b	(* (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))) (- y x))
8.6b	(+ (* (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))) (- y x)) x)

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

82×	`frac-times`
76×	`cbrt-div`
56×	`flip3--` `flip--`
53×	`associate-*l/`
37×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
31×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `add-exp-log`
17×	`associate-*r/`
16×	`add-cbrt-cube`
13×	`pow1`
11×	`prod-exp` `cbrt-unprod`
10×	`cbrt-prod`
6×	`pow-prod-down` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `sub-neg` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `pow1/3` `div-exp`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

4 → 178

Calls

4 calls:

10.0ms	(cbrt (- z t))
11.0ms	(cbrt (- z t))
812.0ms	(* (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))) (- y x))
787.0ms	(+ (* (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))) (- y x)) x)

series2.1s

Counts

4 → 12

Calls

4 calls:

417.0ms	(cbrt (- z t))
381.0ms	(cbrt (- z t))
798.0ms	(* (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))) (- y x))
457.0ms	(+ (* (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))) (- y x)) x)

simplify8.1s

Counts

190 → 190

Iterations

Iter	Nodes
done	5000
2	4482
1	1096
0	350

prune3.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.1b

localize179.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
8.7b	(fma (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t)))) (- y x) x)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 65

Calls

4 calls:

21.0ms	(cbrt (- a t))
19.0ms	(cbrt (- a t))
10.0ms	(cbrt (- a t))
1.0ms	(fma (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t)))) (- y x) x)

series1.5s

Counts

4 → 12

Calls

4 calls:

397.0ms	(cbrt (- a t))
414.0ms	(cbrt (- a t))
405.0ms	(cbrt (- a t))
294.0ms	(fma (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t)))) (- y x) x)

simplify3.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	5005
3	1435
2	468
1	208
0	99

prune1.3s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 4.1b

regimes2.5s

Accuracy

11.3% (7.5b remaining)

Error of 11.0b against oracle of 3.4b and baseline of 11.9b

bsearch364.0ms

Steps

Iters	Range		Point
10	2.9642541751437196e+165	1.5103631757520522e+180	1.6000865785138779e+168
7	-1.1684716751749842e+56	-1.0725097879575952e+54	-1.142451209668467e+56
9	-1.6730117821319332e+152	-2.8834586378180107e+144	-3.101992109502826e+145
8	-2.30054748327762e+232	-9.561475931205302e+227	-1.1505776834338363e+228

simplify22.0ms

Iterations

Iter	Nodes
done	53
1	53
0	43

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	7793×	body	80	valid
210.0ms	471×	body	640	valid
136.0ms	261×	body	1280	valid
121.0ms	414×	body	320	valid
37.0ms	241×	body	160	valid
4.0ms	8×	body	2560	valid