Details

sample27.0ms

Algorithm

intervals

Results

10.0ms

271×

body

valid

simplify137.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	43	8
2	75	8
3	120	8
4	156	8
5	189	8
6	265	8
7	451	8
8	1023	8
9	3632	8
10	5001	8
done	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
0.5b	(+ (* x y) (* z (- t a)))
25.5b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`prod-diff`
52×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+r+`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1`
6×	`sub-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 161

Calls

4 calls:

23.0ms	(* z (- t a))
27.0ms	(* z (- b y))
14.0ms	(+ (* x y) (* z (- t a)))
49.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series526.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* z (- t a))
45.0ms	(* z (- b y))
50.0ms	(+ (* x y) (* z (- t a)))
391.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify87.0ms

Counts

173 → 173

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	623	1398
1	2536	1029
2	5002	1026
done	5002	1026

prune487.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.5b	(+ (* x y) (* z (- t a)))
0.6b	(/ 1 (+ y (* z (- b y))))
25.2b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
46×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
20×	`times-frac` `associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `prod-exp` `flip-+`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r/` `associate-/r` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3--` `pow-flip` `fma-def` `frac-2neg` `clear-num` `sum-log` `un-div-inv` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 161

Calls

4 calls:

22.0ms	(* z (- b y))
13.0ms	(+ (* x y) (* z (- t a)))
10.0ms	(/ 1 (+ y (* z (- b y))))
58.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series579.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* z (- b y))
50.0ms	(+ (* x y) (* z (- t a)))
97.0ms	(/ 1 (+ y (* z (- b y))))
384.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify96.0ms

Counts

173 → 173

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	658	1375
1	2830	1048
2	5001	1011
done	5001	1011

prune498.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt b)
0.6b	(cbrt b)
0.6b	(cbrt b)
25.5b	(/ (+ (* x y) (* z (- t a))) (+ y (+ (* z (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1)))) (* z (fma (- y) 1 y)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
9×	`cbrt-prod`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`pow1/3` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 76

Calls

4 calls:

1.0ms	(cbrt b)
1.0ms	(cbrt b)
1.0ms	(cbrt b)
57.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (+ (* z (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1)))) (* z (fma (- y) 1 y)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt b)
215.0ms	(cbrt b)
203.0ms	(cbrt b)
1.8s	(/ (+ (* x y) (* z (- t a))) (+ y (+ (* z (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1)))) (* z (fma (- y) 1 y)))))

simplify58.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	273	1127
1	1142	1032
2	5001	1009
done	5001	1009

prune477.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.5b

localize19.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (+ y (* z (- b y))))
15.5b	(cbrt (+ y (* z (- b y))))
15.5b	(cbrt (+ y (* z (- b y))))
25.2b	(* (+ (* x y) (* z (- t a))) (/ (/ 1 (* (cbrt (+ y (* z (- b y)))) (cbrt (+ y (* z (- b y)))))) (cbrt (+ y (* z (- b y))))))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
96×	`associate-r`
80×	`cbrt-div`
69×	`add-sqr-sqrt`
57×	`cbrt-prod`
53×	`*-un-lft-identity`
51×	`add-cube-cbrt`
50×	`associate-/r/`
42×	`flip3-+` `flip-+`
32×	`add-exp-log`
26×	`frac-times`
14×	`associate-*l/`
13×	`associate-*r/` `add-cbrt-cube`
11×	`div-exp` `prod-exp`
7×	`div-inv` `unswap-sqr`
6×	`pow1`
5×	`cbrt-undiv` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l`
2×	`rec-exp` `1-exp`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 179

Calls

4 calls:

3.0ms	(cbrt (+ y (* z (- b y))))
3.0ms	(cbrt (+ y (* z (- b y))))
3.0ms	(cbrt (+ y (* z (- b y))))
139.0ms	(* (+ (* x y) (* z (- t a))) (/ (/ 1 (* (cbrt (+ y (* z (- b y)))) (cbrt (+ y (* z (- b y)))))) (cbrt (+ y (* z (- b y))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

290.0ms	(cbrt (+ y (* z (- b y))))
288.0ms	(cbrt (+ y (* z (- b y))))
296.0ms	(cbrt (+ y (* z (- b y))))
391.0ms	(* (+ (* x y) (* z (- t a))) (/ (/ 1 (* (cbrt (+ y (* z (- b y)))) (cbrt (+ y (* z (- b y)))))) (cbrt (+ y (* z (- b y))))))

simplify72.0ms

Counts

191 → 191

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1069	3671
1	5001	3292
done	5001	3292

prune928.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.5b

regimes513.0ms

Accuracy

50.3% (5.2b remaining)

Error of 18.2b against oracle of 13.0b and baseline of 23.4b

bsearch117.0ms

Steps

Iters	Range		Point
8	2.3069922374741435e+70	5.645474500853968e+74	1.8025388190473185e+72
10	-8.016544794788831e+91	-2.210389803822427e+75	-2.081581403037953e+85

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	14
1	39	14
done	39	14

end0.0ms

sample721.0ms

Algorithm

intervals

Results

334.0ms

8449×

body

valid