Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	228×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	2560	valid

simplify9.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (44.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	52	13
3	109	13
4	203	12
5	451	12
6	748	12
7	1078	12
8	1400	12
9	1655	12
10	2153	12
11	2683	12
12	3847	12
done	5001	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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:

25.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series252.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- t z) (- a t))
205.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify1.1s

Counts

70 → 70

Iterations

Useful iterations: 3 (350.0ms)

Iter	Nodes	Cost
0	113	906
1	258	878
2	622	826
3	1643	824
done	5000	824

prune223.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
0.9b	(* (/ (- t z) (- a t)) y)
2.5b	(+ (* (/ (- t z) (- a t)) y) (+ x y))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 124

Calls

3 calls:

26.0ms	(/ (- t z) (- a t))
46.0ms	(* (/ (- t z) (- a t)) y)
33.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

series379.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- t z) (- a t))
105.0ms	(* (/ (- t z) (- a t)) y)
228.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

simplify951.0ms

Counts

133 → 133

Iterations

Useful iterations: done (948.0ms)

Iter	Nodes	Cost
0	195	1736
1	541	1646
2	1652	1560
done	5001	1549

prune366.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
0.5b	(* (cbrt (- a t)) (cbrt (- a t)))
8.4b	(fma (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) y (+ x y))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
8×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 102

Calls

4 calls:

4.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
42.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
0.0ms	(fma (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) y (+ x y))

series577.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (- a t))
174.0ms	(cbrt (- a t))
138.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
95.0ms	(fma (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) y (+ x y))

simplify1.5s

Counts

114 → 114

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	157	1591
1	318	1483
2	818	1361
3	2250	1151
done	5002	1124

prune428.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
1.0b	(* (/ (- t z) (- a t)) (* (cbrt y) (cbrt y)))
8.9b	(+ (* (* (/ (- t z) (- a t)) (* (cbrt y) (cbrt y))) (cbrt y)) (+ x y))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
31×	`associate-l`
26×	`times-frac`
17×	`add-cube-cbrt`
16×	`add-exp-log`
12×	`add-cbrt-cube`
10×	`distribute-lft-out--` `difference-of-squares`
9×	`pow1` `add-log-exp`
6×	`cbrt-prod` `prod-exp` `cbrt-unprod`
5×	`associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `sum-log`
2×	`cbrt-undiv` `flip3-+` `pow1/3` `div-exp` `frac-add` `associate-/r/` `flip-+` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `flip3--` `fma-def` `associate-r` `*-commutative` `flip--` `div-inv`

Counts

4 → 99

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
65.0ms	(* (/ (- t z) (- a t)) (* (cbrt y) (cbrt y)))
132.0ms	(+ (* (* (/ (- t z) (- a t)) (* (cbrt y) (cbrt y))) (cbrt y)) (+ x y))

series972.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt y)
195.0ms	(cbrt y)
271.0ms	(* (/ (- t z) (- a t)) (* (cbrt y) (cbrt y)))
300.0ms	(+ (* (* (/ (- t z) (- a t)) (* (cbrt y) (cbrt y))) (cbrt y)) (+ x y))

simplify1.1s

Counts

111 → 111

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	177	1612
1	524	1561
2	1751	1143
done	5001	1132

prune338.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

regimes208.0ms

Accuracy

30.4% (5.7b remaining)

Error of 9.1b against oracle of 3.4b and baseline of 11.6b

bsearch100.0ms

Steps

Iters	Range		Point
10	3.5203588644576918e-146	5.218300859785189e-131	1.1414954976872053e-132
8	-2.4677707646982767e-157	-5.66920234740041e-160	-4.973743978705261e-158

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	65
1	37	63
done	37	63

end0.0ms

sample750.0ms

Algorithm

intervals

Results

238.0ms	7352×	body	80	valid
50.0ms	447×	body	640	valid
38.0ms	246×	body	1280	valid
32.0ms	376×	body	320	valid
15.0ms	266×	body	160	valid
3.0ms	17×	body	2560	valid