Details

sample79.0ms

Algorithm

intervals

Results

20.0ms	16×	body	640	valid
19.0ms	246×	body	80	valid
4.0ms	10×	body	1280	valid
3.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid

simplify9.7s

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.0b

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
16.4b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite59.0ms

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:

53.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series306.0ms

Counts

2 → 6

Calls

2 calls:

108.0ms	(/ (- y x) (- a t))
198.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.6s

Counts

70 → 70

Iterations

Useful iterations: done (1.6s)

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

prune334.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.9b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- y x) (/ 1 (- a t)))
16.3b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

25.0ms	(/ 1 (- a t))
85.0ms	(* (- y x) (/ 1 (- a t)))
0.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series334.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/ 1 (- a t))
92.0ms	(* (- y x) (/ 1 (- a t)))
179.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify2.8s

Counts

114 → 114

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	155	1285
1	345	1052
2	954	948
3	3237	946
done	5001	946

prune438.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.9b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
2.7b	(+ (* (- z t) (/ (- y x) (- a t))) x)
6.6b	(* (- z t) (/ (- y x) (- a t)))

rewrite206.0ms

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:

38.0ms	(/ (- y x) (- a t))
26.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
134.0ms	(* (- z t) (/ (- y x) (- a t)))

series587.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(/ (- y x) (- a t))
275.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
214.0ms	(* (- z t) (/ (- y x) (- a t)))

simplify1.5s

Counts

135 → 135

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	189	1881
1	486	1765
2	1766	1669
done	5001	1667

prune644.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
9.5b	(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

rewrite465.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

4.0ms	(cbrt (- a t))
5.0ms	(cbrt (- a t))
5.0ms	(cbrt (- a t))
448.0ms	(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

250.0ms	(cbrt (- a t))
270.0ms	(cbrt (- a t))
240.0ms	(cbrt (- a t))
255.0ms	(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

simplify3.2s

Counts

77 → 77

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	112	1336
1	273	1300
2	788	884
3	4182	761
done	5000	761

prune479.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.1b

regimes605.0ms

Accuracy

35.9% (5.6b remaining)

Error of 9.2b against oracle of 3.6b and baseline of 12.4b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	103
1	43	103
done	43	103

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s	7719×	body	80	valid
142.0ms	495×	body	640	valid
97.0ms	423×	body	320	valid
71.0ms	262×	body	1280	valid
32.0ms	288×	body	160	valid
6.0ms	18×	body	2560	valid