Details

sample48.0ms

Algorithm

intervals

Results

14.0ms	241×	body	80	valid
3.0ms	13×	body	640	valid
2.0ms	12×	body	320	valid
2.0ms	14×	body	160	valid
2.0ms	5×	body	1280	valid
1.0ms	2×	body	2560	valid

simplify9.1s

Counts

1 → 1

Iterations

Useful iterations: 3 (18.0ms)

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
13.9b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite36.0ms

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:

30.0ms	(/ (- y x) (- a t))
0.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series291.0ms

Counts

2 → 6

Calls

2 calls:

108.0ms	(/ (- y x) (- a t))
182.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.7s

Counts

70 → 70

Iterations

Useful iterations: done (1.7s)

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

prune312.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- y x) (/ 1 (- a t)))
13.9b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite137.0ms

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))
104.0ms	(* (- y x) (/ 1 (- a t)))
1.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series331.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ 1 (- a t))
112.0ms	(* (- y x) (/ 1 (- a t)))
168.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify2.6s

Counts

114 → 114

Iterations

Useful iterations: 3 (1.3s)

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

prune419.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 6.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
4.7b	(* (- z t) (/ (- y x) (- a t)))
5.0b	(+ (* (- z t) (/ (- y x) (- a t))) x)

rewrite205.0ms

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:

51.0ms	(/ (- y x) (- a t))
108.0ms	(* (- z t) (/ (- y x) (- a t)))
40.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)

series585.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ (- y x) (- a t))
222.0ms	(* (- z t) (/ (- y x) (- a t)))
269.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)

simplify1.4s

Counts

135 → 135

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	189	1881
1	486	1765
2	1768	1669
done	5001	1667

prune573.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 3.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y x))
0.6b	(cbrt (- y x))
0.8b	(* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))))
8.4b	(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

rewrite610.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

8.0ms	(cbrt (- y x))
8.0ms	(cbrt (- y x))
160.0ms	(* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))))
427.0ms	(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

series1.7s

Counts

4 → 12

Calls

4 calls:

222.0ms	(cbrt (- y x))
694.0ms	(cbrt (- y x))
537.0ms	(* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))))
252.0ms	(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

simplify1.9s

Counts

106 → 106

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	256	2637
1	688	2520
2	2494	1866
done	5002	1722

prune584.0ms

Pruning

21 alts after pruning (18 fresh and 3 done)

Merged error: 3.6b

regimes736.0ms

Accuracy

23.5% (7.0b remaining)

Error of 10.7b against oracle of 3.6b and baseline of 12.8b

bsearch192.0ms

Steps

Iters	Range		Point
8	2.0007789822909896e-198	1.0099514213797079e-194	3.085625866310274e-197
7	-5.925413525790681e-145	-6.231127244252839e-147	-5.181595524895995e-145

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	102
1	42	102
done	42	102

end0.0ms

sample1.7s

Algorithm

intervals

Results

570.0ms	7591×	body	80	valid
203.0ms	423×	body	320	valid
143.0ms	500×	body	640	valid
120.0ms	289×	body	1280	valid
33.0ms	288×	body	160	valid
8.0ms	23×	body	2560	valid