Details

sample65.0ms

Algorithm

intervals

Results

19.0ms	243×	body	80	valid
9.0ms	18×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	3×	body	1280	valid
1.0ms	1×	body	2560	valid

simplify8.4s

Counts

1 → 1

Iterations

Useful iterations: 3 (17.0ms)

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
15.0b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite40.0ms

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:

36.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series215.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(/ (- y x) (- a t))
116.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.4s

Counts

70 → 70

Iterations

Useful iterations: done (1.4s)

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

prune250.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* (- y x) (/ 1 (- a t)))
14.9b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite85.0ms

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:

14.0ms	(/ 1 (- a t))
66.0ms	(* (- y x) (/ 1 (- a t)))
0.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series225.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ 1 (- a t))
71.0ms	(* (- y x) (/ 1 (- a t)))
109.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify2.9s

Counts

114 → 114

Iterations

Useful iterations: 3 (1.7s)

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

prune371.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.9b	(+ (* (- z t) (/ (- y x) (- a t))) x)
5.4b	(* (- z t) (/ (- y x) (- a t)))

rewrite184.0ms

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:

31.0ms	(/ (- y x) (- a t))
40.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
108.0ms	(* (- z t) (/ (- y x) (- a t)))

series493.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ (- y x) (- a t))
206.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
217.0ms	(* (- z t) (/ (- y x) (- a t)))

simplify1.3s

Counts

135 → 135

Iterations

Useful iterations: done (1.3s)

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

prune558.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 3.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
2.1b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t))))
7.8b	(+ (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t)))) x)

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 143

Calls

4 calls:

5.0ms	(cbrt (- a t))
5.0ms	(cbrt (- a t))
212.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t))))
147.0ms	(+ (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t)))) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt (- a t))
222.0ms	(cbrt (- a t))
451.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t))))
253.0ms	(+ (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t)))) x)

simplify1.8s

Counts

155 → 155

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	261	3480
1	737	3292
2	2816	2749
done	5001	2561

prune620.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.7b

regimes439.0ms

Accuracy

13.1% (7.4b remaining)

Error of 11.1b against oracle of 3.7b and baseline of 12.3b

bsearch115.0ms

Steps

Iters	Range		Point
7	1.8535951948600626e+171	1.07622919242428e+173	1.2558832831296409e+172
7	-3.826349898080599e+239	-1.2700546258789921e+238	-1.8613957186985918e+239

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	67
1	35	56
done	35	56

end0.0ms

sample1.8s

Algorithm

intervals

Results

641.0ms	7760×	body	80	valid
378.0ms	463×	body	640	valid
130.0ms	275×	body	1280	valid
70.0ms	441×	body	320	valid
28.0ms	254×	body	160	valid
7.0ms	21×	body	2560	valid