Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	240×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	2560	valid

simplify6.5s

Counts

1 → 1

Iterations

Useful iterations: 3 (12.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	114	12
4	278	12
5	614	12
6	1246	12
7	2304	12
8	4050	12
done	5000	12

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
15.1b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite23.0ms

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:

20.0ms	(/ (- y x) (- a t))
0.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series150.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- y x) (- a t))
96.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify2.1s

Counts

70 → 70

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	118	918
1	270	890
2	628	838
3	1591	836
4	4632	828
done	5000	828

prune248.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
4.3b	(* (/ (- y x) (- a t)) (- z t))
4.5b	(+ (* (/ (- y x) (- a t)) (- z t)) x)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

16.0ms	(/ (- y x) (- a t))
36.0ms	(* (/ (- y x) (- a t)) (- z t))
15.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)

series442.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- y x) (- a t))
231.0ms	(* (/ (- y x) (- a t)) (- z t))
158.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)

simplify1.6s

Counts

179 → 179

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	256	3107
1	676	2740
2	2102	2516
done	5001	2480

prune520.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.6b	(* (- y x) (/ (- z t) (- a t)))
3.7b	(+ (* (- y x) (/ (- z t) (- a t))) x)

rewrite66.0ms

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:

12.0ms	(/ (- z t) (- a t))
36.0ms	(* (- y x) (/ (- z t) (- a t)))
12.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

series342.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- z t) (- a t))
127.0ms	(* (- y x) (/ (- z t) (- a t)))
163.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: 2 (304.0ms)

Iter	Nodes	Cost
0	189	1881
1	492	1765
2	1724	1669
done	5000	1669

prune402.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y x))
0.5b	(cbrt (- y x))
0.5b	(cbrt (- y x))
15.0b	(fma (* (* (cbrt (- y x)) (cbrt (- y x))) (/ (cbrt (- y x)) (- a t))) (- z t) x)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

2.0ms	(cbrt (- y x))
2.0ms	(cbrt (- y x))
2.0ms	(cbrt (- y x))
0.0ms	(fma (* (* (cbrt (- y x)) (cbrt (- y x))) (/ (cbrt (- y x)) (- a t))) (- z t) x)

series595.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (- y x))
169.0ms	(cbrt (- y x))
167.0ms	(cbrt (- y x))
95.0ms	(fma (* (* (cbrt (- y x)) (cbrt (- y x))) (/ (cbrt (- y x)) (- a t))) (- z t) x)

simplify2.0s

Counts

73 → 73

Iterations

Useful iterations: 4 (909.0ms)

Iter	Nodes	Cost
0	96	925
1	199	907
2	441	749
3	1134	678
4	4168	636
done	5000	636

prune285.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.5b

regimes297.0ms

Accuracy

11.9% (6.8b remaining)

Error of 11.0b against oracle of 4.2b and baseline of 11.9b

bsearch140.0ms

Steps

Iters	Range		Point
10	7.906484867512465e-140	4.121783404495045e-129	1.093513748929993e-133
11	-3.777324016597175e-247	-3.5673237559096386e-267	-3.543954312374929e-257

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	23	47
1	31	35
done	31	35

end0.0ms

sample689.0ms

Algorithm

intervals

Results

252.0ms	7734×	body	80	valid
60.0ms	483×	body	640	valid
43.0ms	271×	body	1280	valid
35.0ms	409×	body	320	valid
21.0ms	298×	body	160	valid
3.0ms	16×	body	2560	valid