Details

sample63.0ms

Algorithm

intervals

Results

17.0ms	231×	body	80	valid
4.0ms	12×	body	1280	valid
4.0ms	14×	body	640	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3379
5	728
4	242
3	111
2	52
1	22
0	11

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.6b	(fma y (/ (- t z) (- a t)) (+ y 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-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

35.0ms	(/ (- t z) (- a t))
0.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

series275.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- t z) (- a t))
219.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

simplify2.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4441
2	825
1	263
0	114

prune483.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
4.1b	(fma y (* (- t z) (/ 1 (- a t))) (+ y x))

rewrite83.0ms

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-/r` `associate-l*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 105

Calls

3 calls:

10.0ms	(/ 1 (- a t))
69.0ms	(* (- t z) (/ 1 (- a t)))
1.0ms	(fma y (* (- t z) (/ 1 (- a t))) (+ y x))

series320.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ 1 (- a t))
76.0ms	(* (- t z) (/ 1 (- a t)))
178.0ms	(fma y (* (- t z) (/ 1 (- a t))) (+ y x))

simplify4.2s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2794
1	357
0	150

prune742.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
9.0b	(fma y (/ (/ (/ (- t z) (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t))) (+ y x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `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:

6.0ms	(cbrt (- a t))
6.0ms	(cbrt (- a t))
7.0ms	(cbrt (- a t))
1.0ms	(fma y (/ (/ (/ (- t z) (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t))) (+ y x))

series835.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(cbrt (- a t))
236.0ms	(cbrt (- a t))
211.0ms	(cbrt (- a t))
166.0ms	(fma y (/ (/ (/ (- t z) (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t))) (+ y x))

simplify839.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	1576
2	472
1	191
0	95

prune630.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.5b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- t z) y)
1.9b	(+ (/ (* (- t z) y) (- a t)) (+ y x))
10.7b	(/ (* (- t z) y) (- a t))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 85

Calls

3 calls:

32.0ms	(* (- t z) y)
69.0ms	(+ (/ (* (- t z) y) (- a t)) (+ y x))
19.0ms	(/ (* (- t z) y) (- a t))

series341.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* (- t z) y)
186.0ms	(+ (/ (* (- t z) y) (- a t)) (+ y x))
103.0ms	(/ (* (- t z) y) (- a t))

simplify1.2s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	2393
1	446
0	153

prune622.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.5b

regimes650.0ms

Accuracy

35.1% (5.5b remaining)

Error of 8.6b against oracle of 3.1b and baseline of 11.6b

bsearch56.0ms

Steps

Iters	Range		Point
3	4.0356565631473004e-100	5.070879917928193e-100	4.776220601035188e-100
3	-7.713673533084189e-160	-5.677852690405708e-160	-7.329630304780208e-160

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample1.8s

Algorithm

intervals

Results

851.0ms	7334×	body	80	valid
162.0ms	453×	body	640	valid
93.0ms	394×	body	320	valid
75.0ms	263×	body	1280	valid
63.0ms	251×	body	160	valid
6.0ms	18×	body	2560	valid