Details

sample73.0ms

Algorithm

intervals

Results

37.0ms

256×

body

valid

simplify7.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (112.0ms)

Iter	Nodes	Cost
0	16	21
1	33	20
2	79	20
3	201	20
4	405	19
5	766	19
6	1278	19
7	2257	19
8	4193	19
done	5000	19

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.9b	(+ (* (+ x y) z) (* (+ t y) a))
2.6b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.6b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

22.0ms	(* (+ x y) z)
16.0ms	(+ (* (+ x y) z) (* (+ t y) a))
95.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
231.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series1.1s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (+ x y) z)
82.0ms	(+ (* (+ x y) z) (* (+ t y) a))
159.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
815.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify1.4s

Counts

117 → 117

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	194	2540
1	569	2317
2	2313	2102
done	5000	2080

prune795.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.3b	(fma (+ x y) z (* (+ t y) a))
7.0b	(/ (* y b) (+ (+ x t) y))
22.0b	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `times-frac`
19×	`distribute-lft-out`
18×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`pow1`
4×	`expm1-log1p-u` `associate-l` `associate-/r/` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `flip3-+` `div-exp` `associate-r` `flip-+`
2×	`frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`
1×	`pow-prod-down` `*-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

27.0ms	(* (+ t y) a)
1.0ms	(fma (+ x y) z (* (+ t y) a))
57.0ms	(/ (* y b) (+ (+ x t) y))
77.0ms	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

series583.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (+ t y) a)
90.0ms	(fma (+ x y) z (* (+ t y) a))
124.0ms	(/ (* y b) (+ (+ x t) y))
333.0ms	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: 2 (234.0ms)

Iter	Nodes	Cost
0	153	1722
1	347	1667
2	1246	1511
done	5000	1511

prune428.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ b (+ (+ x t) y))
1.3b	(fma (+ x y) z (* (+ t y) a))
8.2b	(* y (/ b (+ (+ x t) y)))
22.0b	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
46×	`times-frac`
39×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
33×	`distribute-lft-out`
21×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`pow1` `associate-/r/` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3-+` `div-exp` `associate-l` `flip-+` `div-inv`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`associate-r/` `pow-prod-down` `-commutative` `fma-udef`

Counts

4 → 130

Calls

4 calls:

36.0ms	(/ b (+ (+ x t) y))
0.0ms	(fma (+ x y) z (* (+ t y) a))
86.0ms	(* y (/ b (+ (+ x t) y)))
43.0ms	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

series502.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ b (+ (+ x t) y))
82.0ms	(fma (+ x y) z (* (+ t y) a))
110.0ms	(* y (/ b (+ (+ x t) y)))
264.0ms	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

simplify1.6s

Counts

142 → 142

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	156	2135
1	329	2042
2	941	1880
3	3196	1880
done	5000	1880

prune451.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ x t) y) b)
1.3b	(fma (+ x y) z (* (+ t y) a))
8.5b	(/ y (/ (+ (+ x t) y) b))
22.0b	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

180×	`*-un-lft-identity`
147×	`times-frac`
80×	`add-sqr-sqrt` `add-cube-cbrt`
60×	`distribute-lft-out`
27×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
7×	`div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`fma-udef`

Counts

4 → 184

Calls

4 calls:

72.0ms	(/ (+ (+ x t) y) b)
0.0ms	(fma (+ x y) z (* (+ t y) a))
46.0ms	(/ y (/ (+ (+ x t) y) b))
37.0ms	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

series502.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (+ (+ x t) y) b)
57.0ms	(fma (+ x y) z (* (+ t y) a))
157.0ms	(/ y (/ (+ (+ x t) y) b))
256.0ms	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

simplify836.0ms

Counts

196 → 196

Iterations

Useful iterations: done (830.0ms)

Iter	Nodes	Cost
0	237	3362
1	501	3172
2	1614	3000
done	5000	2996

prune595.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

regimes487.0ms

Accuracy

13.3% (18.1b remaining)

Error of 21.3b against oracle of 3.2b and baseline of 24.1b

bsearch347.0ms

Steps

Iters	Range		Point
9	2.1803922908798076e+171	7.072525562547444e+178	7.771333049681688e+171
7	5.9441740639567975e-127	7.43629017999154e-125	1.1109812864093013e-125
8	-3.573736598920861e-281	-2.393187721161772e-285	-1.1697432588930248e-281
9	-5.320099813365907e-147	-4.4799452299119005e-156	-1.1186437150469275e-149
8	-3.308581562083972e-50	-2.7093398866571204e-53	-1.3750283862412348e-50
10	-3.1218882103167235e+194	-1.2128916191228806e+181	-1.343517699116082e+182

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	150
1	54	150
done	54	150

end0.0ms

sample1.4s

Algorithm

intervals

Results

913.0ms	7998×	body	80	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid