Details

sample30.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	33	10
1	79	10
2	210	10
3	483	10
4	910	10
5	1516	10
6	2818	10
7	5001	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.6b	(+ (* (+ x y) z) (* (+ t y) a))
2.2b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
26.2b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite142.0ms

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:

12.0ms	(* (+ t y) a)
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
38.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
83.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series835.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (+ t y) a)
51.0ms	(+ (* (+ x y) z) (* (+ t y) a))
106.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
656.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify84.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	564	1186
1	2509	1087
2	5002	1077

prune440.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.4b

localize19.0ms

Local error

Found 3 expressions with local error:

1.0b	(fma y (- a b) (* a t))
2.0b	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
26.2b	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
15×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`associate-/r/` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 66

Calls

3 calls:

0.0ms	(fma y (- a b) (* a t))
5.0ms	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
29.0ms	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

series421.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma y (- a b) (* a t))
108.0ms	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
279.0ms	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

simplify43.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	257	793
1	937	736
2	5001	736

prune258.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
1.0b	(fma y (- a b) (* a t))
2.0b	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
26.2b	(* (+ (* (+ x y) z) (fma y (- a b) (* a t))) (/ 1 (+ (+ x t) y)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
32×	`times-frac`
31×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`flip3-+` `associate-/r*` `flip-+`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `fma-udef` `div-inv`
1×	`+-commutative` `associate-+r+` `pow-flip` `fma-def` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 118

Calls

4 calls:

18.0ms	(/ 1 (+ (+ x t) y))
0.0ms	(fma y (- a b) (* a t))
5.0ms	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
59.0ms	(* (+ (* (+ x y) z) (fma y (- a b) (* a t))) (/ 1 (+ (+ x t) y)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1 (+ (+ x t) y))
40.0ms	(fma y (- a b) (* a t))
123.0ms	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
285.0ms	(* (+ (* (+ x y) z) (fma y (- a b) (* a t))) (/ 1 (+ (+ x t) y)))

simplify66.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	380	1050
1	1673	925
2	5003	875

prune414.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
0.3b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
1.7b	(- (* (+ t y) a) (* y b))
26.2b	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
132×	`times-frac`
70×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
22×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `flip3--` `pow-flip` `flip3-+` `fma-neg` `diff-log` `prod-diff` `associate-/r/` `flip--` `flip-+` `fma-udef` `inv-pow`

Counts

4 → 167

Calls

4 calls:

21.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
0.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
6.0ms	(- (* (+ t y) a) (* y b))
33.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

series937.0ms

Counts

4 → 12

Calls

4 calls:

654.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
121.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
33.0ms	(- (* (+ t y) a) (* y b))
129.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify84.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	496	2605
1	2228	2401
2	5002	2286

prune438.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.0b

regimes607.0ms

Accuracy

49.4% (11.4b remaining)

Error of 16.0b against oracle of 4.6b and baseline of 27.1b

bsearch229.0ms

Steps

Iters	Range		Point
7	1.2927464493965476e+42	1.2368034649258586e+44	1.1685265508795281e+44
9	1.8698515406784921e-88	1.56037796305268e-83	1.8899870319995665e-88
8	1.236282004049312e-101	1.1240443505265923e-97	1.168556559047249e-98
7	-1.5469128537712558e+88	-1.8722682592897245e+86	-2.0925390482027694e+87

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (2.0ms)

Iter	Nodes	Cost
0	44	26
1	49	26
2	55	11
3	58	11
4	64	11
5	75	11
6	82	11
7	83	11
8	83	11

end0.0ms

sample687.0ms

Algorithm

intervals

Results

393.0ms	7995×	body	80	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid