Details

sample29.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify99.0ms

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: 26.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.1b	(+ (* (+ x y) z) (* (+ t y) a))
2.1b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.0b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite138.0ms

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:

11.0ms	(* (+ t y) a)
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
38.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
80.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series863.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (+ t y) a)
54.0ms	(+ (* (+ x y) z) (* (+ t y) a))
112.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
674.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify93.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (76.0ms)

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

prune481.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.8b	(fma y (- a b) (* a t))
2.0b	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
25.0b	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

rewrite40.0ms

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)))
32.0ms	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

series452.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(fma y (- a b) (* a t))
113.0ms	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
304.0ms	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

simplify50.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 1 (11.0ms)

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

prune279.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
0.5b	(fma (+ x y) z (* (+ t y) a))
9.0b	(/ (* y b) (+ (+ x t) y))
23.4b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

2010×	`*-un-lft-identity`
1804×	`times-frac`
804×	`add-sqr-sqrt`
792×	`add-cube-cbrt`
781×	`prod-diff`
729×	`distribute-lft-out`
174×	`associate-/r/`
153×	`div-inv`
87×	`flip3-+` `flip-+`
71×	`fma-neg`
16×	`add-exp-log`
14×	`add-cbrt-cube` `associate-/l*`
10×	`associate-/r*`
7×	`div-exp`
6×	`add-log-exp`
5×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `1-exp` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `fma-udef` `associate-/l/` `distribute-lft-out--` `sub-div`

Counts

4 → 1018

Calls

4 calls:

221.0ms	(- (/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
0.0ms	(fma (+ x y) z (* (+ t y) a))
18.0ms	(/ (* y b) (+ (+ x t) y))
21.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series1.1s

Counts

4 → 12

Calls

4 calls:

720.0ms	(- (/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
54.0ms	(fma (+ x y) z (* (+ t y) a))
83.0ms	(/ (* y b) (+ (+ x t) y))
250.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify413.0ms

Algorithm

egg-herbie

Counts

1030 → 1030

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1572	39523
1	4906	29750
2	5001	29750

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ b (+ (+ x t) y))
0.5b	(fma (+ x y) z (* (+ t y) a))
8.3b	(* y (/ b (+ (+ x t) y)))
23.4b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

185×	`*-un-lft-identity`
150×	`times-frac`
85×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
63×	`distribute-lft-out`
21×	`associate-r`
18×	`add-exp-log`
16×	`add-cbrt-cube` `associate-/l*`
10×	`associate-/r*`
9×	`div-inv`
7×	`div-exp`
6×	`pow1` `associate-/r/`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-l` `flip-+`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`1-exp` `associate-r/` `pow-prod-down` `-commutative` `fma-udef` `associate-/l/`

Counts

4 → 194

Calls

4 calls:

17.0ms	(/ b (+ (+ x t) y))
0.0ms	(fma (+ x y) z (* (+ t y) a))
39.0ms	(* y (/ b (+ (+ x t) y)))
25.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series426.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ b (+ (+ x t) y))
52.0ms	(fma (+ x y) z (* (+ t y) a))
83.0ms	(* y (/ b (+ (+ x t) y)))
245.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify79.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	572	2047
1	2448	1871
2	5001	1770

prune532.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.9b

regimes448.0ms

Accuracy

18.8% (17.8b remaining)

Error of 21.0b against oracle of 3.2b and baseline of 25.1b

bsearch182.0ms

Steps

Iters	Range	Point
8	1.4335675947829838e+174	4.6274022444189675e+176	2.0673661513817186e+176
9	2.3144144560510123e+88	2.0064946183526016e+94	2.570722063616475e+90
8	-3.3874302974164365e+82	-7.3623446530485255e+78	-9.596217258396559e+78

Iters

Range

Point

1.4335675947829838e+174

4.6274022444189675e+176

2.0673661513817186e+176

2.3144144560510123e+88

2.0064946183526016e+94

2.570722063616475e+90

-3.3874302974164365e+82

-7.3623446530485255e+78

-9.596217258396559e+78

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	36
1	39	36

end0.0ms

sample642.0ms

Algorithm

intervals

Results

375.0ms	7999×	body	80	valid
0.0ms	1×	body	1280	valid