Details

sample27.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.5b	(+ (* (+ x y) z) (* (+ t y) a))
4.1b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.2b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite42.0ms

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:

6.0ms	(* (+ x y) z)
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
15.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series792.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ x y) z)
52.0ms	(+ (* (+ x y) z) (* (+ t y) a))
102.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
616.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify76.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	568	1186
1	2526	1087
2	5001	1076

prune404.0ms

Filtered

117 candidates to 93 candidates (79.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
1.0b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
2.8b	(- (* (+ t y) a) (* y b))
25.2b	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite31.0ms

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:

9.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
1.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
6.0ms	(- (* (+ t y) a) (* y b))
8.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

series817.0ms

Counts

4 → 12

Calls

4 calls:

586.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
97.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
30.0ms	(- (* (+ t y) a) (* y b))
105.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify69.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (46.0ms)

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

prune372.0ms

Filtered

179 candidates to 93 candidates (52.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
1.0b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
2.8b	(- (* (+ t y) a) (* y b))
25.3b	(* (/ 1 (+ (+ x t) y)) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

8.0ms	(/ 1 (+ (+ x t) y))
1.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
6.0ms	(- (* (+ t y) a) (* y b))
11.0ms	(* (/ 1 (+ (+ x t) y)) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

series780.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1 (+ (+ x t) y))
98.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
34.0ms	(- (* (+ t y) a) (* y b))
594.0ms	(* (/ 1 (+ (+ x t) y)) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify58.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	397	1050
1	1754	922
2	5003	881

prune327.0ms

Filtered

128 candidates to 80 candidates (62.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
1.0b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
2.8b	(- (* (+ t y) a) (* y b))
24.2b	(* (+ (+ x t) y) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

3.0ms	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
1.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
6.0ms	(- (* (+ t y) a) (* y b))
11.0ms	(* (+ (+ x t) y) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
103.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
29.0ms	(- (* (+ t y) a) (* y b))
101.0ms	(* (+ (+ x t) y) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	386	1147
1	1866	1013
2	5001	981

prune306.0ms

Filtered

115 candidates to 77 candidates (67.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.4b

regimes541.0ms

Accuracy

84.9% (3.4b remaining)

Error of 7.9b against oracle of 4.5b and baseline of 27.0b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	32
1	43	32

end0.0ms

sample617.0ms

Algorithm

intervals

Results

362.0ms	7996×	body	80	valid
0.0ms	2×	body	640	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid