Details

sample30.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify74.0ms

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 24.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
2.0b	(+ (* (+ x y) z) (* (+ t y) a))
2.4b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
22.9b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite41.0ms

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	(* (+ t y) a)
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))

series727.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ t y) a)
48.0ms	(+ (* (+ x y) z) (* (+ t y) a))
94.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
565.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify74.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (61.0ms)

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

prune345.0ms

Filtered

117 candidates to 93 candidates (79.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	107	11	118

Merged error: 6.6b

Counts

118 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
2.0b	(+ (* (+ x y) z) (* (+ t y) a))
2.4b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
23.0b	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

6.0ms	(* (+ t y) a)
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
19.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

series734.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ t y) a)
47.0ms	(+ (* (+ x y) z) (* (+ t y) a))
93.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
573.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

simplify84.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	647	1224
1	3142	1071
2	5001	1047

prune335.0ms

Filtered

125 candidates to 94 candidates (75.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	125	11	136

Merged error: 6.6b

Counts

136 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
1.3b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
1.7b	(- (* (+ t y) a) (* y b))
22.9b	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite34.0ms

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))))

series775.0ms

Counts

4 → 12

Calls

4 calls:

556.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
94.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
28.0ms	(- (* (+ t y) a) (* y b))
97.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify69.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (45.0ms)

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

prune327.0ms

Filtered

179 candidates to 93 candidates (52.0%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	177	13	190

Merged error: 3.5b

Counts

190 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
1.3b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
1.7b	(- (* (+ t y) a) (* y b))
21.9b	(* (+ (+ x t) y) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

rewrite27.0ms

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)))
9.0ms	(- (* (+ t y) a) (* y b))
11.0ms	(* (+ (+ x t) y) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
94.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
28.0ms	(- (* (+ t y) a) (* y b))
98.0ms	(* (+ (+ x t) y) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (43.0ms)

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

prune254.0ms

Filtered

115 candidates to 77 candidates (67.0%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	9	9
Picked	0	1	1
Done	0	3	3
Total	115	13	128

Merged error: 3.5b

Counts

128 → 13

regimes559.0ms

Accuracy

85.9% (3.1b remaining)

Error of 7.4b against oracle of 4.2b and baseline of 26.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	32
1	36	32

end0.0ms

sample724.0ms

Algorithm

intervals

Results

450.0ms	7996×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid