Details

sample29.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify80.0ms

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: 27.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
2.0b	(+ (* (+ x y) z) (* (+ t y) a))
2.1b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.5b	(/ (- (+ (* (+ 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))
16.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series764.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ x y) z)
49.0ms	(+ (* (+ x y) z) (* (+ t y) a))
115.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
580.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify71.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (58.0ms)

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

prune367.0ms

Filtered

117 candidates to 93 candidates (79.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 7.8b

Counts

118 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma x z (* z y))
2.0b	(+ (fma x z (* z y)) (* (+ t y) a))
2.1b	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
25.5b	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

1.0ms	(fma x z (* z y))
4.0ms	(+ (fma x z (* z y)) (* (+ t y) a))
6.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
11.0ms	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series429.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(fma x z (* z y))
52.0ms	(+ (fma x z (* z y)) (* (+ t y) a))
104.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
237.0ms	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify61.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	368	1067
1	1651	987
2	5001	975

prune285.0ms

Filtered

103 candidates to 76 candidates (73.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	103	11	114

Merged error: 7.8b

Counts

114 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.3b	(fma (+ x y) z (* (+ t y) a))
7.5b	(/ (* y b) (+ (+ x t) y))
21.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

146×	`*-un-lft-identity`
124×	`times-frac`
66×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
49×	`distribute-lft-out`
18×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`associate-/l*`
10×	`associate-/r*`
8×	`div-inv`
7×	`div-exp`
6×	`pow1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-l` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+`
2×	`frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`1-exp` `pow-prod-down` `*-commutative` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

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

series355.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ t y) a)
47.0ms	(fma (+ x y) z (* (+ t y) a))
71.0ms	(/ (* y b) (+ (+ x t) y))
216.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify71.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	588	1846
1	2585	1673
2	5001	1572

prune355.0ms

Filtered

177 candidates to 96 candidates (54.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	173	4	177
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	176	12	188

Merged error: 3.9b

Counts

188 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.3b	(fma (+ x y) z (* (+ t y) a))
8.6b	(* y (/ b (+ (+ x t) y)))
21.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

159×	`*-un-lft-identity`
135×	`times-frac`
79×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
52×	`distribute-lft-out`
24×	`associate-r`
18×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`pow1` `div-inv`
7×	`associate-l`
6×	`div-exp`
5×	`associate-/r*`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`frac-2neg` `1-exp` `associate-*r/` `clear-num` `fma-udef` `associate-/l/`

Counts

4 → 178

Calls

4 calls:

6.0ms	(* (+ t y) a)
1.0ms	(fma (+ x y) z (* (+ t y) a))
12.0ms	(* y (/ b (+ (+ x t) y)))
11.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series354.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (+ t y) a)
47.0ms	(fma (+ x y) z (* (+ t y) a))
71.0ms	(* y (/ b (+ (+ x t) y)))
212.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify78.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	641	1911
1	2797	1739
2	5001	1638

prune367.0ms

Filtered

190 candidates to 104 candidates (54.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	192	10	202

Merged error: 2.6b

Counts

202 → 10

regimes464.0ms

Accuracy

15.9% (18.1b remaining)

Error of 21.0b against oracle of 2.9b and baseline of 24.4b

bsearch200.0ms

Steps

Iters	Range		Point
8	2.265916191991471e+141	4.965461357868195e+145	3.1135092197043987e+143
7	9.651847403853559e-204	2.3171891508789683e-201	9.590167992060039e-203
7	-6.839508133948694e-210	-1.7010959355894162e-211	-2.729197251649235e-211
10	-6.902909240076935e+103	-6.492537590380074e+92	-3.7659166463064465e+102

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	41
1	42	41

end0.0ms

sample731.0ms

Algorithm

intervals

Results

453.0ms	7997×	body	80	valid
0.0ms	2×	body	640	valid
0.0ms	1×	body	1280	valid