Details

sample32.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify77.0ms

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: 26.0b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.7b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
1.7b	(+ (* (+ x y) z) (* (+ t y) a))
24.3b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite45.0ms

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)
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
16.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series743.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ t y) a)
97.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
49.0ms	(+ (* (+ x y) z) (* (+ t y) a))
576.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify75.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	564	1186
1	2509	1087
2	5001	1077

prune350.0ms

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: 10.2b

Counts

118 → 11

localize15.0ms

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)))
1.4b	(- (* (+ t y) a) (* y b))
24.3b	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite32.0ms

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:

10.0ms	(/ 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))))

series791.0ms

Counts

4 → 12

Calls

4 calls:

567.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
94.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
31.0ms	(- (* (+ t y) a) (* y b))
99.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify73.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (48.0ms)

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

prune335.0ms

Filtered

179 candidates to 92 candidates (51.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	178	12	190

Merged error: 5.6b

Counts

190 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.3b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
1.4b	(- (* (+ t y) a) (* y b))
24.4b	(* (/ 1 (+ (+ x t) y)) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `associate-l`
17×	`times-frac`
16×	`add-cube-cbrt`
15×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`distribute-lft-out`
8×	`pow1`
6×	`associate-r` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`associate-*l/` `cbrt-unprod` `fma-udef`
2×	`flip3-+` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `flip-+`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `rec-exp` `flip3--` `distribute-lft-in` `fma-neg` `diff-log` `1-exp` `prod-diff` `flip--` `div-inv`

Counts

4 → 96

Calls

4 calls:

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

series727.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ t y) a)
97.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
33.0ms	(- (* (+ t y) a) (* y b))
578.0ms	(* (/ 1 (+ (+ x t) y)) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify57.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	424	905
1	1794	797
2	5002	781

prune286.0ms

Filtered

108 candidates to 79 candidates (73.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	108	12	120

Merged error: 5.6b

Counts

120 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

19.7b	(cbrt (+ (* (+ x y) z) (* (+ t y) a)))
19.7b	(cbrt (+ (* (+ x y) z) (* (+ t y) a)))
19.7b	(cbrt (+ (* (+ x y) z) (* (+ t y) a)))
24.3b	(/ (- (* (* (cbrt (+ (* (+ x y) z) (* (+ t y) a))) (cbrt (+ (* (+ x y) z) (* (+ t y) a)))) (cbrt (+ (* (+ x y) z) (* (+ t y) a)))) (* y b)) (+ (+ x t) y))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

6.0ms	(cbrt (+ (* (+ x y) z) (* (+ t y) a)))
6.0ms	(cbrt (+ (* (+ x y) z) (* (+ t y) a)))
6.0ms	(cbrt (+ (* (+ x y) z) (* (+ t y) a)))
71.0ms	(/ (- (* (* (cbrt (+ (* (+ x y) z) (* (+ t y) a))) (cbrt (+ (* (+ x y) z) (* (+ t y) a)))) (cbrt (+ (* (+ x y) z) (* (+ t y) a)))) (* y b)) (+ (+ x t) y))

series1.3s

Counts

4 → 12

Calls

4 calls:

239.0ms	(cbrt (+ (* (+ x y) z) (* (+ t y) a)))
244.0ms	(cbrt (+ (* (+ x y) z) (* (+ t y) a)))
244.0ms	(cbrt (+ (* (+ x y) z) (* (+ t y) a)))
584.0ms	(/ (- (* (* (cbrt (+ (* (+ x y) z) (* (+ t y) a))) (cbrt (+ (* (+ x y) z) (* (+ t y) a)))) (cbrt (+ (* (+ x y) z) (* (+ t y) a)))) (* y b)) (+ (+ x t) y))

simplify77.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	556	2556
1	2141	2364
2	5002	2138

prune437.0ms

Filtered

111 candidates to 97 candidates (87.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	111	12	123

Merged error: 5.6b

Counts

123 → 12

regimes610.0ms

Accuracy

86.3% (3.1b remaining)

Error of 7.6b against oracle of 4.5b and baseline of 27.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	32
1	44	32

end0.0ms

sample755.0ms

Algorithm

intervals

Results

457.0ms	7995×	body	80	valid
1.0ms	4×	body	640	valid
0.0ms	1×	body	320	valid