Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify82.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.1b	(+ (* (+ x y) z) (* (+ t y) a))
1.2b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
23.6b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite43.0ms

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))
11.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
15.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series819.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ x y) z)
49.0ms	(+ (* (+ x y) z) (* (+ t y) a))
103.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
640.0ms	(/ (- (+ (* (+ 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

prune422.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.0b	(fma (+ x y) z (* (+ t y) a))
1.2b	(- (fma (+ x y) z (* (+ t y) a)) (* y b))
23.6b	(/ (- (fma (+ x y) z (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

6.0ms	(* (+ t y) a)
1.0ms	(fma (+ x y) z (* (+ t y) a))
3.0ms	(- (fma (+ x y) z (* (+ t y) a)) (* y b))
9.0ms	(/ (- (fma (+ x y) z (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series801.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (+ t y) a)
51.0ms	(fma (+ x y) z (* (+ t y) a))
104.0ms	(- (fma (+ x y) z (* (+ t y) a)) (* y b))
617.0ms	(/ (- (fma (+ x y) z (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify52.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	371	966
1	1480	894
2	5001	889

prune357.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
1.0b	(fma (+ x y) z (* (+ t y) a))
6.9b	(/ (* y b) (+ (+ x t) y))
20.8b	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

483×	`*-un-lft-identity`
306×	`times-frac`
231×	`prod-diff`
189×	`distribute-lft-out`
171×	`add-sqr-sqrt`
166×	`add-cube-cbrt`
74×	`associate-/r/`
37×	`flip3-+` `flip-+` `div-inv`
21×	`fma-neg`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `div-exp`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `sub-div`

Counts

4 → 352

Calls

4 calls:

33.0ms	(- (/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
1.0ms	(fma (+ x y) z (* (+ t y) a))
8.0ms	(/ (* y b) (+ (+ x t) y))
8.0ms	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

series1.0s

Counts

4 → 12

Calls

4 calls:

666.0ms	(- (/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
56.0ms	(fma (+ x y) z (* (+ t y) a))
79.0ms	(/ (* y b) (+ (+ x t) y))
234.0ms	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

simplify152.0ms

Algorithm

egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	752	11384
1	2663	8770
2	5001	8538

prune758.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y)) (* y (/ b (+ (+ x t) y))))
1.0b	(fma (+ x y) z (* (+ t y) a))
6.4b	(* y (/ b (+ (+ x t) y)))
20.8b	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

107×	`*-un-lft-identity`
61×	`times-frac`
47×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
39×	`distribute-lft-out`
21×	`fma-neg` `associate-r` `prod-diff`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
6×	`pow1` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv`
3×	`associate-r/` `associate-l` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `*-commutative` `frac-sub` `flip--` `fma-udef` `sub-div`

Counts

4 → 149

Calls

4 calls:

14.0ms	(- (/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y)) (* y (/ b (+ (+ x t) y))))
1.0ms	(fma (+ x y) z (* (+ t y) a))
12.0ms	(* y (/ b (+ (+ x t) y)))
8.0ms	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

series1.4s

Counts

4 → 12

Calls

4 calls:

963.0ms	(- (/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y)) (* y (/ b (+ (+ x t) y))))
58.0ms	(fma (+ x y) z (* (+ t y) a))
90.0ms	(* y (/ b (+ (+ x t) y)))
260.0ms	(/ (fma (+ x y) z (* (+ t y) a)) (+ (+ x t) y))

simplify74.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	457	1769
1	1975	1612
2	5002	1590

prune459.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

regimes452.0ms

Accuracy

13.4% (18.6b remaining)

Error of 21.5b against oracle of 3.0b and baseline of 24.4b

bsearch303.0ms

Steps

Iters	Range		Point
9	3.630040045473873e+55	3.608477260869243e+64	3.5316267040404663e+64
11	1.0265792944946071e-14	166951548.0487144	2.5131929146897947e-06
6	4.396833976898134e-75	2.5305637891924426e-74	5.974762403403444e-75
4	3.7227669268757736e-276	6.7296188014080665e-276	6.635654680328932e-276
7	-5.169514974318156e-130	-2.0116201226414365e-131	-4.1840463071979065e-131
9	-4.822275328546856e+205	-9.730667668626506e+198	-1.2515023271751886e+200

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	56
1	44	56

end0.0ms

sample619.0ms

Algorithm

intervals

Results

360.0ms	7996×	body	80	valid
0.0ms	2×	body	320	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid