Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify85.0ms

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

localize15.0ms

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))

rewrite47.0ms

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)
10.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
17.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series792.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ x y) z)
50.0ms	(+ (* (+ x y) z) (* (+ t y) a))
103.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
617.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify82.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (65.0ms)

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

localize16.0ms

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	(/ (pow (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) 1) (+ (+ x t) y))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
35×	`times-frac`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
25×	`distribute-lft-out`
18×	`unpow-prod-down`
11×	`add-exp-log` `add-log-exp`
10×	`associate-*l/`
8×	`add-cbrt-cube`
7×	`flip3-+` `flip-+` `associate-/l*`
6×	`pow1` `sqr-pow`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `div-exp` `associate-r` `prod-diff`
2×	`diff-log` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `flip3--` `fma-def` `frac-2neg` `pow-prod-down` `pow-exp` `prod-exp` `associate--l+` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 128

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))
20.0ms	(/ (pow (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) 1) (+ (+ x t) y))

series801.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (+ x y) z)
49.0ms	(+ (* (+ x y) z) (* (+ t y) a))
104.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
620.0ms	(/ (pow (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) 1) (+ (+ x t) y))

simplify83.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	591	1675
1	2589	1491
2	5001	1485

prune444.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow 1 1) (/ (+ (+ x t) y) (pow (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) 1)))
1.1b	(+ (* (+ x y) z) (* (+ t y) a))
1.2b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
23.7b	(/ (+ (+ x t) y) (pow (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) 1))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

588×	`times-frac`
570×	`*-un-lft-identity`
258×	`unpow-prod-down`
250×	`add-sqr-sqrt` `add-cube-cbrt`
192×	`distribute-lft-out`
86×	`sqr-pow`
46×	`associate-/r*`
41×	`add-exp-log`
31×	`div-exp`
13×	`pow-exp`
12×	`associate-/l*`
11×	`add-cbrt-cube` `add-log-exp`
10×	`div-inv`
9×	`pow-to-exp`
8×	`associate-*l/`
6×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `1-exp` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`frac-2neg` `diff-log` `clear-num` `sum-log` `associate-/l/`
1×	`+-commutative` `sub-neg` `flip3--` `fma-def` `associate--l+` `associate-/r/` `flip--`

Counts

4 → 455

Calls

4 calls:

27.0ms	(/ (pow 1 1) (/ (+ (+ x t) y) (pow (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) 1)))
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
11.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
21.0ms	(/ (+ (+ x t) y) (pow (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) 1))

series876.0ms

Counts

4 → 12

Calls

4 calls:

616.0ms	(/ (pow 1 1) (/ (+ (+ x t) y) (pow (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) 1)))
49.0ms	(+ (* (+ x y) z) (* (+ t y) a))
104.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
107.0ms	(/ (+ (+ x t) y) (pow (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) 1))

simplify178.0ms

Algorithm

egg-herbie

Counts

467 → 467

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1266	9623
1	4832	7991
2	5001	7991

prune726.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
0.4b	(- (* (+ t y) a) (* y b))
1.0b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
23.7b	(* (/ 1 (+ (+ x t) y)) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite34.0ms

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:

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

series821.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ 1 (+ (+ x t) y))
31.0ms	(- (* (+ t y) a) (* y b))
106.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
622.0ms	(* (/ 1 (+ (+ x t) y)) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify56.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (45.0ms)

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

prune332.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

regimes500.0ms

Accuracy

38.5% (13.5b remaining)

Error of 17.9b against oracle of 4.4b and baseline of 26.3b

bsearch211.0ms

Steps

Iters	Range		Point
10	1.6589270034838515e-52	2.334101998262839e-41	2.29423840239453e-41
7	2.086804021164162e-289	1.4246959020857144e-287	2.135448137295958e-289
9	-2.9188174999700146e-273	-1.0308405028667604e-278	-1.0932202536774648e-278
7	-2.453036913458998e+60	-8.403828943164457e+58	-1.2836464793001568e+60

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	40	30
1	43	30
2	49	14
3	52	14
4	58	14
5	69	14
6	76	14
7	77	14
8	77	14

end0.0ms

sample616.0ms

Algorithm

intervals

Results

356.0ms	7996×	body	80	valid
0.0ms	2×	body	320	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid