Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify67.0ms

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: 27.5b

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)) (* y b))
2.1b	(+ (* (+ x y) z) (* (+ t y) a))
25.7b	(/ (- (+ (* (+ 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	(* (+ t y) a)
12.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
15.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series746.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ t y) a)
96.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
47.0ms	(+ (* (+ x y) z) (* (+ t y) a))
583.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify75.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (60.0ms)

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

prune362.0ms

Filtered

117 candidates to 93 candidates (79.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 9.1b

Counts

118 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.3b	(fma y (- a b) (* a t))
2.9b	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
25.7b	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`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` `flip3-+` `associate-l` `flip-+` `log1p-expm1-u`
3×	`associate-r` `associate-/l*`
2×	`associate-*l/` `associate-/r/` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `fma-def` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

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

series404.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ x y) z)
30.0ms	(fma y (- a b) (* a t))
100.0ms	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
253.0ms	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

simplify43.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	334	876
1	1269	814
2	5002	814

prune255.0ms

Filtered

101 candidates to 75 candidates (74.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	101	10	111

Merged error: 9.1b

Counts

111 → 10

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)))
1.3b	(- (* (+ t y) a) (* y b))
25.7b	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite30.0ms

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

series782.0ms

Counts

4 → 12

Calls

4 calls:

559.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
93.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
28.0ms	(- (* (+ t y) a) (* y b))
101.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify68.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (45.0ms)

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

prune494.0ms

Filtered

179 candidates to 93 candidates (52.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	179	10	189

Merged error: 6.1b

Counts

189 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

10.6b	(/ (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
26.5b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
26.5b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
26.5b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
16×	`add-exp-log`
9×	`cbrt-prod` `flip3--` `flip--`
8×	`frac-times` `associate-/r/` `add-cbrt-cube` `associate-/l/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

35.0ms	(/ (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

series1.5s

Counts

4 → 12

Calls

4 calls:

621.0ms	(/ (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
292.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
291.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
289.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

simplify53.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	434	1903
1	1468	1660
2	5001	1605

prune405.0ms

Filtered

96 candidates to 86 candidates (89.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	95	11	106

Merged error: 6.1b

Counts

106 → 11

regimes457.0ms

Accuracy

48.8% (11.4b remaining)

Error of 16.0b against oracle of 4.6b and baseline of 26.8b

bsearch84.0ms

Steps

Iters	Range		Point
6	6.874475585205962e+31	3.432297290563886e+32	3.0691536757249856e+32
9	-5.9421336172440095e+35	-1.8709239678891313e+26	-3.790053521618505e+35

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	11
1	33	11

end0.0ms

sample655.0ms

Algorithm

intervals

Results

368.0ms	7997×	body	80	valid
0.0ms	2×	body	1280	valid
0.0ms	1×	body	320	valid