Details

sample30.0ms

Algorithm

intervals

Results

7.0ms	253×	body	80	valid
4.0ms	15×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	44	6
2	122	6
3	327	6
4	868	6
5	1727	6
6	3544	6
7	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.3b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.8b	(* (- y z) (/ (- t x) (- a z)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

20.0ms	(/ (- t x) (- a z))
7.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
57.0ms	(* (- y z) (/ (- t x) (- a z)))

series298.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- t x) (- a z))
134.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
115.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify56.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	473	869
1	2012	820
2	5001	820

prune316.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
5.3b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
5.8b	(* (- y z) (* (- t x) (/ 1 (- a z))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-r/` `associate-l` `associate-l/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 146

Calls

4 calls:

11.0ms	(/ 1 (- a z))
43.0ms	(* (- t x) (/ 1 (- a z)))
9.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
66.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (- a z))
44.0ms	(* (- t x) (/ 1 (- a z)))
138.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
116.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

simplify73.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	585	1027
1	2810	910
2	5003	865

prune344.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.3b	(+ x (* 1 (* (/ (- t x) (- a z)) (- y z))))
5.8b	(* (/ (- t x) (- a z)) (- y z))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-l`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
8×	`associate-+r+`
6×	`sub-neg`
5×	`pow1` `flip3--` `associate-r` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+` `distribute-lft-out`

Counts

3 → 132

Calls

3 calls:

22.0ms	(/ (- t x) (- a z))
10.0ms	(+ x (* 1 (* (/ (- t x) (- a z)) (- y z))))
58.0ms	(* (/ (- t x) (- a z)) (- y z))

series365.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (- t x) (- a z))
142.0ms	(+ x (* 1 (* (/ (- t x) (- a z)) (- y z))))
179.0ms	(* (/ (- t x) (- a z)) (- y z))

simplify59.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	553	981
1	2059	925
2	5002	923

prune332.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.4b	(* (- t x) (/ (- y z) (- a z)))
2.1b	(+ x (* 1 (* (- t x) (/ (- y z) (- a z)))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `distribute-lft-out`

Counts

3 → 120

Calls

3 calls:

21.0ms	(/ (- y z) (- a z))
54.0ms	(* (- t x) (/ (- y z) (- a z)))
13.0ms	(+ x (* 1 (* (- t x) (/ (- y z) (- a z)))))

series281.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (- y z) (- a z))
99.0ms	(* (- t x) (/ (- y z) (- a z)))
141.0ms	(+ x (* 1 (* (- t x) (/ (- y z) (- a z)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	492	890
1	2117	834
2	5003	833

prune287.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

regimes239.0ms

Accuracy

20.8% (6.3b remaining)

Error of 10.2b against oracle of 4.0b and baseline of 11.9b

bsearch77.0ms

Steps

Iters	Range		Point
9	1.709955451654599e-144	3.5303979959117466e-138	6.559704169034857e-143
6	-8.689192513681542e-190	-1.0915813278155385e-190	-7.116182529525504e-190

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	13
1	38	13
2	38	13

end0.0ms

sample764.0ms

Algorithm

intervals

Results

250.0ms	7687×	body	80	valid
54.0ms	494×	body	640	valid
40.0ms	290×	body	1280	valid
38.0ms	425×	body	320	valid
15.0ms	258×	body	160	valid
2.0ms	9×	body	2560	valid