Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	260×	body	80	valid
1.0ms	14×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	6×	body	1280	valid
0.0ms	9×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1493	6
6	3393	6
7	5002	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
3.0b	(+ x (/ (* (- y x) (- z t)) (- a t)))
18.4b	(/ (* (- y x) (- z t)) (- a t))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

34.0ms	(* (- y x) (- z t))
19.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
27.0ms	(/ (* (- y x) (- z t)) (- a t))

series276.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* (- y x) (- z t))
147.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
97.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	468	583
1	2162	534
2	5003	534

prune244.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.3b	(* (- y x) (/ (- z t) (- a t)))
3.0b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite87.0ms

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	(/ (- z t) (- a t))
54.0ms	(* (- y x) (/ (- z t) (- a t)))
7.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series287.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (- z t) (- a t))
100.0ms	(* (- y x) (/ (- z t) (- a t)))
145.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify59.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	476	869
1	2018	820
2	5001	820

prune277.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- z t) (/ 1 (- a t)))
2.3b	(* (- y x) (* (- z t) (/ 1 (- a t))))
3.7b	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

rewrite131.0ms

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 t))
42.0ms	(* (- z t) (/ 1 (- a t)))
64.0ms	(* (- y x) (* (- z t) (/ 1 (- a t))))
9.0ms	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

series326.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (- a t))
42.0ms	(* (- z t) (/ 1 (- a t)))
99.0ms	(* (- y x) (* (- z t) (/ 1 (- a t))))
150.0ms	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	586	1027
1	2802	910
2	5003	865

prune337.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
2.3b	(* (- y x) (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))))
6.9b	(+ x (* (- y x) (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t)))))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

82×	`frac-times`
76×	`cbrt-div`
56×	`flip3--` `flip--`
38×	`associate-*l/`
32×	`associate-*r/`
22×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`pow1` `add-sqr-sqrt` `*-un-lft-identity`
11×	`prod-exp` `cbrt-unprod`
10×	`cbrt-prod`
7×	`add-cube-cbrt`
6×	`pow-prod-down` `add-log-exp`
5×	`associate-l`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `pow1/3` `div-exp`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

4 → 121

Calls

4 calls:

4.0ms	(cbrt (- z t))
4.0ms	(cbrt (- z t))
215.0ms	(* (- y x) (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))))
20.0ms	(+ x (* (- y x) (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t)))))

series719.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (- z t))
136.0ms	(cbrt (- z t))
303.0ms	(* (- y x) (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))))
140.0ms	(+ x (* (- y x) (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	775	2047
1	2882	1874
2	5001	1853

prune398.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.0b

regimes258.0ms

Accuracy

13.6% (6.6b remaining)

Error of 10.7b against oracle of 4.1b and baseline of 11.7b

bsearch86.0ms

Steps

Iters	Range		Point
9	7.576911721620079e-263	3.1445148399796725e-255	1.7696393260069873e-255
8	-1.255868730469884e-255	-2.1858701083154153e-260	-6.169776304608412e-256

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	19
1	38	19

end0.0ms

sample763.0ms

Algorithm

intervals

Results

245.0ms	7822×	body	80	valid
50.0ms	474×	body	640	valid
35.0ms	268×	body	1280	valid
33.0ms	405×	body	320	valid
15.0ms	278×	body	160	valid
2.0ms	15×	body	2560	valid