Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	245×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	14×	body	160	valid
1.0ms	5×	body	1280	valid

simplify64.0ms

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: 23.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
4.0b	(+ x (/ (* (- y x) (- z t)) (- a t)))
16.8b	(/ (* (- y x) (- z t)) (- a t))

rewrite33.0ms

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:

9.0ms	(* (- y x) (- z t))
8.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
13.0ms	(/ (* (- y x) (- z t)) (- a t))

series289.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* (- y x) (- z t))
147.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
108.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify51.0ms

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

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.1b	(* (- y x) (/ (- z t) (- a t)))
4.0b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite37.0ms

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:

8.0ms	(/ (- z t) (- a t))
17.0ms	(* (- y x) (/ (- z t) (- a t)))
4.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series306.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (- z t) (- a t))
112.0ms	(* (- y x) (/ (- z t) (- a t)))
147.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify57.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

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

prune305.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.2b	(/ (- y x) (/ (- a t) (- z t)))
4.0b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

8.0ms	(/ (- a t) (- z t))
16.0ms	(/ (- y x) (/ (- a t) (- z t)))
43.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series391.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- a t) (- z t))
190.0ms	(/ (- y x) (/ (- a t) (- z t)))
152.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify103.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1030	3053
1	4263	2984
2	5003	2984

prune662.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 4.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
1.2b	(/ (- y x) (* (/ 1 (* (cbrt (- z t)) (cbrt (- z t)))) (/ (- a t) (cbrt (- z t)))))
8.4b	(+ x (/ (- y x) (* (/ 1 (* (cbrt (- z t)) (cbrt (- z t)))) (/ (- a t) (cbrt (- z t))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-exp-log`
30×	`div-exp`
26×	`add-cbrt-cube`
20×	`prod-exp`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
14×	`cbrt-undiv`
10×	`cbrt-prod`
8×	`add-cube-cbrt` `cbrt-unprod`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`pow1` `rec-exp` `cbrt-div` `1-exp` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `associate-/r/` `flip--`
2×	`pow1/3` `div-sub` `associate-/l/`
1×	`+-commutative` `frac-times` `associate-+r-` `frac-2neg` `flip3-+` `associate-r/` `associate-l/` `clear-num` `associate-/r*` `sum-log` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 92

Calls

4 calls:

3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
28.0ms	(/ (- y x) (* (/ 1 (* (cbrt (- z t)) (cbrt (- z t)))) (/ (- a t) (cbrt (- z t)))))
8.0ms	(+ x (/ (- y x) (* (/ 1 (* (cbrt (- z t)) (cbrt (- z t)))) (/ (- a t) (cbrt (- z t))))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (- z t))
155.0ms	(cbrt (- z t))
112.0ms	(/ (- y x) (* (/ 1 (* (cbrt (- z t)) (cbrt (- z t)))) (/ (- a t) (cbrt (- z t)))))
159.0ms	(+ x (/ (- y x) (* (/ 1 (* (cbrt (- z t)) (cbrt (- z t)))) (/ (- a t) (cbrt (- z t))))))

simplify75.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	673	1318
1	2638	1113
2	5002	998

prune276.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 4.7b

regimes339.0ms

Accuracy

12.9% (6.4b remaining)

Error of 10.5b against oracle of 4.0b and baseline of 11.4b

bsearch289.0ms

Steps

Iters	Range		Point
8	5.4487218390573786e-213	2.015903040355365e-210	1.7888988399164032e-210
7	-2.5962665469001577e-297	-4.1002396814977254e-299	-3.218101976979679e-298

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	32	18

end0.0ms

sample706.0ms

Algorithm

intervals

Results

270.0ms	7772×	body	80	valid
61.0ms	480×	body	640	valid
41.0ms	262×	body	1280	valid
36.0ms	389×	body	320	valid
18.0ms	286×	body	160	valid
3.0ms	17×	body	2560	valid