Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

286×

body

valid

simplify87.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	20	5
1	36	4
2	59	4
3	103	4
4	173	4
5	236	4
6	265	4
7	311	4
8	375	4
9	511	4
10	674	4
11	1179	4
12	1300	4
13	1308	4
14	1308	4

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
0.0b	(+ x (* y (/ (- z t) (- a t))))
2.0b	(* y (/ (- z t) (- a t)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `flip3--` `fma-def` `associate-l` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `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 → 122

Calls

3 calls:

12.0ms	(/ (- z t) (- a t))
3.0ms	(+ x (* y (/ (- z t) (- a t))))
25.0ms	(* y (/ (- z t) (- a t)))

series215.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- z t) (- a t))
88.0ms	(+ x (* y (/ (- z t) (- a t))))
76.0ms	(* y (/ (- z t) (- a t)))

simplify58.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	433	776
1	1705	730
2	5002	730

prune331.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
0.0b	(+ x (* (/ (- z t) (- a t)) y))
2.0b	(* (/ (- z t) (- a t)) y)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-l`
28×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `flip3--` `fma-def` `associate-r` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `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-+`

Counts

3 → 122

Calls

3 calls:

12.0ms	(/ (- z t) (- a t))
3.0ms	(+ x (* (/ (- z t) (- a t)) y))
28.0ms	(* (/ (- z t) (- a t)) y)

series237.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- z t) (- a t))
76.0ms	(+ x (* (/ (- z t) (- a t)) y))
107.0ms	(* (/ (- z t) (- a t)) y)

simplify60.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	446	781
1	1413	735
2	5001	734

prune336.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (* (- z t) (/ 1 (- a t)))))
0.0b	(/ 1 (- a t))
0.3b	(* (- z t) (/ 1 (- a t)))
2.0b	(* y (* (- z t) (/ 1 (- a t))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
26×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-r/` `associate-l*` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`flip3--` `div-exp` `flip--` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `associate-*l/` `associate-/r/` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `fma-def` `1-exp` `associate-/l*` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 141

Calls

4 calls:

3.0ms	(+ x (* y (* (- z t) (/ 1 (- a t)))))
6.0ms	(/ 1 (- a t))
24.0ms	(* (- z t) (/ 1 (- a t)))
26.0ms	(* y (* (- z t) (/ 1 (- a t))))

series249.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ x (* y (* (- z t) (/ 1 (- a t)))))
37.0ms	(/ 1 (- a t))
54.0ms	(* (- z t) (/ 1 (- a t)))
70.0ms	(* y (* (- z t) (/ 1 (- a t))))

simplify63.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	468	829
1	2047	715
2	5003	668

prune348.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- z t))
0.5b	(cbrt (- z t))
0.5b	(* (cbrt (- z t)) (cbrt (- z t)))
6.9b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) 1) (* (/ (cbrt (- z t)) (- a t)) y))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
38×	`cbrt-prod`
36×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
32×	`prod-exp`
31×	`add-cbrt-cube`
19×	`cbrt-unprod`
17×	`div-exp`
16×	`pow1` `add-cube-cbrt` `cbrt-div`
15×	`associate-l`
10×	`swap-sqr`
9×	`cbrt-undiv` `associate-r`
8×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
6×	`1-exp` `difference-of-squares`
5×	`frac-times` `pow-prod-down` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`times-frac` `associate-*r/`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus` `div-inv`

Counts

4 → 139

Calls

4 calls:

2.0ms	(cbrt (- z t))
2.0ms	(cbrt (- z t))
22.0ms	(* (cbrt (- z t)) (cbrt (- z t)))
51.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) 1) (* (/ (cbrt (- z t)) (- a t)) y))

series564.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (- z t))
159.0ms	(cbrt (- z t))
141.0ms	(* (cbrt (- z t)) (cbrt (- z t)))
107.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) 1) (* (/ (cbrt (- z t)) (- a t)) y))

simplify97.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	586	1377
1	2750	1119
2	5001	982

prune410.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes197.0ms

Accuracy

63.1% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 1.4b

bsearch95.0ms

Steps

Iters	Range		Point
8	6.284385024126243e-88	2.901425453076359e-84	8.869338664451681e-85
8	-1.588366725550566e+37	-2.610116308888546e+34	-6.29140239783561e+35

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	11
1	33	11
2	33	11

end0.0ms

sample569.0ms

Algorithm

intervals

Results

294.0ms	8747×	body	80	valid
0.0ms	1×	body	320	valid