Details

sample30.0ms

Algorithm

intervals

Results

18.0ms

284×

body

valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* y (/ (- z t) (- a t))))
0.0b	(/ (- z t) (- a t))
2.6b	(* 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:

2.0ms	(+ x (* y (/ (- z t) (- a t))))
12.0ms	(/ (- z t) (- a t))
24.0ms	(* y (/ (- z t) (- a t)))

series186.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(+ x (* y (/ (- z t) (- a t))))
49.0ms	(/ (- z t) (- a t))
61.0ms	(* y (/ (- z t) (- a t)))

simplify53.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (12.0ms)

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

prune300.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (- (/ z (- a t)) (/ t (- a t)))))
0.0b	(/ z (- a t))
0.0b	(/ t (- a t))
2.6b	(* y (- (/ z (- a t)) (/ t (- a t))))

rewrite623.0ms

Algorithm

rewrite-expression-head

Rules

2591×	`*-un-lft-identity`
2583×	`add-sqr-sqrt`
2568×	`times-frac`
1764×	`prod-diff`
1541×	`add-cube-cbrt`
886×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
524×	`distribute-lft-out--`
518×	`difference-of-squares`
344×	`associate-/r/`
173×	`flip3--` `flip--`
172×	`div-inv`
18×	`associate-r`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u`
3×	`distribute-rgt-out--` `fma-def` `associate-l`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `sub-div` `unswap-sqr`

Counts

4 → 1905

Calls

4 calls:

132.0ms	(+ x (* y (- (/ z (- a t)) (/ t (- a t)))))
5.0ms	(/ z (- a t))
9.0ms	(/ t (- a t))
222.0ms	(* y (- (/ z (- a t)) (/ t (- a t))))

series249.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ x (* y (- (/ z (- a t)) (/ t (- a t)))))
30.0ms	(/ z (- a t))
43.0ms	(/ t (- a t))
78.0ms	(* y (- (/ z (- a t)) (/ t (- a t))))

simplify429.0ms

Algorithm

egg-herbie

Counts

1917 → 1917

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	3351	49171
1	5001	44380

prune4.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ t (- a t))
0.0b	(/ 1 (- a t))
0.1b	(fma z (/ 1 (- a t)) (- (/ t (- a t))))
1.3b	(fma (fma z (/ 1 (- a t)) (- (/ t (- a t)))) y x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
24×	`add-cube-cbrt`
10×	`add-exp-log` `associate-/r*`
8×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`div-exp`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `flip--` `fma-udef` `div-inv`
1×	`rec-exp` `pow-flip` `1-exp` `inv-pow`

Counts

4 → 102

Calls

4 calls:

5.0ms	(/ t (- a t))
5.0ms	(/ 1 (- a t))
0.0ms	(fma z (/ 1 (- a t)) (- (/ t (- a t))))
0.0ms	(fma (fma z (/ 1 (- a t)) (- (/ t (- a t)))) y x)

series316.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ t (- a t))
37.0ms	(/ 1 (- a t))
72.0ms	(fma z (/ 1 (- a t)) (- (/ t (- a t))))
166.0ms	(fma (fma z (/ 1 (- a t)) (- (/ t (- a t)))) y x)

simplify64.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	253	589
1	798	531
2	2410	506
3	5001	506

prune345.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* y (* (cbrt (- (/ z (- a t)) (/ t (- a t)))) (cbrt (- (/ z (- a t)) (/ t (- a t))))))
4.2b	(cbrt (- (/ z (- a t)) (/ t (- a t))))
4.2b	(cbrt (- (/ z (- a t)) (/ t (- a t))))
4.2b	(cbrt (- (/ z (- a t)) (/ t (- a t))))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
63×	`add-sqr-sqrt`
54×	`cbrt-prod` `times-frac`
52×	`cbrt-div`
36×	`distribute-lft-out--`
28×	`associate-*r/`
19×	`flip3--` `flip--`
18×	`difference-of-squares`
16×	`frac-times`
14×	`add-cube-cbrt`
13×	`frac-sub` `sub-div`
12×	`associate-/r/`
9×	`pow1` `add-exp-log` `distribute-rgt-out--`
7×	`add-cbrt-cube`
6×	`div-inv`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

222.0ms	(* y (* (cbrt (- (/ z (- a t)) (/ t (- a t)))) (cbrt (- (/ z (- a t)) (/ t (- a t))))))
35.0ms	(cbrt (- (/ z (- a t)) (/ t (- a t))))
34.0ms	(cbrt (- (/ z (- a t)) (/ t (- a t))))
37.0ms	(cbrt (- (/ z (- a t)) (/ t (- a t))))

series719.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* y (* (cbrt (- (/ z (- a t)) (/ t (- a t)))) (cbrt (- (/ z (- a t)) (/ t (- a t))))))
189.0ms	(cbrt (- (/ z (- a t)) (/ t (- a t))))
190.0ms	(cbrt (- (/ z (- a t)) (/ t (- a t))))
186.0ms	(cbrt (- (/ z (- a t)) (/ t (- a t))))

simplify77.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	452	1884
1	964	1783
2	2440	1773
3	5001	1746

prune564.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes141.0ms

Accuracy

-3.6% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 1.3b

bsearch107.0ms

Steps

Iters	Range		Point
9	1.4146022273320929e+26	8.53263360529498e+34	5.180730893440952e+31
10	-1.046268335803921e-166	-1.3542147510990014e-185	-1.1255726070759915e-177

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	28
1	49	28
2	51	28
3	51	28

end0.0ms

sample769.0ms

Algorithm

intervals

Results

507.0ms	8695×	body	80	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	1280	valid