Details

sample120.0ms

Algorithm

intervals

Results

32.0ms	63×	body	1280	valid
27.0ms	46×	body	10240	exit
11.0ms	40×	body	640	valid
7.0ms	109×	body	80	valid
6.0ms	4×	body	2560	valid
5.0ms	24×	body	320	valid
3.0ms	75×	body	80	nan
2.0ms	18×	body	160	valid
2.0ms	6×	body	1280	nan
2.0ms	8×	body	640	nan
1.0ms	6×	body	320	nan
0.0ms	3×	body	160	nan

simplify256.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.2b	(log (+ (- 1.0 y) (* y (exp z))))
2.6b	(+ (- 1.0 y) (* y (exp z)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1` `associate-+l+`
9×	`prod-diff` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

11.0ms	(* y (exp z))
55.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
19.0ms	(log (+ (- 1.0 y) (* y (exp z))))
36.0ms	(+ (- 1.0 y) (* y (exp z)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* y (exp z))
164.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
78.0ms	(log (+ (- 1.0 y) (* y (exp z))))
37.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify71.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune420.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* y (exp z)))
0.3b	(* (cbrt (* y (exp z))) (cbrt (* y (exp z))))
3.1b	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
13.4b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`pow1`
11×	`associate-+l+`
9×	`prod-diff` `add-log-exp`
7×	`add-exp-log` `pow1/3`
5×	`cbrt-prod` `fma-def`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod`
2×	`log-div` `flip3-+` `pow-prod-down` `sum-log` `pow-sqr` `pow-prod-up` `flip-+`
1×	`+-commutative` `pow2` `associate-+l-` `sub-neg` `pow-plus` `diff-log` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

7.0ms	(cbrt (* y (exp z)))
17.0ms	(* (cbrt (* y (exp z))) (cbrt (* y (exp z))))
57.0ms	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
55.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (* y (exp z)))
120.0ms	(* (cbrt (* y (exp z))) (cbrt (* y (exp z))))
97.0ms	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
63.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	458	1247
1	1926	944
2	5002	790

prune413.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
3.4b	(/ (* z y) t)
7.5b	(/ (* (pow z 2) y) t)
9.7b	(* (pow z 2) y)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
7×	`prod-exp`
6×	`times-frac` `div-exp` `associate-/r*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `associate-/l*` `unpow2` `sqr-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
10.0ms	(/ (* z y) t)
12.0ms	(/ (* (pow z 2) y) t)
16.0ms	(* (pow z 2) y)

series160.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
20.0ms	(/ (* z y) t)
21.0ms	(/ (* (pow z 2) y) t)
20.0ms	(* (pow z 2) y)

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	300	473
1	1353	406
2	5002	406

prune361.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

localize19.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma (/ 1 (/ t (* z y))) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
3.4b	(/ t (* z y))
7.5b	(/ (* (pow z 2) y) t)
9.7b	(* (pow z 2) y)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
7×	`prod-exp`
6×	`times-frac` `div-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
3×	`associate-r` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `unpow2` `sqr-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma (/ 1 (/ t (* z y))) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
8.0ms	(/ t (* z y))
12.0ms	(/ (* (pow z 2) y) t)
16.0ms	(* (pow z 2) y)

series214.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(fma (/ 1 (/ t (* z y))) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
25.0ms	(/ t (* z y))
20.0ms	(/ (* (pow z 2) y) t)
20.0ms	(* (pow z 2) y)

simplify55.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	304	486
1	1315	414
2	5002	412

prune351.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

regimes532.0ms

Accuracy

70.7% (5.1b remaining)

Error of 9.2b against oracle of 4.1b and baseline of 21.6b

bsearch143.0ms

Steps

Iters	Range		Point
4	1.1340209900861153e-217	2.058987835970268e-217	2.0088638342293223e-217
9	-2.123435313099661e-25	-7.410899193841486e-31	-2.0867858317590094e-25

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	34
1	46	34

end0.0ms

sample3.4s

Algorithm

intervals

Results

808.0ms	1505×	body	1280	valid
766.0ms	1466×	body	10240	exit
465.0ms	1552×	body	640	valid
214.0ms	3481×	body	80	valid
174.0ms	909×	body	320	valid
104.0ms	78×	body	2560	valid
88.0ms	2448×	body	80	nan
59.0ms	498×	body	160	valid
58.0ms	273×	body	640	nan
29.0ms	96×	body	1280	nan
28.0ms	187×	body	320	nan
10.0ms	118×	body	160	nan